# Mechanism of Ag++-induced Folding of a Bacterial Peptide from Replica-Exchange Molecular Simulations

Florian E.C. Blanc, Maggy Hologne, Marion Girod, Mélodie Demontrond,

Henry Chermette, Olivier Walker

► To cite this version:

Florian E.C. Blanc, Maggy Hologne, Marion Girod, Mélodie Demontrond, Henry Chermette, et al.  
Mechanism of Ag++-induced Folding of a Bacterial Peptide from Replica-Exchange Molecular Simula-  
tions. 2026. hal-05492425

HAL Id: hal-05492425

https://hal.science/hal-05492425v1

Preprint submitted on 4 Feb 2026

**HAL** is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Mechanism of Ag⁺-induced Folding of a Bacterial Peptide from Replica-Exchange Molecular Simulations

Florian E.C. Blanc¹, Maggy Hologne¹, Marion Girod¹, Mélodie Demontrond¹, Henry Chermette¹, Olivier Walker¹

1. Université de Lyon, CNRS, UCB Lyon1, Institut des Sciences Analytiques, UMR5280, Villeurbanne, France

## Abstract

Interactions between proteins and metal cations are central to biochemical processes and shape protein structures. SilE, an intrinsically disordered protein involved in bacterial silver-resistance, folds into #-helices upon binding Ag⁺ ions. Focusing on the B1 peptide fragment from SilE, we investigate the mechanism of Ag⁺-induced folding with atomistic simulations and experiments. Guided by Mass Spectrometry and NMR, we prepare a structural model of Ag⁺-bound B1, which we parametrize using DFT. Then, with replica-exchange simulations and deep learning, we map B1's folding landscape and how it is shaped by Ag⁺. Specifically, Ag⁺ binding promotes folding by lowering the entropy of the disordered state and stabilizing the folded state. We also describe how Ag⁺ alters the folding pathways. Overall, we improve the understanding of metal-induced protein folding and lay the groundwork for further computational investigations of the bacterial silver-resistance machinery.

## Keywords

Metal-protein interactions, Peptide folding, Silver, Molecular Dynamics, Free energy calculations, NMR, Autoencoders
Mechanism of Ag⁺-induced Folding of a
Bacterial Peptide from Replica-Exchange
Molecular Simulations

Florian E.C. Blanc ID,* Maggy Hologne ID, Marion Girod ID, Mélodie Demontrond, Henry Chermette ID, and Olivier Walker ID*

Université de Lyon, CNRS, UCB Lyon1, Institut des Sciences Analytiques, UMR5280,
Villeurbanne, France

E-mail: florian.blanc@isa-lyon.fr; olivier.walker@univ-lyon1.fr
Abstract

Interactions between proteins and metal cations are central to biochemical processes and shape protein structures. SilE, an intrinsically disordered protein involved in bacterial silver-resistance, folds into α-helices upon binding Ag⁺ ions. Focusing on the B1 peptide fragment from SilE, we investigate the mechanism of Ag⁺-induced folding with atomistic simulations and experiments. Guided by Mass Spectrometry and NMR, we prepare a structural model of Ag⁺-bound B1, which we parametrize using DFT. Then, with replica-exchange simulations and deep learning, we map B1's folding landscape and how it is shaped by Ag⁺. Specifically, Ag⁺ binding promotes folding by lowering the entropy of the disordered state and stabilizing the folded state. We also describe how Ag⁺ alters the folding pathways. Overall, we improve the understanding of metal-induced protein folding and lay the groundwork for further computational investigations of the bacterial silver-resistance machinery.

TOC Graphic

<figure><img src="image_2.png" /></figure>
Interaction with metal cations can shape the conformational landscapes of proteins in
several ways. Metals can promote protein unfolding¹, misfolding or aggregation, which may
lead to neurodegenerative disorders²,³. Conversely, metals at an optimum concentration are
essential for proteins, and ≈ 33% of protein structures in the PDB have at least one metal
ion (https://www.rcsb.org/). Metals can be involved in folding ⁴,⁵ and help maintain
the 3D structure of proteins⁶. For example, recent research by our group⁷⁻⁹ and others¹⁰
has showed that the bacterial intrinsically disordered protein SilE locally folds into α-helices
upon binding silver cations Ag⁺. The present paper is concerned with understanding the
mechanism and energetics of this Ag⁺-induced folding through Molecular Dynamics (MD)
simulations and experiments.

SilE (Fig 1A) is an essential member of the *sil* silver-efflux machinery, which confers
Gram-negative Bacteria resistance against silver toxicity¹¹⁻¹³. The antimicrobial proper-
ties of silver have been used since Antiquity¹⁴. Novel silver-based antibacterials could help
counter rising antibioresistance ¹⁵,¹⁶, but for this it is critical to address bacterial resistance
to silver¹⁷. Understanding the molecular underpinnings of the silver resistance machinery
would facilitate this endeavour by guiding drug discovery efforts.

SilE is natively disordered, but folds locally into α-helical segments upon binding Ag⁺
cations⁹. This feature is retained by peptide fragments encompassing the silver binding sites
composed of HXXM or MXXH motifs⁷,⁸,¹⁸,¹⁹. The ability of SilE to bind free Ag⁺ is crucial
for the *sil* machinery, which makes SilE an attractive —albeit challenging— pharmacological
target. However, the functional importance of its folding upon binding Ag⁺ is not well
understood. For instance, it is unclear whether the helical motifs modulate the affinity of SilE
for Ag⁺, or enable functional interactions with other *sil* proteins²⁰,²¹. More generally, how
silver cations could stabilize helical structures in peptides and proteins is poorly described.

Addressing this question with atomically-detailed simulations of Ag⁺-induced folding is
challenging for two reasons. First, MD simulations of peptide folding require extensive sam-
pling and a force-field that can describe the unfolded state accurately²²,²³. Second, classical
force-fields struggle to describe d-group metallic cations and their interactions with pro-
teins<sup>24</sup>. Polarizable force-fields and Quantum Mechanics/Molecular Mechanics (QM/MM)
can accurately describe metal centers in proteins while enabling some conformational sam-
pling<sup>25-27</sup>, but their computational cost makes their use for folding simulations challenging<sup>28</sup>.
Despite their limitations, fixed-charge force-fields have shown successes in metal modelling
<sup>24</sup>, for example when *ad-hoc* modifications are incorporated to approximate the effects of
polarization <sup>29-31</sup>. Parametrization of transition metal cations for fixed-charge or polarizable
force-fields remains an active topic of research. Lennard-Jones parameters for non-bonded
cations including Ag<sup>+</sup> have been developed by Merz et al.<sup>32,33</sup>. Their most recent parameter
set describes His-Ag<sup>+</sup> interactions well<sup>34-36</sup>, but requires a non-standard "12-6-4" interac-
tion potential<sup>37,38</sup> that precludes widespread adoption. Very recently, Manciocchi et al.
reported on a standard ("12-6") Ag<sup>+</sup> model<sup>39</sup> calibrated to reproduce binding affinities to
SilE tetrapeptide fragments<sup>7</sup>. This model is promising, but it remains unclear whether it can
capture how interactions with Ag<sup>+</sup> affect protein conformations, as discussed below. Alter-
natively, bonded models that treat the interaction with Ag<sup>+</sup> as effectively covalent have been
proposed. Chen et al. developed a bonded model for the interaction with cytosine<sup>40</sup>, and
Lithgo et al. for the interaction with the SilF protein<sup>27</sup>. In both studies, parameters were
developed for the AMBER force-fields; we are not aware of similar efforts for the CHARMM
force-fields. In addition, to our knowledge, no previous work has specifically investigated the
structural consequences of Ag<sup>+</sup> binding to proteins with an atomistic level of details.

Here, we lay the groundwork towards atomistic simulations of full-length SilE Ag<sup>+</sup>-induced folding by focusing on an 11-residue peptide fragment from SilE<sup>8</sup>, called B1 (HQKMVESHQRM), which contains two HXXM silver-binding motifs. First, we collect experimental evidence from Mass spectrometry and NMR in favour of a "binding, then folding" mechanism. This motivates simulating the folding of B1 with a bonded Ag<sup>+</sup> model. We then develop a CHARMM-compatible bonded model for the His-Ag<sup>+</sup>-Met coordination complex using electronic structure calculations. In so doing, we address the gap of Ag<sup>+</sup>-protein bonded
model for the CHARMM force-field family. Next, we explore the conformational space of B1
in the presence and in the absence of Ag⁺ using Temperature Replica-Exchange Molecular
Dynamics (T-REMD) simulations in explicit solvent (200 µs of aggregate MD sampling).
Analysis of the simulations by rigorous free-energy reweighting and deep learning maps the
conformational landscape of B1 and shows that our model correctly captures Ag⁺-induced
α-helix stabilization. We evaluate the effect of alternative parametrizations of our bonded
model on the folding equilibrium. We introduce a post-processing procedure based on the
string method<sup>41</sup> to reveal the mechanistic pathways of B1 folding and how they change when
Ag⁺ is bound. Overall, our study provides a comprehensive picture of B1’s Ag⁺-induced fold-
ing.

<figure><img src="image_3.png" /><figcaption>Figure 1: Description of the B1 peptide and the bonded model for His–Ag⁺–Met.
A. Representative structure of Ag⁺-bound full-length SilE from SAXS measurements<sup>9</sup> show-
ing the folded α-helical silver-binding regions. B. NMR structure of the Ag⁺-bound B1
peptide<sup>8</sup>. For clarity, only polar hydrogens are shown. C. C-RESP2 partial charges for His-
Nδ, Ag and Met-S derived from DFT calculations. The full list of partial charges is given in
Table S2.</figcaption></figure>

Previous NMR experiments have shown that B1's folding and binding to Ag⁺ are cou-
pled<sup>8</sup>, but did not address whether this coupling proceeds through a conformational selection
mechanism —Ag⁺ binds preferentially to minority folded conformers, shifting the equilibrium towards the folded state — or whether Ag⁺ binds to disordered conformers and directly induces folding. We first set out to answer this question experimentally. Mass Spectrometry (MS) shows unambiguously that the major form of B1 under saturating Ag⁺ conditions is bound to two Ag⁺ ions (Fig 2A). Since MS samples were prepared in strongly denaturating conditions (≈12 M methanol, Supplementary Text 6), this demonstrates that Ag⁺ binding by B1 does not require pre-folding into an α-helix. NMR characterization of a B1 E6Q mutant provides additional information (Supplementary Text 5). Similar to wild-type B1<sup>8</sup>, the 1D <sup>1</sup>H NMR spectrum of B1 E6Q indicates that this mutant is disordered in the free form (Fig 2B). In the presence of Ag⁺, the <sup>1</sup>H chemical shifts are perturbed (Fig 2B), indicating that B1 E6Q retains the capacity to bind Ag⁺. Yet, unlike wild-type B1, the 2D NOESY spectrum of B1 E6Q shows only sequential *i*, *i* + 1 correlations, indicating a disordered state (Fig 2C). Thus, B1 E6Q is able to bind Ag⁺ but unable to fold. Therefore, folding is not required for Ag⁺ binding; instead, Ag⁺ binding precedes and promotes folding in wild-type B1. This justifies developing and using a bonded model to investigate this process with MD simulations.

We thus developed a bonded model of His—Ag⁺—Met in a linear geometry (Fig 1C), calibrated on Density Functional Theory (DFT) calculations and compatible with the CHARMM force-fields (Supplementary Text 1). We used the Seminario method to determine force constants from the Hessian matrix computed at the DFT-optimized geometry<sup>42</sup>, see Table S1. Deriving CHARMM-compatible partial charges for systems containing transition metals, such as silver, is non-trivial because the standard parametrization approach relies on HF/6-31G* calculations, which are likely to describe such systems less accurately than correlated methods such as DFT. To address this challenge, we used an appropriate level of theory (PBE0/def2-TZVP)<sup>43–46</sup>, and we introduced two key modifications to the RESP procedure<sup>47</sup>. First, we constrained partial charges of most atoms to their CHARMM standard values during the RESP calculation<sup>48</sup> (Table S2, Fig S1), a procedure we term C-RESP (for
<figure><img src="image_4.png" /><figcaption>Figure 2: **Experimental data on B1.** A. MS spectrum of B1+Ag⁺, with the main peak corresponding to B1+2Ag⁺. B. 1D ¹H NMR spectra of B1 E6Q with and without Ag⁺ recorded at a ¹H frequency of 700 MHz and 293 K. The rectangle indicates the amide and aromatic protons region. C. 2D ¹H-¹H NOESY spectrum of B1 E6Q in the presence of Ag⁺.</figcaption></figure>
CHARMM-RESP). Second, we approximately accounted for solvent polarization using the RESP2 procedure by Gilson et al. ⁴⁹. Motivations for these parametrization decisions are provided in Supplementary Text 1. Together, they yield the C-RESP2 procedure for partial charge derivation.

We prepared 8 simulation systems that differed in three aspects: (i) presence or absence of Ag⁺, (ii) whether the B1 peptide was wild-type or the B1E6Q mutant, and (iii) the parametrization scheme used for the His–Ag⁺–Met motif, see Table S3. The observation that B1 folds into an α-helix when bound to Ag⁺⁸ points to a binding pattern in which the first Ag⁺ crosslinks the sidechains of His1 and Met4, and the second Ag⁺ crosslinks His8 and Met11 (Fig 1B). All B1+Ag⁺ simulations were prepared with this binding pattern. The alternative binding mode in which Ag⁺ ions crosslink His1 to Met11, and His8 to Met4, would not be compatible with an α-helix. Instead, it may stabilize a β-hairpin configuration, which is not observed by NMR. We energy-minimized and equilibrated each model in a cubic box filled with CHARMM TIP3P water molecules⁵⁰ and 150 mM of Na⁺ + Cl⁻. From each equilibrated system, we ran T-REMD simulations⁵¹,⁵², with 64 replicas and temperatures ranging from 293 K to 470 K chosen to balance extensive conformational sampling with efficient exchange⁵³; see Supplementary Text 2 for the simulation parameters. Our replica-exchange simulations aggregate 200 µs of sampling (Table S3). For Ag⁺-free B1 and B1+Ag⁺ with the C-RESP2 parametrization, we ran two independent T-REMD simulations to assess the robustness of our findings. In all T-REMD simulations, the ≈ 20% observed exchange acceptance rate, reversible diffusion of replicas over temperature space (Fig S2), and overlapping potential energy distributions (Fig S3) suggest that the simulations have correctly explored the conformational space.

To get a global view of how Ag⁺ binding affects the energetics of B1 folding, we evaluated the two-dimensional free energy landscapes at 293 K (i.e., the temperature of the NMR measurements⁸) along the radius of gyration R_g and the α-helix content⁵⁴ α of B1, see Figs 3 and S4. α = 1.0 for a perfect α-helix and 0 for a fully disordered configuration. We
used Multistate State Bennett Acceptance Ratio (MBAR) reweighting to combine the data
collected at all temperatures, making optimal use of our simulations⁵⁵. We then evaluated
free energy landscapes by weighted Gaussian kernel density estimation (KDE), using the
MBAR weights as implemented in *pymbar*⁵⁶ (see Table S4 for KDE bandwidths). The free
energy landscapes show how Ag⁺-binding shapes the folding landscape of the B1 peptide.

Both in the presence and in the absence of Ag⁺, the free energy landscape exhibits two
main local minima: the folded state encompasses compact (R_g ≈ 6.5 Å), α-helical configura-
tions (α ≈ 0.9); and, the unfolded state comprises a range of conformers with low α-helical
content (α < 0.4). Thus, our T-REMD simulations successfully capture the folding of B1.
In addition, we observe a marked effect of Ag⁺ on the folding landscape. Whereas the
simulations predict a preference for the unfolded state in the absence of Ag⁺, Ag⁺-binding
stabilizes the folded state by ≈1.5 kcal mol⁻¹ relative to the unfolded state. These trends are
observed in two independent T-REMD simulations, both in the absence (simulations Free
B1 (1) and (2)) and the presence (simulations B1+Ag⁺ C-RESP2 (1) and (2)) of Ag⁺. This
suggests that our bonded model of the His–Ag⁺–Met motif reproduces the experimentally-
observed preference of B1 for an α-helical conformation when bound to Ag⁺⁸. We assessed
the parametrization sensitivity of the folding equilibrium by performing T-REMD simula-
tions of models with partial charges derived through alternative procedures (Supplementary
Text 1). With default C36m partial charges (with +1 charge on Ag), the predicted ground
state is disordered rather than folded (Fig S6A). This suggests that accounting for the re-
arranged electronic density upon Ag⁺ binding is important to capture the stabilization of
the helical state. A model with C-RESP partial charges stabilizes the folded state slightly
less than C-RESP2 charges, suggesting that accounting for polarization in water may add a
small but important contribution (Fig S6B). Surprisingly, C-RESP or C-RESP2 charges av-
eraged over conformational fluctuations (Supplementary Text 1) predict a disordered ground
state (Fig S6C,D). Although the physical basis for this effect is currently unclear, these find-
ings empirically support our C-RESP2 parametrization methodology as the one that best
reproduces the experimentally observed conformational equilibrium.

<figure><img src="image_5.png" /><figcaption>Figure 3: Free energy profiles along ($R_g, \alpha$) reveal how Ag$^+$-binding shapes the folding landscape of B1. A. Simulation Free B1 (1). B. Simulation B1+Ag$^+$ C-RESP2 (1). Representative frames are shown; for clarity, only polar hydrogens are shown.</figcaption></figure>

Bound Ag$^+$ ions stabilize the folded state in two ways. First, the positively charged His–Ag$^+$–Met motifs are positioned opposite to K3 and R10; this charge pattern may make the helix rigid through electrostatic repulsion. Second, bound Ag$^+$ ions promote the formation of helical turns H1:V5 and S7:M11 by restricting the conformational freedom of the peptide backbone. This is apparent from the reduced range of $R_g$ values sampled in the unfolded state when Ag$^+$ is present (Fig 3), indicating that Ag$^+$ destabilizes both very compact or very extended conformers. This reduces the conformational entropy of the
156 unfolded state, shifting the equilibrium towards the helical configuration in the presence of
157 Ag⁺.

158 In the folded state, residues K3 and R10 can both form salt-bridges with residue E6;
159 these salt-bridges are colinear to the helical axis, which could stabilize the α-helix (Fig
160 3A,B) independently of whether Ag⁺ is present. This observation explains why the B1 E6Q
161 mutant does not fold into an α-helix when bound to Ag⁺. T-REMD simulations of B1 E6Q
162 show that without Ag⁺, the disordered state is favoured even more than in the wild-type,
163 in agreement with NMR (Fig S5). With bound Ag⁺, the predicted ground state is helical,
164 which may be inconsistent with NMR; however, the conformational preference for the helix
165 is decreased relative to wild-type B1+Ag⁺, suggesting our model captures the trend. These
166 findings support that E6 stabilizes the helical conformation through salt-bridges with K3
167 and R10. Thus, in addition to H:M cross-linking by Ag⁺, a centrally-positioned, negative
168 side-chain also promotes helical folding.

169 To get a finer view of the conformational landscape of B1 than afforded by R_g and α, we
170 turned to machine learning. We trained an autoencoder (AE) neural network to reduce the
171 dimensionality of the conformational space to 6. The AE takes as input a vector of atomic
172 coordinates, projects it onto a 6-dimensional latent space, then attempts to reconstruct the
173 input from the projection. In so doing, the AE discovers 6 latent variables that describe the
174 conformational landscape. Inspired by previous work$^{57-59}$, we used a loss function combining
175 the reconstruction error, a term enforcing decorrelation of the latent variables, and a "sketch-
176 map" term that helps latent variables distinguish between conformational basins on medium
177 distance scale, *i.e.*, the most likely relevant substates$^{60}$. We trained the AE on ≈20 millions
178 T-REMD simulation frames. Details on the AE architecture, training, and loss function are
179 provided in Supplementary Text 3 and Fig S7. To visualize the 6-dimensional latent space, we
180 reduced it to 2 dimensions with Isomap$^{61,62}$, yielding variables *l*₁ and *l*₂. Next, we evaluated
181 the free energy landscapes along *l*₁ and *l*₂ in the presence and the absence of Ag⁺ (Fig 4). This
182 analysis reveals several metastable conformational states that are defined by their degree of
183 folding. For example, the completely disordered state is found at ($l_1 \approx -1, l_2 \approx -1$), and
184 the completely folded state encompasses two basins (($l_1 \approx 2, l_2 \approx -2$) and ($l_1 \approx 3, l_2 \approx 0$)).
185 Partially folded conformers are also identified, e.g. at ($l_1 \approx -0.5, l_2 \approx 2.5$) where the N-
186 terminal half is folded whereas the C-terminal half is disordered. Most of these states are
187 present in both the apo and Ag$^+$-bound B1 peptide, and Ag$^+$-binding shifts the population
188 towards partially or fully folded conformations.

<figure><img src="image_6.png" /><figcaption>Figure 4: Free energy profiles of B1 in the absence (A) and the presence (B) of Ag⁺ along Isomap-transformed latent variables from the deep autoencoder reveal conformational substates. A. Simulation Free B1 (1). B. Simulation B1+Ag⁺ C-RESP2 (1). Note that the free energy levels go up to 6 kcal mol⁻¹. For each metastable state, a representative simulation frame is shown; for clarity, only polar hydrogens are shown.</figcaption></figure>
The AE thus yields a detailed picture of the folding landscape of B1 and its modulation by Ag⁺. However, it is not designed to identify folding pathways. We therefore developed a *post-hoc* variant of the string method in collective variables (CVSM)41,63-65 to extract Minimum Free Energy Paths from our *T*-REMD simulations (described in Supplementary Text 4). We used it to compute folding MFEPs in a subspace defined by 6 collective variables describing the folding process (Table S6). These Human-designed CVs reflect on the secondary structure content of B1, its global shape, and the formation of K3-E6 and E6-R10 salt-bridges. Interestingly, we find that they are well correlated with the AE-learned descriptors *l*₁ and *l*₂ (Figs S8 and S9). From the string method analysis, we infer detailed sequences of events for α-helical folding of B1, compare competing pathways, and assess how the mechanism changes when Ag⁺ is present.

Because the string method is sensitive to the guess path⁶⁶, we considered two hypotheses for the folding pathway: N-ter-initiated folding (in which helical turns first form in N-terminal and propagate towards C-terminal), or conversely C-ter-initiated folding. In both the presence and the absence of Ag⁺, we prepared a guess path in CV-space corresponding to each hypothesis, independently relaxed these paths with our string method, and compared their highest free energy barriers to evaluate their contribution to the total folding flux. The results suggest that Ag⁺-binding may amplify a pre-existing preference for N-ter-initiated folding (Fig 5, Figs S11,S13,S15,S17).

In the absence of Ag⁺ (Simulation Free B1 (1)), N-ter-initiated folding starts with the formation of the K3-E6 salt-bridge, which remains stably formed throughout the transition. This promotes the formation of N-terminal helical turns H1:V5 and Q2:E6. Then, the remainder of the peptide progressively folds from N-ter to C-ter (Fig 5 A). Conversely, late formation of the E6-R10 salt-bridge does not seem required for folding from N-ter, though configurations in which it is formed are seen. The transition state (+1.5 kcal mol⁻¹ higher in free energy than the disordered configuration) exhibits formed K3-E6 salt-bridges and H1:V5 helix turn, and a partially formed Q2:E6 helix turn, suggesting that the formation
<figure><img src="image_7.png" /><figcaption>Figure 5: Folding pathways of B1 with and without Ag⁺ from *post-hoc* string method analysis of the replica-exchange simulations. A. Folding pathways in the absence of Ag⁺, Simulation Free B1 (1). B. Folding pathways in the presence of Ag⁺, Simulation B1+Ag⁺ C-RESP2 (1). Orange: N-ter-initiated folding mechanism. Green: C-ter-initiated folding mechanism. TS: Transition State. The red shaded ellipse materializes the K3-E6 and E6-R10 salt-bridges. Free energy levels are evaluated with respect to the folded state, and correspond to the free energy profiles of Figs S11A and S15A. For clarity, only polar hydrogens are shown.</figcaption></figure>
of this turn is rate-limiting for N-ter initiated folding in the absence of Ag⁺ ions. C-ter-
initiated folding starts with the formation of the E6-R10 salt-bridge, favouring the formation
of a bent intermediate from which the backbone H-bond E6:R10 forms, followed by the
backbone H-bonds V5:Q9, M4:H8, and S7:M11. The transition state (+1.6 kcal mol⁻¹ higher
in free energy than the disordered configuration) immediately precedes the formation of the
first helical turn. The E6-R10 salt-bridge, although important for the early stages of C-
ter-initiated folding, does not persist throughout the transition and is generally less stable
than the K3-E6 one. Thus, although they exhibit similar energetics (and therefore rates),
N-ter and C-ter-initiated folding proceed through qualitatively different pathways. The
independent Free B1 (2) simulation yields essentially the same picture, except that the K3-E6
salt-bridge forms halfway through N-ter-initiated folding. This suggests that the formation
of this salt-bridge is not strictly required to initiate folding from N-ter. Additionally, the
barrier for C-ter-initiated folding is higher (2.2 kcal mol⁻¹) whereas the barrier for N-ter-
initiated folding is virtually unchanged (1.6 kcal mol⁻¹). This may reflect a slight intrinsic
preference for N-ter-initiated folding.

In the presence of Ag⁺ (Simulation B1+Ag⁺ C-RESP2 (1)), the preference for N-ter-
initiated folding is more marked. The highest transition state for N-ter-initiated folding
lies +2.5 kcal mol⁻¹ higher in free energy than the folded state, versus +3.5 kcal mol⁻¹ for
C-ter-initiated folding. This 1 kcal mol⁻¹ difference translates into N-ter-initiated folding
accounting for a predicted ≈ 85% of the folding flux at 293 K. The independent B1+Ag⁺
C-RESP2 (2) simulation predicts a smaller, 0.7 kcal mol⁻¹ difference between the free energy
barriers, but still favoring N-ter folding over C-ter, suggesting Ag⁺ amplifies the pre-existing
bias. Overall, our results suggest that Ag⁺-induced folding of B1 is determined by partial pre-
structuration of the N-terminal and proceeds directionally from N-ter to C-ter. Interestingly,
the first step of the mechanism entails the formation of an intermediate in which E6 interacts
electrostatically with K3 and the Ag⁺ bound to H8:M11, revealing that Ag⁺ changes the
sequence of structural states along the folding pathway.
Using enhanced sampling simulations in explicit solvent with a bespoke bonded model, we describe in atomistic details how Ag⁺ binding to His-Met motifs promotes α-helical folding of a bacterial peptide fragment. We evaluate the relative thermodynamic stability of the folded state with respect to the disordered state, in the absence and the presence of Ag⁺. We deploy a self-supervised neural network to map the conformational landscape and assess how it is modulated by Ag⁺. We find that Ag⁺ binding shifts the balance in favour of the helical state by several effects. First, it creates a favourable charge repartition that provides electrostatic stabilization. Second, it pre-organizes a helix nucleation site in N-ter by keeping the peptide groups of H1 and V5 in close proximity. Last, the His-Ag⁺-Met crosslink restricts the accessible conformational space in the unfolded state, creating an entropic penalty in comparison to the free peptide. These effects are reminiscent of how Human-designed stapled peptides promote α-helical folding⁶⁷. SilE peptides like B1 represent a unique case of naturally-occuring metal-controlled stapling, and could inspire novel switchable metal-crosslinked peptides⁶⁸,⁶⁹, a purpose for which Ag⁺ has seldom been used⁷⁰. In fact, our study illustrates how simulations can rationalize and even predict how metals induce α-helices to help design peptide-based supramolecular architectures⁷¹.

Our results suggest that Ag⁺ binding amplifies a pre-existing preference for N→C helical propagation in the peptide's folding mechanism. This is consistent with earlier computational and experimental evidence for N→C helical propagation in the folding of α-helical peptides⁷²,⁷³. In fact, the laser-induced temperature-jump infrared spectroscopy technique used by Acharrya et al.⁷³ could be directly applied to validate our proposed folding mechanism for the B1 peptide. In addition, we note that our string method analysis, although effective to infer dominant folding pathways, cannot account for off-pathway states —kinetic traps—that would slow down folding⁷⁴. Determining how these may influence folding kinetics would require complementary analyses with e.g. Markov State Models⁷³.

We used a bonded model in which Ag⁺ binding to His and Met is effectively covalent and irreversible, which assumes that Ag⁺ binding precedes helix folding and cannot capture
alternative scenarios in which helix pre-folding is required for binding ⁴. This choice is sup-
ported by our simulations of the free B1 peptide, which show only marginal helix formation
in the absence of Ag⁺, by our MS and NMR measurements indicating Ag⁺ binding without
helix formation, and by the ability of HXXM tetrapeptides — too short to form helices —
to bind Ag⁺ ⁷,¹⁹.

By construction, the bonded model enables enhanced sampling of the bound state without "contamination" from unbound configurations, which helps isolate the reduction of conformational entropy brought about by Ag⁺ binding. Although this may bias the folding mechanism, our experimental evidence for folding after binding suggest that the resulting pathways remain physically representative. In this sense, simulations with a bonded model provide a clearer separation between binding and folding than is accessible to MS and NMR, highlighting the complementarity of these approaches.

Because of the lack of an adequate method for transition metal parametrization in
CHARMM force-fields, we adopted a non-standard scheme for partial charge derivation.
This scheme, termed C-RESP2, seeks to recover missing polarization effects through lin-
ear combination of vacuum and aqueous RESP charges, following the approach of Gilson
et al. ⁴⁹. Empirical comparison with alternative parametrizations indicates that C-RESP2
best reproduces the experimental folding equilibrium, making it suitable for the present
mechanistic analysis. Whether this approach can be readily generalized to other transition-
metal-containing systems remains an open question.

More broadly, our results support the use of bonded models to investigate protein-metal
interactions. Lithgo and co-workers recently reported on a joint experimental and compu-
tational study of SilF<sup>27</sup>, another Sil protein<sup>21</sup>. These authors parametrized Ag<sup>+</sup> binding to
SilF as a bonded model for the AMBER force-fields, which they find agrees with QM/MM
simulations. Our parametrization follows similar lines but is tailored for CHARMM force-
fields instead. Thus, both our work and Lithgo et al.'s suggest that bonded models for Ag<sup>+</sup>
binding to proteins can enable functional insight. Moreover, we note that SilF is a struc-
297 tured protein for which no major rearrangement occurs upon Ag⁺ binding, unlike the B1
298 peptide studied here. At the same time, Manciocchi et al. developed a non-bonded model of
299 the Ag⁺ cation optimized to reproduce the thermodynamics of interaction with proteins³⁹.
300 These investigators performed µs-scale conventional MD simulations of a 14-residue peptide
301 fragment encompassing the B1 peptide, in the presence of their model of Ag⁺. Interest-
302 ingly, they observe a marginal increase in peptide helicity, suggesting that a non-bonded
303 approach might be suited to simulate silver-induced folding. However, they do not com-
304 ment on the structural mechanism involved, nor do they evaluate the helix propensity by
305 quantitative simulation methods. Therefore, their study indicates that non-bonded models
306 might constitute a valuable direction for the computational investigation of the structural
307 consequences of silver-binding to proteins, to be pursued alongside the bonded approach.
308 Overall, together with complementary recent reports²⁷,³⁹, our study contributes to under-
309 standing silver-protein interactions and sets the stage for computational investigations of
310 the bacterial silver resistance machinery.

311 Supporting Information

312 SI Appendix: Supplementary Texts S1 to S6, Figures S1 to S17, Tables S1 to S6. References
313 75–109 are cited in Supporting Information.

314 Acknowledgments

315 This project received funding from French Agence Nationale de la Recherche (ANR) Re-
sist2Silver (grant ANR-22-CE11-00-01). This project was provided with HPC and stor-
age resources by GENCI at CINES and IDRIS thanks to the grants AD010714601 and
316 A0180716223 on the supercomputer Adastra's MI250x partition and on the supercomputer
317 Jean Zay's V100 partition. We thank the support engineers at CINES and IDRIS for tech-
nical assistance.
318
319
320
(1) Sharma, S. K.; Goloubinoff, P.; Christen, P. Heavy Metal Ions Are Potent Inhibitors of Protein Folding. *Biochemical and Biophysical Research Communications* **2008**, *372*, 341–345.

(2) Leal, S. S.; Botelho, H. M.; Gomes, C. M. Metal Ions as Modulators of Protein Conformation and Misfolding in Neurodegeneration. *Coordination Chemistry Reviews* **2012**, *256*, 2253–2270.

(3) Tamás, M.; Sharma, S.; Istedt, S.; Jacobson, T.; Christen, P. Heavy Metals and Metalloids As a Cause for Protein Misfolding and Aggregation. *Biomolecules* **2014**, *4*, 252–267.

(4) Wilson, C. J.; Apiyo, D.; Wittung-Stafshede, P. Role of Cofactors in Metalloprotein Folding. *Quarterly Reviews of Biophysics* **2004**, *37*, 285–314.

(5) Besold, A. N.; Michel, S. L. J. Neural Zinc Finger Factor/Myelin Transcription Factor Proteins: Metal Binding, Fold, and Function. *Biochemistry* **2015**, *54*, 4443–4452.

(6) Ariöz, C.; Wittung-Stafshede, P. Folding of Copper Proteins: Role of the Metal? *Quarterly Reviews of Biophysics* **2018**, *51*, e4.

(7) Chabert, V.; Hologne, M.; Sénèque, O.; Crochet, A.; Walker, O.; Fromm, K. M. Model Peptide Studies of Ag⁺ Binding Sites from the Silver Resistance Protein SilE. *Chemical Communications* **2017**, *53*, 6105–6108.

(8) Chabert, V.; Hologne, M.; Sénèque, O.; Walker, O.; M. Fromm, K. Alpha-Helical Folding of SilE Models upon Ag(His)(Met) Motif Formation. *Chemical Communications* **2018**, *54*, 10419–10422.

(9) Monneau, Y.; Arrault, C.; Duroux, C.; Martin, M.; Chirot, F.; Mac Aleese, L.; Girod, M.; Comby-Zerbino, C.; Hagège, A.; Walker, O. et al. Structural and Dy-
namical Insights into SilE Silver Binding from Combined Analytical Probes. *Physical Chemistry Chemical Physics* **2023**, *25*, 3061–3071.

(10) Asiani, K. R.; Williams, H.; Bird, L.; Jenner, M.; Searle, M. S.; Hobman, J. L.; Scott, D. J.; Soultanas, P. SilE Is an Intrinsically Disordered Periplasmic “Molecular Sponge” Involved in Bacterial Silver Resistance. *Molecular Microbiology* **2016**, *101*, 731–742.

(11) Gupta, A.; Matsui, K.; Lo, J.-F.; Silver, S. Molecular Basis for Resistance to Silver Cations in Salmonella. *Nature Medicine* **1999**, *5*, 183–188.

(12) Silver, S. Bacterial Silver Resistance: Molecular Biology and Uses and Misuses of Silver Compounds. *FEMS Microbiology Reviews* **2003**, *27*, 341–353.

(13) McNeilly, O.; Mann, R.; Hamidian, M.; Gunawan, C. Emerging Concern for Silver Nanoparticle Resistance in Acinetobacter Baumannii and Other Bacteria. *Frontiers in Microbiology* **2021**, *12*, 894.

(14) Medici, S.; Peana, M.; Nurchi, V. M.; Zoroddu, M. A. Medical Uses of Silver: History, Myths, and Scientific Evidence. *Journal of Medicinal Chemistry* **2019**, *62*, 5923–5943.

(15) Morones-Ramirez, J. R.; Winkler, J. A.; Spina, C. S.; Collins, J. J. Silver Enhances Antibiotic Activity Against Gram-Negative Bacteria. *Science Translational Medicine* **2013**, *5*, 190ra81–190ra81.

(16) Wang, H.; Wang, M.; Xu, X.; Gao, P.; Xu, Z.; Zhang, Q.; Li, H.; Yan, A.; Kao, R. Y.-T.; Sun, H. Multi-Target Mode of Action of Silver against Staphylococcus Aureus Endows It with Capability to Combat Antibiotic Resistance. *Nature Communications* **2021**, *12*, 3331.

(17) Frei, A.; Verderosa, A. D.; Elliott, A. G.; Zuegg, J.; Blaskovich, M. A. T. Metals to Combat Antimicrobial Resistance. *Nature Reviews Chemistry* **2023**, *7*, 202–224.
369

370

371

(18) Zingale, G. A.; Oliveri, V.; Grasso, G. Insights into the Binding of Ag Ions with SilE Model Peptides: An NMR and MS Coupled Approach. *Metallomics* **2023**, *15*, mfad015.

372

373

374

(19) Bianchi, A.; Marquenet, F.; Manciocchi, L.; Spichty, M.; Fromm, K. M. Toward Predicting Silver Ion Binding in Proteins. *Chemical Communications* **2025**, 10.1039.D4CC06612J.

375

376

377

(20) Babel, L.; Nguyen, M.-H.; Mittelheisser, C.; Martin, M.; M. Fromm, K.; Walker, O.; Hologne, M. NMR Reveals the Interplay between SilE and SilB Model Peptides in the Context of Silver Resistance. *Chemical Communications* **2021**, 57, 8726-8729.

378

379

380

381

(21) Arrault, C.; Monneau, Y. R.; Martin, M.; Cantrelle, F.-X.; Boll, E.; Chirot, F.; Comby Zerbino, C.; Walker, O.; Hologne, M. The Battle for Silver Binding: How the Interplay between the SilE, SilF and SilB Proteins Contributes to the Silver Ef-flux Pump Mechanism. *Journal of Biological Chemistry* **2023**, 105004.

382

383

384

(22) Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; de Groot, B. L.; Grub-müller, H.; MacKerell Jr, A. D. CHARMM36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins. *Nature Methods* **2017**, *14*, 71-73.

385

386

387

(23) Robustelli, P.; Piana, S.; Shaw, D. E. Developing a Molecular Dynamics Force Field for Both Folded and Disordered Protein States. *Proceedings of the National Academy of Sciences* **2018**, *115*, E4758-E4766.

388

389

(24) Li, P.; Merz, K. M. Metal Ion Modeling Using Classical Mechanics. *Chemical Reviews* **2017**, *117*, 1564-1686.

390

391

(25) Vidossich, P.; Magistrato, A. QM/MM Molecular Dynamics Studies of Metal Binding Proteins. *Biomolecules* **2014**, *4*, 616-645.
392

393

394

(26) Chakravorty, D. K.; Wang, B.; Ucisik, M. N.; Merz, K. M. Insight into the Cation-π Interaction at the Metal Binding Site of the Copper Metallochaperone CusF. *Journal of the American Chemical Society* **2011**, *133*, 19330–19333.

395

396

397

398

(27) Lithgo, R. M.; Hanževački, M.; Harris, G.; Kamps, J. J.; Holden, E.; Gianga, T.-M.; Benesch, J. L.; Jäger, C. M.; Croft, A. K.; Hussain, R. et al. The Adaptability of the Ion-Binding Site by the Ag(I)/Cu(I) Periplasmic Chaperone SilF. *Journal of Biological Chemistry* **2023**, *299*, 105331.

399

400

401

(28) Hazel, A. J.; Walters, E. T.; Rowley, C. N.; Gumbart, J. C. Folding Free Energy Landscapes of β-Sheets with Non-Polarizable and Polarizable CHARMM Force Fields. *The Journal of Chemical Physics* **2018**, *149*, 072317.

402

403

(29) Leontyev, I. V.; Stuchebrukhov, A. A. Electronic Continuum Model for Molecular Dynamics Simulations. *The Journal of Chemical Physics* **2009**, *130*, 085102.

404

405

406

(30) Leontyev, I. V.; Stuchebrukhov, A. A. Electronic Continuum Model for Molecular Dynamics Simulations of Biological Molecules. *Journal of Chemical Theory and Computation* **2010**, *6*, 1498–1508.

407

408

409

(31) Du, S.; Fu, H.; Shao, X.; Chipot, C.; Cai, W. Addressing Polarization Phenomena in Molecular Machines Containing Transition Metal Ions with an Additive Force Field. *Journal of Chemical Theory and Computation* **2019**, *15*, 1841–1847.

410

411

412

(32) Li, P.; Roberts, B. P.; Chakravorty, D. K.; Merz, K. M. Rational Design of Particle Mesh Ewald Compatible Lennard-Jones Parameters for +2 Metal Cations in Explicit Solvent. *Journal of Chemical Theory and Computation* **2013**, *9*, 2733–2748.

413

414

415

(33) Li, P.; Song, L. F.; Merz, K. M. J. Systematic Parameterization of Monovalent Ions Employing the Nonbonded Model. *Journal of Chemical Theory and Computation* **2015**, *11*, 1645–1657.
416

417

(34) Song, L. F.; Sengupta, A.; Merz, K. M. Thermodynamics of Transition Metal Ion Binding to Proteins. *Journal of the American Chemical Society* **2020**, *142*, 6365–6374.

418

419

(35) Li, Z.; Song, L. F.; Sharma, G.; Koca Fındık, B.; Merz, K. M. J. Accurate Metal–Imidazole Interactions. *Journal of Chemical Theory and Computation* **2023**, *19*, 619–625.

420

421

422

423

(36) Li, Z.; Bhowmik, S.; Sagresti, L.; Brancato, G.; Smith, M.; Benson, D. E.; Li, P.; Merz, K. M. Simulating Metal-Imidazole Complexes. *Journal of Chemical Theory and Computation* **2024**, *20*, 6706–6716.

424

425

426

(37) Li, P.; Merz, K. M. J. Taking into Account the Ion-Induced Dipole Interaction in the Nonbonded Model of Ions. *Journal of Chemical Theory and Computation* **2014**, *10*, 289–297.

427

428

429

(38) Li, P.; Song, L. F.; Merz, K. M. J. Parameterization of Highly Charged Metal Ions Using the 12-6-4 LJ-Type Nonbonded Model in Explicit Water. *The Journal of Physical Chemistry B* **2015**, *119*, 883–895.

430

431

432

(39) Manciocchi, L.; Bianchi, A.; Mazan, V.; Potapov, M.; Fromm, K. M.; Spichty, M. Modeling the Interaction Between Silver(I) Ion and Proteins with 12-6 Lennard-Jones Potential: A Bottom-Up Parameterization Approach. *Biophysica* **2025**, *5*, 7.

433

434

(40) Chen, X.; Karpenko, A.; Lopez-Acevedo, O. Silver-Mediated Double Helix: Structural Parameters for a Robust DNA Building Block. *ACS Omega* **2017**, *2*, 7343–7348.

435

436

437

(41) Maragliano, L.; Fischer, A.; Vanden-Eijnden, E.; Ciccotti, G. String Method in Collective Variables: Minimum Free Energy Paths and Isocommittor Surfaces. *The Journal of Chemical Physics* **2006**, *125*, 024106.

438

439

(42) Seminario, J. M. Calculation of Intramolecular Force Fields from Second-Derivative Tensors. *International Journal of Quantum Chemistry* **1996**, *60*, 1271–1277.
440

441

(43) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. *PHYSICAL REVIEW LETTERS* **1996**, 77.

442

443

444

(44) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Ad- justable Parameters: The PBE0 Model. *The Journal of Chemical Physics* **1999**, 110, 6158–6170.

445

446

447

(45) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. *Physical Chemistry Chemical Physics* **2005**, 7, 3297.

448

449

450

(46) Andrae, D.; Häussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-Adjustedab Initio Pseudopotentials for the Second and Third Row Transition Elements. *Theoretica Chimica Acta* **1990**, 77, 123–141.

451

452

453

(47) Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The RESP Model. *The Journal of Physical Chemistry* **1993**, 97, 10269–10280.

454

455

456

(48) Pavlova, A.; Parks, J. M.; Gumbart, J. C. Development of CHARMM-Compatible Force-Field Parameters for Cobalamin and Related Cofactors from Quantum Mechanical Calculations. *Journal of Chemical Theory and Computation* **2018**, 14, 784–798.

457

458

459

(49) Schauperl, M.; Nerenberg, P. S.; Jang, H.; Wang, L.-P.; Bayly, C. I.; Mobley, D. L.; Gilson, M. K. Non-Bonded Force Field Model with Advanced Restrained Electrostatic Potential Charges (RESP2). *Communications Chemistry* **2020**, 3, 1–11.

460

461

(50) Durell, S. R.; Brooks, B. R.; Ben-Naim, A. Solvent-Induced Forces between Two Hydrophilic Groups. *The Journal of Physical Chemistry* **1994**, 98, 2198–2202.

462

463

(51) Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding. *Chemical Physics Letters* **1999**, 314, 141–151.
464

465

466

(52) Okabe, T.; Kawata, M.; Okamoto, Y.; Mikami, M. Replica-Exchange Monte Carlo Method for the Isobaric-Isothermal Ensemble. *Chemical Physics Letters* **2001**, *335*, 435-439.

467

468

(53) Patriksson, A.; van der Spoel, D. A Temperature Predictor for Parallel Tempering Simulations. *Physical Chemistry Chemical Physics* **2008**, *10*, 2073-2077.

469

470

(54) Fiorin, G.; Klein, M. L.; Hénin, J. Using Collective Variables to Drive Molecular Dynamics Simulations. *Molecular Physics* **2013**, *111*, 3345-3362.

471

472

(55) Shirts, M. R.; Chodera, J. D. Statistically Optimal Analysis of Samples from Multiple Equilibrium States. *The Journal of Chemical Physics* **2008**, *129*, 124105.

473

474

475

(56) Shirts, M. R.; Ferguson, A. L. Statistically Optimal Continuous Free Energy Surfaces from Biased Simulations and Multistate Reweighting. *Journal of Chemical Theory and Computation* **2020**, *16*, 4107-4125.

476

477

478

479

(57) Ward, M. D.; Zimmerman, M. I.; Meller, A.; Chung, M.; Swamidass, S. J.; Bowman, G. R. Deep Learning the Structural Determinants of Protein Biochemical Properties by Comparing Structural Ensembles with DiffNets. *Nature Communications* **2021**, *12*, 3023.

480

481

482

(58) Lemke, T.; Peter, C. EncoderMap: Dimensionality Reduction and Generation of Molecule Conformations. *Journal of Chemical Theory and Computation* **2019**, *15*, 1209-1215.

483

484

485

(59) Lemke, T.; Berg, A.; Jain, A.; Peter, C. EncoderMap(II): Visualizing Important Molecular Motions with Improved Generation of Protein Conformations. *Journal of Chemical Information and Modeling* **2019**, *59*, 4550-4560.

486

(60) Ceriotti, M.; Tribello, G. A.; Parrinello, M. Simplifying the Representation of Complex
Free-Energy Landscapes Using Sketch-Map. *Proceedings of the National Academy of Sciences* **2011**, *108*, 13023–13028.

(61) Tenenbaum, J. B.; de Silva, V.; Langford, J. C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. *Science* **2000**, *290*, 2319–2323.

(62) Das, P.; Moll, M.; Stamati, H.; Kavraki, L. E.; Clementi, C. Low-Dimensional, Free-Energy Landscapes of Protein-Folding Reactions by Nonlinear Dimensionality Reduction. *Proceedings of the National Academy of Sciences* **2006**, *103*, 9885–9890.

(63) E, W.; Ren, W.; Vanden-Eijnden, E. String Method for the Study of Rare Events. *Physical Review B* **2002**, *66*.

(64) Pan, A. C.; Sezer, D.; Roux, B. Finding Transition Pathways Using the String Method with Swarms of Trajectories. *The Journal of Physical Chemistry B* **2008**, *112*, 3432–3440.

(65) Moradi, M.; Enkavi, G.; Tajkhorshid, E. Atomic-Level Characterization of Transport Cycle Thermodynamics in the Glycerol-3-Phosphate:Phosphate Antiporter. *Nature Communications* **2015**, *6*, 8393.

(66) Blanc, F. E. C.; Houdusse, A.; Cecchini, M. A Weak Coupling Mechanism for the Early Steps of the Recovery Stroke of Myosin VI: A Free Energy Simulation and String Method Analysis. *PLOS Computational Biology* **2024**, *20*, e1012005.

(67) Kutchukian, P. S.; Yang, J. S.; Verdine, G. L.; Shakhnovich, E. I. All-Atom Model for Stabilization of α-Helical Structure in Peptides by Hydrocarbon Staples. *Journal of the American Chemical Society* **2009**, *131*, 4622–4627.

(68) Smith, S. J.; Du, K.; Radford, R. J.; Tezcan, F. A. Functional, Metal-Based Crosslinkers for α-Helix Induction in Short Peptides. *Chemical Science* **2013**, *4*, 3740.
510

511

512

(69) Smith, S. J.; Radford, R. J.; Subramanian, R. H.; Barnett, B. B.; Figueroa, J. S.; Tezcan, F. A. Tunable Helicity, Stability and DNA-binding Properties of Short Peptides with Hybrid Metal Coordination Motifs. *Chemical Science* **2016**, 7, 5453–5461.

513

514

515

(70) Fischer, N.; Tóth, A.; Jancsó, A.; Thulstrup, P.; Diness, F. Inducing α-Helicity in Peptides by Silver Coordination to Cysteine. *Chemistry – A European Journal* **2024**, 30, e202304064.

516

517

518

(71) Richardson-Matthews, R.; Velko, K.; Bhunia, B.; Ghosh, S.; Oktawiec, J.; Brunzelle, J. S.; Dang, V. T.; Nguyen, A. I. Metal-α-Helix Peptide Frameworks. *Journal of the American Chemical Society* **2025**, 147, 17433–17447.

519

520

521

(72) Monticelli, L.; Tieleman, D. P.; Colombo, G. Mechanism of Helix Nucleation and Propagation: Microscopic View from Microsecond Time Scale MD Simulations. *The Journal of Physical Chemistry B* **2005**, 109, 20064–20067.

522

523

524

(73) Acharyya, A.; Ge, Y.; Wu, H.; DeGrado, W. F.; Voelz, V. A.; Gai, F. Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study. *The Journal of Physical Chemistry B* **2019**, 123, 1797–1807.

525

526

527

(74) Lin, M. M.; Shorokhov, D.; Zewail, A. H. Dominance of Misfolded Intermediates in the Dynamics of α-Helix Folding. *Proceedings of the National Academy of Sciences* **2014**, 111, 14424–14429.

528

529

(75) Li, P.; Merz, K. M. J. MCPB.Py: A Python Based Metal Center Parameter Builder. *Journal of Chemical Information and Modeling* **2016**, 56, 599–604.

530

531

532

(76) Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. *Journal of Cheminformatics* **2012**, 4, 17.
533

534

(77) Neese, F. Software Update: The ORCA Program System—Version 5.0. *WIREs Computational Molecular Science* **2022**, 12, e1606.

535

536

537

(78) Talmazan, R. A.; Podewitz, M. PyConSolv: A Python Package for Conformer Generation of (Metal-Containing) Systems in Explicit Solvent. *Journal of Chemical Information and Modeling* **2023**, 63, 5400–5407.

538

539

540

541

(79) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S. et al. All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. *The Journal of Physical Chemistry B* **1998**, 102, 3586–3616.

542

543

(80) Chermette, H. Density Functional Theory: A Powerful Tool for Theoretical Studies in Coordination Chemistry. *Coordination Chemistry Reviews* **1998**, 178–180, 699–721.

544

545

546

(81) Mayne, C. G.; Saam, J.; Schulten, K.; Tajkhorshid, E.; Gumbart, J. C. Rapid Parame-
terization of Small Molecules Using the Force Field Toolkit. *Journal of Computational
Chemistry* **2013**, 34, 2757–2770.

547

548

549

550

(82) de Hatten, X.; Cournia, Z.; Huc, I.; Smith, J. C.; Metzler-Nolte, N. Force-Field De-
velopment and Molecular Dynamics Simulations of Ferrocene–Peptide Conjugates as
a Scaffold for Hydrogenase Mimics. *Chemistry – A European Journal* **2007**, *13*, 8139–
8152.

551

552

553

554

(83) Filippini, G.; Goujon, F.; Bonal, C.; Malfreyt, P. Energetic Competition Effects on Thermodynamic Properties of Association between β-CD and Fc Group: A Potential of Mean Force Approach. *The Journal of Physical Chemistry C* **2012**, *116*, 22350–22358.

555

556

557

(84) Mayaan, E.; Moser, A.; MacKerell Jr, A. D.; York, D. M. CHARMM Force Field Parameters for Simulation of Reactive Intermediates in Native and Thio-Substituted Ribozymes. *Journal of Computational Chemistry* **2007**, *28*, 495–507.
558

(85) Pavlova, A.; Gumbart, J. C. Parametrization of Macrolide Antibiotics Using the Force Field Toolkit. *Journal of Computational Chemistry* **2015**, *36*, 2052–2063.

559

560

(86) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. *Journal of Computational Chemistry* **2012**, *33*, 580–592.

561

562

(87) Zhang, J.; Lu, T. Efficient Evaluation of Electrostatic Potential with Computerized Optimized Code. *Physical Chemistry Chemical Physics* **2021**, *23*, 20323–20328.

563

564

(88) Marcus, Y. Ionic Radii in Aqueous Solutions. *Chemical Reviews* **1988**, *88*, 1475–1498.

565

(89) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. *The Journal of Chemical Physics* **1983**, *79*, 926–935.

566

567

568

(90) Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O. MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations. *Journal of Computational Chemistry* **2011**, *32*, 2319–2327.

569

570

571

(91) Gowers, R.; Linke, M.; Barnoud, J.; Reddy, T.; Melo, M.; Seyler, S.; Domański, J.; Dotson, D.; Buchoux, S.; Kenney, I. et al. MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations. Python in Science Conference. Austin, Texas, 2016; pp 98–105.

572

573

574

575

(92) Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High Performance Molecular Simulations through Multi-Level Parallelism from Laptops to Supercomputers. *SoftwareX* **2015**, *1–2*, 19–25.

576

577

578

(93) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. *The Journal of Chemical Physics* **2007**, *126*, 014101.

579

580

(94) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. *Journal of Applied Physics* **1981**, *52*, 7182–7190.

581
582

(95) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. *Journal of Molecular Graphics* **1996**, *14*, 33–38.

583

584

(96) Hénin, J.; Lopes, L. J. S.; Fiorin, G. Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD. *Journal of Chemical Theory and Computation* **2022**, *18*, 1945–1956.

585

586

587

(97) Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V. et al. Scikit-Learn: Machine Learning in Python. *Journal of Machine Learning Research* **2011**, *12*, 2825–2830.

588

589

590

(98) Hinton, G. E.; Salakhutdinov, R. R. Reducing the Dimensionality of Data with Neural Networks. *Science* **2006**, *313*, 504–507.

591

592

(99) Chen, W.; Ferguson, A. L. Molecular Enhanced Sampling with Autoencoders: On-the-fly Collective Variable Discovery and Accelerated Free Energy Landscape Exploration. *Journal of Computational Chemistry* **2018**, *39*, 2079–2102.

593

594

595

(100) He, K.; Zhang, X.; Ren, S.; Sun, J. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. *arXiv:1502.01852 [cs.CV]* **2015**,

596

597

(101) Wehmeyer, C.; Noé, F. Time-Lagged Autoencoders: Deep Learning of Slow Collective Variables for Molecular Kinetics. *The Journal of Chemical Physics* **2018**, *148*, 241703.

598

599

(102) Tschannen, M.; Bachem, O.; Lucic, M. Recent Advances in Autoencoder-Based Representation Learning. *arXiv:1812.05069 [cs.LG]* **2018**,

600

601

(103) Ceriotti, M.; Tribello, G. A.; Parrinello, M. Demonstrating the Transferability and the Descriptive Power of Sketch-Map. *Journal of Chemical Theory and Computation* **2013**, *9*, 1521–1532.

602

603

604

(104) Paszke, A.; Gross, S.; Chintala, S.; Chanan, G.; Yang, E.; DeVito, Z.; Lin, Z.; Desmaison, A.; Antiga, L.; Lerer, A. Automatic Differentiation in PyTorch. 31st Conference

605
606

on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA. 2017; p 4.

607

608

(105) Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L. et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library. *Advances in Neural Information Processing Systems* **2019**, 12.

609

610

611

612

(106) Kingma, D. P.; Ba, J. Adam: A Method for Stochastic Optimization. arXiv:1412.6980 [cs] 2017,

613

614

(107) Srivastava, N.; Hinton, G.; Krizhevsky, A.; Sutskever, I.; Salakhutdinov, R. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. *J. Mach. Learn. Res.* **2014**, *15*, 1929–1958.

615

616

617

(108) E, W.; Ren, W.; Vanden-Eijnden, E. Finite Temperature String Method for the Study of Rare Events. *The Journal of Physical Chemistry B* **2005**, *109*, 6688–6693.

618

619

(109) Vanden-Eijnden, E.; Venturoli, M. Revisiting the Finite Temperature String Method for the Calculation of Reaction Tubes and Free Energies. *The Journal of Chemical Physics* **2009**, *130*, 194103.

620

621
Mechanism of Ag⁺-induced Folding of a
Bacterial Peptide from Replica-Exchange
Molecular Simulations (Supporting Information)

Florian E.C. Blanc ID,* Maggy Hologne ID, Marion Girod ID, Mélodie

Demontrond, Henry Chermette ID, and Olivier Walker ID*

Université de Lyon, CNRS, UCB Lyon1, Institut des Sciences Analytiques, UMR5280,
Villeurbanne, France

E-mail: florian.blanc@isa-lyon.fr; olivier.walker@univ-lyon1.fr
## Supplementary Text 1 - Details of the modelling procedure

The His–Ag⁺–Met motif was implemented as a CHARMM patch modifying residue types HSE and MET by introducing a covalent bond between atoms Nô of HSE and AG, and another one between atoms AG and SD of MET (Fig 1C). For this, we derived bonded parameters (reference values for angles and distances, force constants) for these covalent bonds, and modified partial charges. We adapted the Metal Center Parameter Builder (MCPB) method by Li and Merz⁷⁵. This method involves preparing two models of the motif, a small model used to derive bonded parameters, and a large model used to derive partial charges, see Fig S1.

### Bonded parameters

First, we built the small model containing the His and Met sidechains (with capping methyl groups replacing the CA atoms) and an Ag⁺ cation (Figs S1A and 1C). We extracted the initial coordinates of the small model from the α-helical structure of the B1 peptide, replaced the C-alpha atoms with capping methyl groups, and positioned an Ag atom between the His and Met sidechain, such that Ag interacted with atoms His-ND and Met-SD. We used Avogadro2 for these tasks⁷⁶. Following previous NMR observations, we modelled the His side chain with a protonated Nε⁸. We then optimized the geometry of the small model at the PBE0/def2-TZVP level (using the corresponding effective core potential for the Ag atom) in vacuum⁴³⁻⁴⁶. All atoms were allowed to relax freely; notably, we observed only negligible displacements of the carbon atoms in the capping methyl groups. We selected the PBE0 hybrid functional due to its good performance on transition-metal-containing systems.

<footnote n="1">¹References ¹⁻⁷⁴ are cited in Main Text.</footnote>
All DFT calculations were performed with ORCA 5.0 or 6.1<sup>77</sup>. We used the built-in ORCA routine to compute analytically the Hessian matrix at the energy-minimized geometry. Then, we determined force constants for the N-Ag and S-Ag bonds and corresponding angles from the Hessian matrix using the Seminario method<sup>42</sup> as implemented in PyConSolv<sup>78</sup>. Because the CHARMM and AMBER force-field families have the same functional forms for bond and angle terms, these force-constants can be used with any of the two force-fields. The bonded parameters are shown in Table S1.

## Partial charges

Ag<sup>+</sup> binding perturbs the electron density on the coordinating atoms. To reflect this effect, we derived several partial charge distributions (see Table S2) from single-point DFT calculations on the large model. In the following, we justify our not using the standard CHARMM procedure for partial charge derivation, then describe our proposed alternative approach C-RESP2.

## Challenges for CHARMM parametrization of transition-metal-containing systems and C-RESP

Partial charge determination for CHARMM parametrization normally involves fitting reference energies computed at the Hartree-Fock/6-31G(d) level<sup>79</sup>. However, Hartree-Fock calculations do not capture electron correlation and thus should not be applied to transition-metal-containing systems<sup>80</sup>. A popular alternative is to use partial charges that reproduce the electrostatic potential computed with a correlated quantum method such as DFT with a larger basis set, even if CHARMM developers advise against this strategy<sup>81</sup>. Using this approach for CHARMM force-fields has been successful in the past. For example, de Hatten et al. used CHELPG charges from B3LYP/DZVPP calculations to parametrize ferrocene-peptide complexes<sup>82</sup>. Later on, Filippini et al. investigated the binding of ferrocene to cyclodextrin, using the de Hatten ferrocene parameters in combination with CHELPG charges for cyclodextrin, and achieved very good agreement with
experimental *K*<sub>D</sub> values<sup>83</sup>. Mayaan et al. used CHELPG charges that were then adjusted to match CHARMM conventions for standard atoms (e.g., aliphatic hydrogens) for ribozymes and thio-substituted ribozymes, including Mg<sup>2+</sup>-bound compounds<sup>84</sup>. Here, inspired by the work of Gumbart et al. on Cobalt-containing systems<sup>48,85</sup>, we computed the partial charges as RESP charges<sup>47</sup> while constraining, in the RESP calculation, the partial charges of all backbone atoms and of sidechains's aliphatic carbons and hydrogens to their default CHARMM values. This retains compatibility with the CHARMM force-field. We term the partial charges obtained in this way C-RESP (for CHARMM-constrained RESP).

**Accounting for polarization by water with C-RESP2** HF/6-31G\* vacuum calculations typically yield molecular dipole moments larger than experimental gas-phase values<sup>79</sup>. Therefore, RESP charges computed at this level effectively incorporate an overpolarization in fixed-charge force-fields. Empirically, this was found to partially compensate for the absence of explicit electronic polarization by solvent, which motivates the use of HF/6-31G\*-based charge derivation in both CHARMM and AMBER force fields for aqueous-phase simulations with a non-polarizable water model such as TIP3P. In CHARMM parametrization protocols, charge optimization further reinforces this effect through empirical adjustment of dipole moments and solute-water interaction energies to ensure force-field consistency and reproduction of condensed-phase properties<sup>79</sup>. The higher level of theory (PBE0/def2-TZVP instead of HF/6-31G\*) used here to accurately describe the silver-containing complex is likely not to result in this fortuitous overpolarization, and thus may not effectively account for solvent polarization. Therefore, an explicit strategy to reintroduce the missing effective polarization is likely required to preserve force-field consistency with nonpolarizable, explicit water models. In the context of the AMBER force field, Gilson et al. introduced the RESP2 approach, in which fixed charges suitable for aqueous-phase simulations are obtained as a linear combination of RESP charges derived from vacuum and implicit-solvent DFT calculations performed at a higher level of theory than HF/6-31G\*<sup>49</sup>. Even though RESP2 was not
specifically developed for transition-metal systems, its rationale suggests that it may pro-
vide a suitable basis for such parametrizations. Accordingly, we used the RESP2 strategy to
account for solvent effects on the charge distribution <sup>49</sup>. For this purpose, we also computed
C-RESP partial charges using an implicit solvent model of water in the DFT calculation.
The final partial charges, termed C-RESP2, were obtained as a linear combination of the
two sets of charges, using 60% aqueous charges and 40% vacuum charges following Gilson et
al.

**Details of the charge calculations** Following the MCPB procedure, we prepared the large model, i.e., a HGGM peptide + an Ag⁺ ion (Fig S1B). The Ag⁺ ion was positioned between the HSE and MET sidechains according to the optimized geometry of the small model. We performed a single-point DFT calculation on this large model in vacuum (PBE0/def2-TZVP), then computed the C-RESP charges with Multiwfn<sup>86,87</sup> using the resulting wavefunction (Table S2, column C-RESP (vacuum)). Next, we performed a single-point DFT calculation in implicit solvent water and computed the corresponding partial charges by the same procedure (Table S2, column C-RESP (water)). The C-RESP2 charges (Table S2) were finally obtained as C-RESP2 charges = 0.4 × C-RESP (vacuum) charges + 0.6 × C-RESP (water) charges.

**Conformational dependence of the partial charge distributions** We evaluated the robustness of the computed partial charge distributions to changes in the conformation of the large model as follows. First, we ran a 100 ns MD simulation of the large model in explicit CHARMM TIP3P water<sup>50</sup>, using the C36m force-field with the C-RESP2 charge distribution for the His–Ag<sup>+</sup>–Met motif. We then extracted the coordinates of the large model every nanosecond. For each of these conformers, we performed a single-point DFT calculation in vacuum, another one in implicit water, and computed the corresponding C-
RESP and C-RESP2 charge distributions. Finally, we time-averaged the charge distributions, resulting in charge distributions C-RESP<sub>avg</sub> and C-RESP2<sub>avg</sub> (Table S2). This approach cannot capture how fluctuations in the charge distribution would influence conformational dynamics (because a fixed-charge force-field is used), but it gives an idea of how sensitive partial charge assignment through C-RESP is to the particular conformation of the large model, and buffers this dependence by averaging over multiple conformers. We found that C-RESP and C-RESP2 charges are fairly sensitive to conformational changes (see Table S2); empirically, we also observed that C-RESP<sub>avg</sub> and C-RESP2<sub>avg</sub> parametrizations do not reproduce the folding equilibrium of B1 as well as C-RESP and C-RESP2 charges computed on the single conformer of the large model.

## Lennard-Jones parameters

All atom types except Ag were assigned their default CHARMM Lennard-Jones parameters. For Ag<sup>+</sup>, we used the Ag<sup>+</sup> "IOD" Lennard-Jones parameters from Li, Song and Merz<sup>33</sup>, i.e., $R_{min}/2 = 1.500$ Å and $\epsilon = 0.038\ 998\ 38$ kcal mol<sup>-1</sup>. These parameters are optimized to reproduce the experimentally measured 2.41±0.02 Å Ion-Oxygen-Distance (IOD)<sup>88</sup> in TIP3P water, and were used by Lithgo et al.<sup>27</sup> and Chen et al.<sup>40</sup>. We note that Li, Song and Merz derived these parameters for the standard TIP3P water model<sup>89</sup>, whereas we performed our simulations with the slightly different CHARMM TIP3P (cTIP3P) water model<sup>50</sup>. From a 25 ns constant temperature (293 K)/constant pressure (1 bar) MD simulation of a solvated Ag<sup>+</sup> cation, we evaluated the IOD in cTIP3P water to 2.355 Å, which we deemed sufficiently close to the experimental value to use Li, Song and Merz's Lennard-Jones parameters. We computed the IOD as the position of the first peak of the radial distribution function (rdf) of water oxygen around the Ag<sup>+</sup> cation, using MDAnalysis<sup>90,91</sup> to evaluate the rdf.
Supplementary Text 2: Temperature Replica-Exchange
Molecular Dynamics Simulations

Classical MD simulations were performed with GROMACS (2023,2024 or 2025)⁹². We used the CHARMM36m force-field to describe protein energetics²², along with the His–Ag⁺–Met patch. Explicit solvent was modeled as CHARMM TIP3P water⁵⁰,⁸⁹. We used our previously reported α-helical NMR structure of the B1 peptide as starting coordinates for system preparation. 8 different systems were prepared, see Table S3). Each system was placed in a cubic simulation box of size 5.6 nm × 5.6 nm × 5.6 nm and solvated CHARMM TIP3P water. Na⁺ and Cl⁻ ions were added to neutralize the system and reach a total salt concentration of 150 mmol dm⁻³. Each system was energy-minimized by steepest descent, using harmonic restraints on the backbone atoms (force constant 10 kcal/mol/Å²) to preserve the helical conformation. Minimized models were equilibrated through 1 ns of NVT simulation (T = 310.0 K) followed by 1 ns of NPT simulation (T = 310.0 K, P = 1 bar), with harmonic active restraints. Replica-exchange simulations were launched from the equilibrated systems. Temperature was maintained using the v-rescale thermostat with a time constant of 1.0 ps⁹³, and the Parrinello-Rahman barostat with a time constant of 5.0 ps⁹⁴. All simulations used a 2 fs timestep. Temperature-Replica Exchange Molecular Dynamics (T-REMD) simulations⁵¹ were performed for each system in the NPT ensemble⁵² starting from the equilibrated systems. Each T-REMD simulation used 64 replicas with temperatures ranging from 293.0 K to 470.0 K. We chose this temperature distribution to ensure an ≈20% exchange-acceptance probability between adjacent replicas, following reference⁵³. Visual analysis of the simulations was done with Pymol, VMD⁹⁵ and the colvars dashboard⁵⁴,⁹⁶. Simulations were analyzed quantitatively with MDAnalysis⁹⁰,⁹¹. Free energy landscapes were computed from the T-REMD trajectories using the Multistate Bennett Acceptance Ratio (MBAR) estimator⁵⁵ as implemented in *pymbar* 4.0, using Gaussian Kernel Density Estimation (KDE) to obtain smooth free energy profiles⁵⁶,⁹⁷. KDE bandwidths for all CVs are reported in Table
Supplementary Text 3: Mapping the conformational
space of B1 with an Autoencoder neural network

We trained an autoencoder (AE)⁹⁸ to reduce the dimensionality of the conformational space of the B1 peptide. An AE is a neural network that learns two non-linear mappings: the encoder, which projects the input onto a *latent space* of user-chosen low dimensionality, and the decoder, which attempts to reconstruct the data from their latent space representation. The AE is trained by minimizing the average error between the inputs and their reconstructions. Because of this dimensional bottleneck, the AE is forced to discover latent variables that capture enough relevant information about the input distribution for reconstruction to be possible; this makes AEs useful for learning collective variables in complex molecular systems ⁵⁷,⁹⁹. Here, we trained an AE to learn a 6-dimensional latent space representation of the conformational landscape of B1 from the frames collected by temperature replica-exchange simulations. The AE architecture is summarized on Fig S7A. The encoder takes as input a flattened, whitened atomic coordinate vector of size 132 (see below for details). The encoder is made of three densely connected hidden layers of sizes 132, 200, 100 separated by Parametric Rectified Linear Units (PReLU) activation functions ¹⁰⁰. The decoder is built as the "mirror image" of the encoder, with a densely connected linear output layer of size 132. The parameters of the decoder are not tied to those of the encoder. Similar architectures were applied on protein structures by other investigators ⁵⁷,¹⁰¹. The loss function (equation S1) comprises:

1. L1 and L2 reconstruction errors (first and second terms in Eq. S1), following reference⁵⁷ in which it is proposed that the combination of these two terms improves training robustness.
2. A term promoting linear decorrelation of the latent variables (third term in Eq. S1), whose purpose is to disentangle the latent space representation to improve its interpretability<sup>57,102</sup>. This term penalizes the deviation of the covariance matrix of the latent variables (evaluated as its empirical, batch-wise estimate) from the identity matrix, which makes individual variances close to 1 and decorrelates latent variables from one another.

3. a "Sketch-Map" term (fourth term in Eq. S1), proposed by Peters et al.<sup>58,59</sup> following earlier work by Parrinello et al.<sup>60,103</sup>. This term steers the AE towards learning latent variables that describe "medium scale" structural differences, i.e., those that are most likely to describe relevant structural states. For this purpose, this term penalizes the deviation between the pairwise distance matrices over latent points, and over reconstructions, after each matrix entry has been transformed by a sigmoid function that saturates at low and high distances. This guides the latent variables towards preserving the "medium scale" distance distribution.

$$ 
\begin{aligned}
L(\{x_i; i = 1, \dots, N_B\}) = & k_1 \cdot \frac{1}{N_B} \sum_{i=1}^{N_B} |x_i - R(x_i)| + k_2 \cdot \frac{1}{N_B} \sum_{i=1}^{N_B} ||x_i - R(x_i)||^2 \\
& + k_3 \cdot \frac{1}{\kappa^2} ||\mathbf{C} - \mathbf{I}_\kappa||_{1,1} \\
& + k_4 \cdot \frac{1}{N_B^2} (||\sigma_h(\mathbf{D}) - \sigma_l(\mathbf{d})||_{2,2})^2
\end{aligned}
\qquad (S1) $$

In Eq. S1, positive coefficients $k_1, k_2, k_3, k_4$ control the relative weight of the terms; $N_B = 1024$ is the batch size; $x_i$ is the input vector with index $i$, and $R(x_i)$ its reconstruction by the AE. $\kappa = 6$ is the dimensionality of latent space; $\mathbf{C}$ is the covariance matrix between latent variables (of size $6 \times 6$) evaluated over the batch; $\mathbf{I}_\kappa$ is the identity matrix in $\kappa$ dimensions. $\sigma_h$ and $\sigma_l$ are two sigmoid functions of the form $\sigma(d) = 1 - (1 + (2^{\frac{a}{b}} - 1)(d/\sigma)^a)^{-\frac{b}{a}}$ (see references<sup>60,103</sup>) with $a = 4, b = 6, \sigma = 1.75$ for $\sigma_l$ and $a = 4, b = 6, \sigma = 1.2$ for $\sigma_h$. $\mathbf{D}$ is the
pairwise Euclidean distance matrix between all reconstructions of the batch's input vectors.

d is the pairwise Euclidean distance between matrix all latent representations of the batch's
inputs. For positive integer p and matrix A, ||A||_{p,p} denotes the matrix norm such that:

$$
\|\mathbf{A}\|_{p,p} = \left( \sum_j \sum_i |A_{ij}|^p \right)^{1/p} \qquad (S2)
$$

We implemented the autoencoder in Pytorch 2.0$^{104,105}$. We prepared a dataset containing structures from all replica exchange simulations sampled every 10 ps, for a total of 20 × 10$^6$ structures, all structurally aligned onto a common reference frame. Each structure was featurized as the flattened 132-vector of Cartesian coordinates of its CA, C, N and CB atoms. Then, feature vectors were centered feature-wise and whitened to remove cross-correlations between features by matrix multiplication with $C^{-1/2}$, where C is the empirical covariance matrix of centered features. This whitening procedure has empirically been shown to improve training stability$^{101}$. Before training, the dataset was randomly shuffled, then randomly split into a training set (80%) and a test set (20%). The AE was trained by batchwise stochastic gradient descent (using the Adam optimizer $^{106}$) and backpropagation. We used a batch size of 1024. We regularized the network during training using dropout for all layers with a 0.1 probability$^{107}$. Dropout was turned off at inference time. Training was performed in three stages as summarized in Table S5. Stages 1 and 2 correspond to a "pre-training" using only the reconstruction terms of the loss function, decreasing the learning rate from stage 1 to stage 2. In the third stage the decorrelation and Sketch-Maps terms are turned on (along with the reconstruction terms) and the AE is trained with a smaller learning rate. Empirically, we found that this procedure led to better training stability than training with the full loss function from the start. The training protocol and hyperparameters, including the loss function coefficients $k_1, k_2, k_3, k_4$ were determined by trial-and-error. It is possible that systematic optimization of these hyperparameters could lead to an improvement in AE performance and descriptiveness; this would however be
costly and would not necessarily have resulted in a significantly more useful AE in practice. Canonical averages of CV $\eta$ conditioned on the value of CVs $l_1, l_2$ (as reported in Figs S8 and S9) were computed according to equation S3.

$$ \langle \eta \rangle_{l_1, l_2} = \frac{\sum_i \eta(x_i) w(x_i) I_{l_1, l_2}(x_i)}{\sum_i w(x_i) I_{l_1, l_2}(x_i)} \qquad (S3) $$

In equation S3, $x_i$ is the Cartesian coordinate vector of simulation frame $i$; $w(x_i)$ the MBAR weight of simulation frame $i$, and $I_{l_1,l_2}$ is an indicator function such that $I_{l_1,l_2}(x_i) = 1$ if $l_1(x_i) = l_1$ and $l_2(x_i) = l_2$. We estimated the indicator functions numerically by discretizing $(l_1, l_2)$ over a square grid with spacing $\Delta l_1 = \Delta l_2 = 0.40625$.

## Supplementary Text 4: String method analysis of B1's folding pathways

The String Method in Collective Variables (CVSM) finds a one-dimensional minimum free energy path (MFEP) between stable states in a space of collective variables$^{41,63,64}$. To do so, it relaxes a guess path, represented as a series of images of the system, along the component of the free energy gradient that is orthogonal to the path while enforcing equal spacing between images. Convergence to an MFEP is attained when the orthogonal component of the gradient vanishes everywhere. In the conventional CVSM, harmonically-restrained MD sampling is used to estimate the free energy gradient. By contrast, here we estimate the gradient of the free energy with respect to arbitrary CVs from the (reweighted) replica-exchange simulation trajectories using a finite-difference estimator. Our approach — described below — is broadly similar to the *post-hoc* string method by Moradi and Tajkhorshid$^{65}$, but uses a different mathematical route to the MFEP.
Development of a gradient-based *post-hoc* string method in collective variables

To extract mechanistic pathways connecting the unfolded and folded states of B1 from the replica-exchange simulations, we developed a variant of the string method in collective variables (CVSM)⁴¹,⁶³,⁶⁴. To better situate this development, we first briefly recall the original formulation of the CVSM. The CVSM works by iteratively evolving a one-dimensional parametric curve that connect stable states (the string), defined in a space of n collectives variables $\xi_1, ..., \xi_n$, towards a Minimum Free Energy Path (MFEP)⁴¹. It does so by relaxing the string along the component of the mean force (that is, the gradient of the free energy profile $F$ along the collective variables) that is orthogonal to the string using a modified steepest-descent dynamics. For this purpose, the string is discretized into $M$ images $(\varphi_j)_{j=1,...,M}$ with $\varphi_j = (\xi_1^{(j)}, ..., \xi_n^{(j)})$ (that is, an image is a point in CV-space).

At iteration $\tau$, each image is first moved along the full free energy gradient, see Eq. S4.

$$ \tilde{\varphi}_i(\tau) = \varphi_i(\tau - 1) - h\mathcal{M}(\varphi_i(\tau - 1))\nabla_{\xi} F(\varphi_i(\tau - 1)) \quad (S4) $$

In Eq. S4, $h$ is a step size vector of size $n$, $\mathcal{M}$ a metric tensor (see reference ⁴¹ for details) and $\nabla_{\xi} F(\varphi_i(\tau - 1))$ the gradient vector of the free energy profile $F$, evaluated at the image $\varphi_i$. In a second step, the string is reparametrized by iteratively redistributing images $(\tilde{\varphi}_i)_{i=1,...,M}$ along the string until successive images are equally-spaced. Finally, the string is smoothed by local averaging according to Eq. S5, in which $s \in [0, 1]$ (leaving the endpoints untouched).

$$ \varphi_i \leftarrow (1-s)\tilde{\varphi}_i + \frac{s}{2}(\tilde{\varphi}_{i-1} + \tilde{\varphi}_{i+1}) \quad (S5) $$

The reparametrization step cancels out image displacement colinear to the string, effectively ensuring that string relaxation happens only along the orthogonal component of the free energy gradient. When the string has converged to an MFEP, this orthogonal component
vanishes by definition; image movement is then exactly cancelled by reparametrization.

In the original formulation by Maragliano et al., the mean force (and the metric tensor) were estimated from harmonically-restrained Molecular Dynamics simulations. A later variant, the string method with swarms of trajectories, updates the string using a mean drift rather than a mean force but similarly requires MD sampling at each iteration⁶⁴.

We now outline our methodological development, which we call gradient-based *post-hoc* string method. We start from the mean-force formulation of the CVSM, but we estimate the free energy gradient *a posteriori* from the MBAR analysis of the replica-exchange trajectories without additional sampling needed. Our implementation relies on the recently released Kernel Density Estimation (KDE)-enabled MBAR analysis package by Ferguson and Shirts (pymbar 4.0)⁵⁶. First, we build an MBAR-weighted KDE estimator in CV-space. With it, we can easily estimate the free energy at any point in CV-space. We exploit this to evaluate the local free energy gradient at this point by finite-differences: each component of the gradient is evaluated using Eq. S6.

$$ \partial_{\xi_i} F(\xi_1, \dots, \xi_i, \dots, \xi_n) = \underset{\text{estimates}}{\frac{F(\xi_1, \dots, \xi_i + \delta\xi_i, \dots, \xi_n) - F(\xi_1, \dots, \xi_i, \dots, \xi_n)}{\delta\xi_i}} \quad (S6) $$

Starting from a guess, the string is optimized following the CVSM procedure outlined above using the finite-difference gradient estimates. The estimation of the free energy gradient at a given point of an *n*-dimensional CV-space requires *n* + 1 calls to the KDE estimator. By contrast, evaluation of the full free energy landscape over a square grid of side *k* would have required *k*⁹ calls to the KDE estimator, highlighting the effectiveness of our approach for high-dimensional free energy calculations. We normalize all CVs by their total variation to make their value comprised between 0 and 1, and therefore assume unit metric tensors. Once the string is converged, calling the KDE estimator for each image directly yields the free energy profile along the string.

Moradi and Tajkhorshid previously proposed a *post-hoc* string method to extract mechanistic pathways from Bias-Exchange Umbrella Sampling simulations *a posteriori*⁶⁵, based
on the finite-temperature string method variant$^{108,109}$. Their method uses an Expectation-Maximization algorithm to identify a principal curve in CV-space. We instead use steepest-descent and finite-differences to converge towards an MFEP. Overall, our method offers a rigorous way of extracting mechanistically-relevant MFEPs from replica-exchange data.

## Determination of B1 folding pathways by the gradient-based *post-hoc* string method

We prepared guess paths with $M = 128$ images in 6-dimensional CV-space manually along an N-ter-initiated mechanism and a C-ter-initiated mechanism for simulations Free B1 (1), Free B1 (2), B1+Ag$^+$ C-RESP2 charges (1) and B1+Ag$^+$ C-RESP2 charges (2), i.e., 8 paths were prepared. All CVs were normalized to [0, 1]. Each path was converged to an MFEP using our gradient-based *post-hoc* string method, using $\delta\xi = 10^{-2}$ (step size for finite difference gradient estimation) and $h = 10^{-3}$ (step size for gradient descent) for each normalized CV. Strings were considered converged upon stabilization of the total string RMSD in normalized CV-space, both with respect to the guess path, and the current string (see Figs S10,S12, S14, S16). For structural interpretation, converged strings were backmapped to Cartesian space by finding the simulation frame closest to each image in normalized CV-space. Free energy profiles along the converged strings were computed with MBAR-weighted KDE (Figures S11A, S13A, S15A, S17A). The projections of the converged strings onto 2D free energy profiles along the supporting CVs are shown on Figures S11B-E, S13B-E, S15B-E, S17B-E.

## Supplementary Text 5: NMR of the B1 E6Q mutant peptide

Following the same methodology used to solve the wild-type B1 structure (see reference$^8$), NMR experiments were recorded on a chemically synthesized mutant peptide B1 E6Q (HQK-
MVQSHQRM). 1D ¹H and 2D homonuclear NMR experiments (¹H-¹H TOCSY, 80 ms mixing time; ¹H-¹H NOESY, 600 ms mixing time) were recorded at a ¹H frequency of 700 MHz on a 2 mM peptide sample without silver ions, and separately in the presence of 8 mM of silver ions (AgNO₃, HEPES buffer 20 mM, pH = 7.2, T = 293 K).

## Supplementary Text 6: Mass Spectrometry of the wild-type B1 peptide

### Chemicals and reagents

Methanol (MeOH) and water (LC-MS Optima grade) were obtained from Fisher Scientific (Strasbourg, France).

### Sample Preparation

The B1 peptide was dissolved in water at 1 mg mL⁻¹. This solution was diluted in MeOH/water 1:1 % v:v containing 150 mM of AgNO₃ to reach a final peptide concentration of 0.689 mM with 5 molar equivalent of Ag⁺. The peptide solution was directly infused at 5 µL min⁻¹.

### Instrumentation and Operating Conditions

Mass spectrometry (MS) analysis were performed on an hybrid quadrupole-orbitrap Q-Exactive® mass spectrometer (Thermo Fisher Scientific, San Jose, CA, USA) equipped with a HESI ion source. Ionization was achieved using electrospray in the positive ionization mode with an ion spray voltage of 4 kV. The sheath gas and the auxiliary gas (nitrogen) flow rates
were respectively set at 25 and 5 (arbitrary unit) with a HESI vaporizer temperature of 300 °C. The ion transfer capillary temperature was 300 °C with a sweep gas (nitrogen) flow rate at 5 (arbitrary unit). The S-lens RF was set at 90 (arbitrary unit). The Automatic Gain Control (AGC) target was 3 × 10⁶ and the maximum injection time was set at 250 ms. Experiments were done in full MS over a m/z 200-1500 range with a resolution of 140 000.

## Detailed results

The B1 peptide incubated with 5 equivalents of Ag⁺ was analyzed by mass spectrometry in positive ion mode. The MS spectrum (Fig 2A) shows several charge state distributions, ranging from 2+ to 4+, corresponding to the peptide (B1) bearing varying numbers of protons and/or silver ions. As an example, the ion detected at m/z 555.164 has been attributed to the two Ag⁺ and one H⁺ adduct of the peptide [B₁+H+2Ag]³⁺. The main distribution corresponds to the peptide complexed with two Ag⁺ ions. In the MeOH/water solution, the peptide adopts an elongated conformation that can accommodate up to four positive charges; nonetheless, binding of two Ag⁺ ions is still observed even in the absence of well-defined structure.
Supplementary Figures

<figure><img src="image_8.png" /><figcaption>Figure S1: Models used for parametrization of the His−Ag⁺−Met force-field. A. Small model used for derivation of the bonded parameters, indicating atom names (except CA and aliphatic hydrogens). B. Large model (HGGM+Ag⁺) used for derivation of the partial charges. C. Large model with atoms colored as follows: in grey, all atoms constrained to their default C36m partial charge during RESP calculation; in magenta, all atoms with unconstrained partial charge during RESP calculation.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

C

B1+Ag⁺ C-RESP2 charges (1)

<figure><img src="image_10.png" /></figure>

E

B1+Ag⁺ C36m charges

<figure><img src="image_11.png" /></figure>

G

B1+Ag⁺ C-RESP2<sub>avg</sub> charges

<figure><img src="image_12.png" /></figure>

I

Free B1E6Q

<figure><img src="image_13.png" /></figure>

B

Free B1 (2)

<figure><img src="image_14.png" /></figure>

D

B1+Ag⁺ C-RESP2 charges (2)

<figure><img src="image_15.png" /></figure>

F

B1+Ag⁺ C-RESP charges

<figure><img src="image_16.png" /></figure>

H

B1+Ag⁺ C-RESP<sub>avg</sub> charges

<figure><img src="image_17.png" /></figure>

J

B1E6Q+Ag⁺ C-RESP2 charges

<figure><img src="image_18.png" /></figure>

Figure S2: T-space trajectories for randomly chosen replicas during T-REMD simulations, illustrating the efficient diffusion of replicas across temperature space.
<figure><img src="image_19.png" /><figcaption>Figure S3: Statistical distribution of potential energy per replica in T-REMD simulations, illustrating the overlap between adjacent replicas.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Figure S4: Free energy landscape along $R_g$ and $\alpha$ for the A. free B1 (2) and B. B1+Ag$^+$ C-RESP2 charges (2) simulations.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure S5: Free energy landscapes along $R_g$ and $\alpha$ for the B1 E6Q mutant. Free energy profiles along ($R_g, \alpha$) reveal how Ag$^+$-binding shapes the folding landscape of B1 E6Q. Representative frames are shown; for clarity, only polar hydrogens are shown.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Figure S6: Free energy landscapes along $R_g$ and $\alpha$ for alternative charge parametrizations. Comparison with Figs 3B and S4B clearly shows that C36m, C-RESP$_{avg}$ and C-RESP2$_{avg}$ charges (panels A,C,D) do not capture the preference for the folded state, whereas C-RESP charges (panel B) do.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Figure S7: **Autoencoder neural network.** A. Architecture of the AE indicating the sizes of the hidden layers. B-E Evolution of the terms of the loss function (Eq. S1) during AE training. Blue vertical lines indicate the training stages. F. Histogram of the RMSD between input structure and reconstructed structure over the whole dataset. G. Distribution of reconstruction RMSD in latent space after Isomap transform, notably showing that the fully helical state exhibits lowest reconstruction error.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Without Ag⁺ (Free B1 (1))</figcaption></figure>

Figure S8: Comparison of autoencoder-learnt and Human-learnt variables for simulation Free B1 (1). For each of the 6 CVs used for the string optimizations, we show its canonical average conditional on the value of the *l*₁, *l*₂ pair as a colormap (see Supplementary Text S3 for details). To facilitate comparison with Fig 4A, contour lines of the free energy landscape over *l*₁, *l*₂ for simulation Free B1 (1) are shown in black; inline numbers indicate free energy levels in kcal mol⁻¹.
With Ag⁺ (B1+Ag⁺ C-RESP2 charges (1))

<figure><img src="image_25.png" /></figure>

Figure S9: Comparison of autoencoder-learnt and Human-learnt variables for simulation B1+Ag⁺ C-RESP2 charges (1). For each of the 6 CVs used for the string optimizations, we show its canonical average conditional on the value of the *l*₁, *l*₂ pair as a colormap (see Supplementary Text S3 for details). To facilitate comparison with Fig 4B, contour lines of the free energy landscape over *l*₁, *l*₂ for simulation B1+Ag⁺ C-RESP2 charges (1) are shown in black; inline numbers indicate free energy levels in kcal mol⁻¹.
<figure><img src="image_26.png" /><figcaption>Figure S10: **Convergence of the strings for Free B1 (1) simulation.** A. RMSD of the string with respect to the guess path for the N-ter-initiated mechanism. B. RMSD of the string with respect to the guess path for the C-ter-initiated mechanism.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>Figure S11: String method analysis of B1 folding in the absence of Ag⁺ (Simulation Free B1 (1)). A. Free energy profiles along the optimized strings for the N-ter-initiated and C-ter-initiated mechanisms. B-F. Projection of the optimized strings onto 2D free energy landscapes.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>Figure S12: **Convergence of the strings for Free B1 (2) simulation.** A. RMSD of the string with respect to the guess path for the N-ter-initiated mechanism. B. RMSD of the string with respect to the guess path for the C-ter-initiated mechanism.</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Figure S13: String method analysis of B1 folding in the absence of Ag⁺ (Simulation Free B1 (2)). A. Free energy profiles along the optimized strings for the N-ter-initiated and C-ter-initiated mechanisms. B-F. Projection of the optimized strings onto 2D free energy landscapes.</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>Figure S14: Convergence of the strings for B1 with Ag⁺ (Simulation B1+Ag⁺ C-RESP2 (1)) A. RMSD of the string with respect to the guess path for the N-ter-initiated mechanism. B. RMSD of the string with respect to the guess path for the C-ter-initiated mechanism.</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>Figure S15: String method analysis of B1 folding in the presence of Ag⁺ (Simulation B1+Ag⁺ C-RESP2 (1)) A. Free energy profiles along the optimized strings for the N-ter-initiated and C-ter-initiated mechanisms. B-F. Projection of the optimized strings onto 2D free energy landscapes.</figcaption></figure>
<figure><img src="image_32.png" /><figcaption>Figure S16: Convergence of the strings for B1 with Ag⁺ (Simulation B1+Ag⁺ C-RESP2 (2)) A. RMSD of the string with respect to the guess path for the N-ter-initiated mechanism. B. RMSD of the string with respect to the guess path for the C-ter-initiated mechanism.</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>Figure S17: String method analysis of B1 folding in the presence of Ag⁺ (Simulation B1+Ag⁺ C-RESP2 (2)) A. Free energy profiles along the optimized strings for the N-ter-initiated and C-ter-initiated mechanisms. B-F. Projection of the optimized strings onto 2D free energy landscapes.</figcaption></figure>
# Supplementary Tables

<table><caption>Table S1: Bonded force-field parameters for the His–Ag⁺–Met motif.*</caption><thead><tr><th>Bond</th><th>Force constant [kcal/mol/Å<sup>2</sup>]</th><th>Reference length [Å]</th></tr></thead><tbody><tr><td>1ND1-AG</td><td>95.6</td><td>2.1081</td></tr><tr><td>AG-2S</td><td>79.6</td><td>2.3699</td></tr></tbody><thead><tr><th>Angle</th><th>Force constant [kcal/mol/rad<sup>2</sup>]</th><th>Reference angle [deg]</th></tr></thead><tbody><tr><td>1CG-1ND1-AG</td><td>73.18</td><td>126.24</td></tr><tr><td>1CE2-1ND1-AG</td><td>70.45</td><td>126.43</td></tr><tr><td>1ND1-AG-2S</td><td>49.83</td><td>180.00<sup>†</sup></td></tr><tr><td>2CG-2S-AG</td><td>87.50</td><td>107.38</td></tr><tr><td>2CE-2S-AG</td><td>89.48</td><td>106.56</td></tr></tbody></table>

* By convention, the name of atoms of the His sidechain begins with 1 and that of atoms of the Met sidechain begins with 2.

† Rounded up from 176.76° to enforce linear geometry.
<table><caption>Table S2: Partial charge distributions.</caption><thead><tr><th>Atom</th><th>C36m</th><th>C-RESP (vacuum)</th><th>C-RESP (water)</th><th>C-RESP2</th><th>C-RESP<sub>avg</sub> (vacuum)</th><th>C-RESP<sub>avg</sub> (water)</th><th>C-RESP<sub>2avg</sub></th></tr></thead><tbody><tr><td>1CB</td><td>-0.080</td><td>-0.088</td><td>-0.037</td><td>-0.058</td><td>+0.034</td><td>-0.216</td><td>-0.116</td></tr><tr><td>1HB1</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>1HB2</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>1ND1</td><td>-0.700</td><td>-0.109</td><td>-0.591</td><td>-0.398</td><td>-0.123</td><td>-0.238</td><td>-0.192</td></tr><tr><td>1CG<sup>†</sup></td><td>+0.220</td><td>+0.030</td><td>+0.353</td><td>+0.225</td><td>+0.053</td><td>+0.359</td><td>+0.238</td></tr><tr><td>1CE1</td><td>+0.250</td><td>+0.013</td><td>+0.156</td><td>+0.099</td><td>-0.133</td><td>-0.099</td><td>-0.113</td></tr><tr><td>1HE1</td><td>+0.130</td><td>+0.181</td><td>+0.142</td><td>+0.157</td><td>+0.198</td><td>+0.199</td><td>+0.198</td></tr><tr><td>1NE2</td><td>-0.360</td><td>-0.160</td><td>-0.085</td><td>-0.115</td><td>-0.021</td><td>-0.059</td><td>-0.044</td></tr><tr><td>1HE2</td><td>+0.320</td><td>+0.369</td><td>+0.347</td><td>+0.356</td><td>+0.338</td><td>+0.357</td><td>+0.349</td></tr><tr><td>1CD2</td><td>-0.050</td><td>-0.249</td><td>-0.370</td><td>-0.322</td><td>-0.385</td><td>-0.395</td><td>-0.391</td></tr><tr><td>1HD2</td><td>+0.090</td><td>+0.231</td><td>+0.251</td><td>+0.243</td><td>+0.264</td><td>+0.259</td><td>+0.261</td></tr><tr><td>2CB</td><td>-0.180</td><td>-0.098</td><td>-0.432</td><td>-0.299</td><td>-0.027</td><td>-0.191</td><td>-0.125</td></tr><tr><td>2HB1</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2HB2</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2CG</td><td>-0.140</td><td>+0.009</td><td>+0.133</td><td>+0.083</td><td>-0.160</td><td>+0.096</td><td>-0.006</td></tr><tr><td>2HG1</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2HG2</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2SD</td><td>-0.090</td><td>-0.043</td><td>-0.213</td><td>-0.145</td><td>+0.085</td><td>-0.201</td><td>-0.087</td></tr><tr><td>2CE</td><td>-0.220</td><td>-0.097</td><td>-0.024</td><td>-0.053</td><td>-0.170</td><td>-0.048</td><td>-0.097</td></tr><tr><td>2HE1</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2HE2</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2HE3</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td><td>+0.090</td></tr><tr><td>2AG</td><td>+1.000</td><td>+0.201</td><td>+0.561</td><td>+0.417</td><td>+0.237</td><td>+0.367</td><td>+0.315</td></tr></tbody></table>

<table><caption>Table S3: List of T-REMD simulations</caption><thead><tr><th>Model</th><th>Aggregate length</th></tr></thead><tbody><tr><td>Free B1 (1)</td><td>9 µs</td></tr><tr><td>Free B1 (2)</td><td>17.5 µs</td></tr><tr><td>B1 + Ag<sup>+</sup> C-RESP2 charges (1)</td><td>15.7 µs</td></tr><tr><td>B1 + Ag<sup>+</sup> C-RESP2 charges (2)</td><td>23.4 µs</td></tr><tr><td>B1 + Ag<sup>+</sup> C-RESP charges</td><td>17.4 µs</td></tr><tr><td>B1 + Ag<sup>+</sup> C36m charges</td><td>24.6 µs</td></tr><tr><td>B1 + Ag<sup>+</sup> C-RESP2<sub>avg</sub> charges</td><td>28.9 µs</td></tr><tr><td>B1 + Ag<sup>+</sup> C-RESP<sub>avg</sub> charges</td><td>30.2 µs</td></tr><tr><td>Free B1 E6Q</td><td>21.3 µs</td></tr><tr><td>B1 E6Q + Ag<sup>+</sup> C-RESP2 charges</td><td>12.7 µs</td></tr></tbody></table>

<footnote>† To correct for rounding errors, the partial charge of atom 1CG was adjusted by ±0.001 to ensure the total charge sums to +1 for each charge distribution.</footnote>
<table><caption>Table S4: Bandwidths used for the computation of free energy profiles using MBAR-weighted KDE.</caption><thead><tr><th>CV</th><th>Bandwidth</th></tr></thead><tbody><tr><td>α</td><td>1.0</td></tr><tr><td>α<sub>N</sub></td><td>1.0</td></tr><tr><td>α<sub>C</sub></td><td>1.0</td></tr><tr><td>R<sub>g</sub></td><td>0.25 Å</td></tr><tr><td>d<sub>EK</sub></td><td>0.5 Å</td></tr><tr><td>d<sub>ER</sub></td><td>0.5 Å</td></tr><tr><td>l<sub>1</sub></td><td>0.35</td></tr><tr><td>l<sub>2</sub></td><td>0.35</td></tr></tbody></table>

<table><caption>Table S5: Autoencoder training protocol and hyperparameters</caption><thead><tr><th>Stage</th><th>Epochs</th><th>Learning rate</th><th>k<sub>1</sub></th><th>k<sub>2</sub></th><th>k<sub>3</sub></th><th>k<sub>4</sub></th></tr></thead><tbody><tr><td>1</td><td>200</td><td>1 × 10<sup>-3</sup></td><td>1.0</td><td>1.0</td><td>0.0</td><td>0.0</td></tr><tr><td>2</td><td>150</td><td>1 × 10<sup>-4</sup></td><td>1.0</td><td>1.0</td><td>0.0</td><td>0.0</td></tr><tr><td>3</td><td>1200</td><td>1 × 10<sup>-5</sup></td><td>1.0</td><td>1.0</td><td>0.1</td><td>0.1</td></tr></tbody></table>

<table><caption>Table S6: Collective variables used in the *post-hoc* string method analysis of B1 peptide folding</caption><thead><tr><th>Collective Variable</th><th>Definition</th><th>Range</th></tr></thead><tbody><tr><td>α</td><td>α-helix content</td><td>0 to 1</td></tr><tr><td>α<sub>N</sub></td><td>α-helix content (N-ter)</td><td>0 to 1</td></tr><tr><td>α<sub>C</sub></td><td>α-helix content (C-ter)</td><td>0 to 1</td></tr><tr><td>R<sub>g</sub></td><td>Radius of gyration</td><td>4.0 Å to 16.0 Å</td></tr><tr><td>d<sub>EK</sub></td><td>Distance E6-K3</td><td>2.0 Å to 16.0 Å</td></tr><tr><td>d<sub>ER</sub></td><td>Distance E6-R10</td><td>2.0 Å to 16.0 Å</td></tr></tbody></table>
References

(1) Sharma, S. K.; Goloubinoff, P.; Christen, P. Heavy Metal Ions Are Potent Inhibitors of Protein Folding. *Biochemical and Biophysical Research Communications* **2008**, *372*, 341–345.

(2) Leal, S. S.; Botelho, H. M.; Gomes, C. M. Metal Ions as Modulators of Protein Conformation and Misfolding in Neurodegeneration. *Coordination Chemistry Reviews* **2012**, *256*, 2253–2270.

(3) Tamás, M.; Sharma, S.; Istedt, S.; Jacobson, T.; Christen, P. Heavy Metals and Metalloids As a Cause for Protein Misfolding and Aggregation. *Biomolecules* **2014**, *4*, 252–267.

(4) Wilson, C. J.; Apiyo, D.; Wittung-Stafshede, P. Role of Cofactors in Metalloprotein Folding. *Quarterly Reviews of Biophysics* **2004**, *37*, 285–314.

(5) Besold, A. N.; Michel, S. L. J. Neural Zinc Finger Factor/Myelin Transcription Factor Proteins: Metal Binding, Fold, and Function. *Biochemistry* **2015**, *54*, 4443–4452.

(6) Ariöz, C.; Wittung-Stafshede, P. Folding of Copper Proteins: Role of the Metal? *Quarterly Reviews of Biophysics* **2018**, *51*, e4.

(7) Chabert, V.; Hologne, M.; Sénèque, O.; Crochet, A.; Walker, O.; Fromm, K. M. Model Peptide Studies of Ag⁺ Binding Sites from the Silver Resistance Protein SilE. *Chemical Communications* **2017**, *53*, 6105–6108.

(8) Chabert, V.; Hologne, M.; Sénèque, O.; Walker, O.; M. Fromm, K. Alpha-Helical Folding of SilE Models upon Ag(His)(Met) Motif Formation. *Chemical Communications* **2018**, *54*, 10419–10422.

(9) Monneau, Y.; Arrault, C.; Duroux, C.; Martin, M.; Chirot, F.; Mac Aleese, L.; Girod, M.; Comby-Zerbino, C.; Hagège, A.; Walker, O. et al. Structural and Dy-
namical Insights into SilE Silver Binding from Combined Analytical Probes. *Physical Chemistry Chemical Physics* **2023**, *25*, 3061–3071.

(10) Asiani, K. R.; Williams, H.; Bird, L.; Jenner, M.; Searle, M. S.; Hobman, J. L.; Scott, D. J.; Soultanas, P. SilE Is an Intrinsically Disordered Periplasmic “Molecular Sponge” Involved in Bacterial Silver Resistance. *Molecular Microbiology* **2016**, *101*, 731–742.

(11) Gupta, A.; Matsui, K.; Lo, J.-F.; Silver, S. Molecular Basis for Resistance to Silver Cations in Salmonella. *Nature Medicine* **1999**, *5*, 183–188.

(12) Silver, S. Bacterial Silver Resistance: Molecular Biology and Uses and Misuses of Silver Compounds. *FEMS Microbiology Reviews* **2003**, *27*, 341–353.

(13) McNeilly, O.; Mann, R.; Hamidian, M.; Gunawan, C. Emerging Concern for Silver Nanoparticle Resistance in Acinetobacter Baumannii and Other Bacteria. *Frontiers in Microbiology* **2021**, *12*, 894.

(14) Medici, S.; Peana, M.; Nurchi, V. M.; Zoroddu, M. A. Medical Uses of Silver: History, Myths, and Scientific Evidence. *Journal of Medicinal Chemistry* **2019**, *62*, 5923–5943.

(15) Morones-Ramirez, J. R.; Winkler, J. A.; Spina, C. S.; Collins, J. J. Silver Enhances Antibiotic Activity Against Gram-Negative Bacteria. *Science Translational Medicine* **2013**, *5*, 190ra81–190ra81.

(16) Wang, H.; Wang, M.; Xu, X.; Gao, P.; Xu, Z.; Zhang, Q.; Li, H.; Yan, A.; Kao, R. Y.-T.; Sun, H. Multi-Target Mode of Action of Silver against Staphylococcus Aureus Endows It with Capability to Combat Antibiotic Resistance. *Nature Communications* **2021**, *12*, 3331.

(17) Frei, A.; Verderosa, A. D.; Elliott, A. G.; Zuegg, J.; Blaskovich, M. A. T. Metals to Combat Antimicrobial Resistance. *Nature Reviews Chemistry* **2023**, *7*, 202–224.
(18) Zingale, G. A.; Oliveri, V.; Grasso, G. Insights into the Binding of Ag Ions with SilE Model Peptides: An NMR and MS Coupled Approach. *Metallomics* **2023**, *15*, mfad015.

(19) Bianchi, A.; Marquenet, F.; Manciocchi, L.; Spichty, M.; Fromm, K. M. Toward Predicting Silver Ion Binding in Proteins. *Chemical Communications* **2025**, 10.1039.D4CC06612J.

(20) Babel, L.; Nguyen, M.-H.; Mittelheisser, C.; Martin, M.; M. Fromm, K.; Walker, O.; Hologne, M. NMR Reveals the Interplay between SilE and SilB Model Peptides in the Context of Silver Resistance. *Chemical Communications* **2021**, 57, 8726–8729.

(21) Arrault, C.; Monneau, Y. R.; Martin, M.; Cantrelle, F.-X.; Boll, E.; Chirot, F.; Comby Zerbino, C.; Walker, O.; Hologne, M. The Battle for Silver Binding: How the Interplay between the SilE, SilF and SilB Proteins Contributes to the Silver Ef-flux Pump Mechanism. *Journal of Biological Chemistry* **2023**, 105004.

(22) Huang, J.; Rauscher, S.; Nawrocki, G.; Ran, T.; Feig, M.; de Groot, B. L.; Grub-müller, H.; MacKerell Jr, A. D. CHARMM36m: An Improved Force Field for Folded and Intrinsically Disordered Proteins. *Nature Methods* **2017**, *14*, 71–73.

(23) Robustelli, P.; Piana, S.; Shaw, D. E. Developing a Molecular Dynamics Force Field for Both Folded and Disordered Protein States. *Proceedings of the National Academy of Sciences* **2018**, *115*, E4758–E4766.

(24) Li, P.; Merz, K. M. Metal Ion Modeling Using Classical Mechanics. *Chemical Reviews* **2017**, *117*, 1564–1686.

(25) Vidossich, P.; Magistrato, A. QM/MM Molecular Dynamics Studies of Metal Binding Proteins. *Biomolecules* **2014**, *4*, 616–645.
(26) Chakravorty, D. K.; Wang, B.; Ucisik, M. N.; Merz, K. M. Insight into the Cation-π Interaction at the Metal Binding Site of the Copper Metallochaperone CusF. *Journal of the American Chemical Society* **2011**, *133*, 19330–19333.

(27) Lithgo, R. M.; Hanževački, M.; Harris, G.; Kamps, J. J.; Holden, E.; Gianga, T.-M.; Benesch, J. L.; Jäger, C. M.; Croft, A. K.; Hussain, R. et al. The Adaptability of the Ion-Binding Site by the Ag(I)/Cu(I) Periplasmic Chaperone SilF. *Journal of Biological Chemistry* **2023**, *299*, 105331.

(28) Hazel, A. J.; Walters, E. T.; Rowley, C. N.; Gumbart, J. C. Folding Free Energy Landscapes of β-Sheets with Non-Polarizable and Polarizable CHARMM Force Fields. *The Journal of Chemical Physics* **2018**, *149*, 072317.

(29) Leontyev, I. V.; Stuchebrukhov, A. A. Electronic Continuum Model for Molecular Dynamics Simulations. *The Journal of Chemical Physics* **2009**, *130*, 085102.

(30) Leontyev, I. V.; Stuchebrukhov, A. A. Electronic Continuum Model for Molecular Dynamics Simulations of Biological Molecules. *Journal of Chemical Theory and Computation* **2010**, *6*, 1498–1508.

(31) Du, S.; Fu, H.; Shao, X.; Chipot, C.; Cai, W. Addressing Polarization Phenomena in Molecular Machines Containing Transition Metal Ions with an Additive Force Field. *Journal of Chemical Theory and Computation* **2019**, *15*, 1841–1847.

(32) Li, P.; Roberts, B. P.; Chakravorty, D. K.; Merz, K. M. Rational Design of Particle Mesh Ewald Compatible Lennard-Jones Parameters for +2 Metal Cations in Explicit Solvent. *Journal of Chemical Theory and Computation* **2013**, *9*, 2733–2748.

(33) Li, P.; Song, L. F.; Merz, K. M. J. Systematic Parameterization of Monovalent Ions Employing the Nonbonded Model. *Journal of Chemical Theory and Computation* **2015**, *11*, 1645–1657.
(34) Song, L. F.; Sengupta, A.; Merz, K. M. Thermodynamics of Transition Metal Ion Binding to Proteins. *Journal of the American Chemical Society* **2020**, *142*, 6365–6374.

(35) Li, Z.; Song, L. F.; Sharma, G.; Koca Fındık, B.; Merz, K. M. J. Accurate Metal-Imidazole Interactions. *Journal of Chemical Theory and Computation* **2023**, *19*, 619–625.

(36) Li, Z.; Bhowmik, S.; Sagresti, L.; Brancato, G.; Smith, M.; Benson, D. E.; Li, P.; Merz, K. M. Simulating Metal-Imidazole Complexes. *Journal of Chemical Theory and Computation* **2024**, *20*, 6706–6716.

(37) Li, P.; Merz, K. M. J. Taking into Account the Ion-Induced Dipole Interaction in the Nonbonded Model of Ions. *Journal of Chemical Theory and Computation* **2014**, *10*, 289–297.

(38) Li, P.; Song, L. F.; Merz, K. M. J. Parameterization of Highly Charged Metal Ions Using the 12-6-4 LJ-Type Nonbonded Model in Explicit Water. *The Journal of Physical Chemistry B* **2015**, *119*, 883–895.

(39) Manciocchi, L.; Bianchi, A.; Mazan, V.; Potapov, M.; Fromm, K. M.; Spichty, M. Modeling the Interaction Between Silver(I) Ion and Proteins with 12-6 Lennard-Jones Potential: A Bottom-Up Parameterization Approach. *Biophysica* **2025**, *5*, 7.

(40) Chen, X.; Karpenko, A.; Lopez-Acevedo, O. Silver-Mediated Double Helix: Structural Parameters for a Robust DNA Building Block. *ACS Omega* **2017**, *2*, 7343–7348.

(41) Maragliano, L.; Fischer, A.; Vanden-Eijnden, E.; Ciccotti, G. String Method in Collective Variables: Minimum Free Energy Paths and Isocommittor Surfaces. *The Journal of Chemical Physics* **2006**, *125*, 024106.

(42) Seminario, J. M. Calculation of Intramolecular Force Fields from Second-Derivative Tensors. *International Journal of Quantum Chemistry* **1996**, *60*, 1271–1277.
(43) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. *PHYSICAL REVIEW LETTERS* **1996**, 77.

(44) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Ad-justable Parameters: The PBE0 Model. *The Journal of Chemical Physics* **1999**, 110, 6158–6170.

(45) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. *Physical Chemistry Chemical Physics* **2005**, 7, 3297.

(46) Andrae, D.; Häussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-Adjustedab Initio Pseudopotentials for the Second and Third Row Transition Elements. *Theoretica Chimica Acta* **1990**, 77, 123–141.

(47) Bayly, C. I.; Cieplak, P.; Cornell, W.; Kollman, P. A. A Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges: The RESP Model. *The Journal of Physical Chemistry* **1993**, 97, 10269–10280.

(48) Pavlova, A.; Parks, J. M.; Gumbart, J. C. Development of CHARMM-Compatible Force-Field Parameters for Cobalamin and Related Cofactors from Quantum Mechanical Calculations. *Journal of Chemical Theory and Computation* **2018**, 14, 784–798.

(49) Schauperl, M.; Nerenberg, P. S.; Jang, H.; Wang, L.-P.; Bayly, C. I.; Mobley, D. L.; Gilson, M. K. Non-Bonded Force Field Model with Advanced Restrained Electrostatic Potential Charges (RESP2). *Communications Chemistry* **2020**, 3, 1–11.

(50) Durell, S. R.; Brooks, B. R.; Ben-Naim, A. Solvent-Induced Forces between Two Hydrophilic Groups. *The Journal of Physical Chemistry* **1994**, 98, 2198–2202.

(51) Sugita, Y.; Okamoto, Y. Replica-Exchange Molecular Dynamics Method for Protein Folding. *Chemical Physics Letters* **1999**, 314, 141–151.
(52) Okabe, T.; Kawata, M.; Okamoto, Y.; Mikami, M. Replica-Exchange Monte Carlo Method for the Isobaric-Isothermal Ensemble. *Chemical Physics Letters* **2001**, *335*, 435-439.

(53) Patriksson, A.; van der Spoel, D. A Temperature Predictor for Parallel Tempering Simulations. *Physical Chemistry Chemical Physics* **2008**, *10*, 2073-2077.

(54) Fiorin, G.; Klein, M. L.; Hénin, J. Using Collective Variables to Drive Molecular Dynamics Simulations. *Molecular Physics* **2013**, *111*, 3345-3362.

(55) Shirts, M. R.; Chodera, J. D. Statistically Optimal Analysis of Samples from Multiple Equilibrium States. *The Journal of Chemical Physics* **2008**, *129*, 124105.

(56) Shirts, M. R.; Ferguson, A. L. Statistically Optimal Continuous Free Energy Surfaces from Biased Simulations and Multistate Reweighting. *Journal of Chemical Theory and Computation* **2020**, *16*, 4107-4125.

(57) Ward, M. D.; Zimmerman, M. I.; Meller, A.; Chung, M.; Swamidass, S. J.; Bowman, G. R. Deep Learning the Structural Determinants of Protein Biochemical Properties by Comparing Structural Ensembles with DiffNets. *Nature Communications* **2021**, *12*, 3023.

(58) Lemke, T.; Peter, C. EncoderMap: Dimensionality Reduction and Generation of Molecule Conformations. *Journal of Chemical Theory and Computation* **2019**, *15*, 1209-1215.

(59) Lemke, T.; Berg, A.; Jain, A.; Peter, C. EncoderMap(II): Visualizing Important Molecular Motions with Improved Generation of Protein Conformations. *Journal of Chemical Information and Modeling* **2019**, *59*, 4550-4560.

(60) Ceriotti, M.; Tribello, G. A.; Parrinello, M. Simplifying the Representation of Complex
Free-Energy Landscapes Using Sketch-Map. *Proceedings of the National Academy of Sciences* **2011**, *108*, 13023–13028.

(61) Tenenbaum, J. B.; de Silva, V.; Langford, J. C. A Global Geometric Framework for Nonlinear Dimensionality Reduction. *Science* **2000**, *290*, 2319–2323.

(62) Das, P.; Moll, M.; Stamati, H.; Kavraki, L. E.; Clementi, C. Low-Dimensional, Free-Energy Landscapes of Protein-Folding Reactions by Nonlinear Dimensionality Reduction. *Proceedings of the National Academy of Sciences* **2006**, *103*, 9885–9890.

(63) E, W.; Ren, W.; Vanden-Eijnden, E. String Method for the Study of Rare Events. *Physical Review B* **2002**, *66*.

(64) Pan, A. C.; Sezer, D.; Roux, B. Finding Transition Pathways Using the String Method with Swarms of Trajectories. *The Journal of Physical Chemistry B* **2008**, *112*, 3432–3440.

(65) Moradi, M.; Enkavi, G.; Tajkhorshid, E. Atomic-Level Characterization of Transport Cycle Thermodynamics in the Glycerol-3-Phosphate:Phosphate Antiporter. *Nature Communications* **2015**, *6*, 8393.

(66) Blanc, F. E. C.; Houdusse, A.; Cecchini, M. A Weak Coupling Mechanism for the Early Steps of the Recovery Stroke of Myosin VI: A Free Energy Simulation and String Method Analysis. *PLOS Computational Biology* **2024**, *20*, e1012005.

(67) Kutchukian, P. S.; Yang, J. S.; Verdine, G. L.; Shakhnovich, E. I. All-Atom Model for Stabilization of α-Helical Structure in Peptides by Hydrocarbon Staples. *Journal of the American Chemical Society* **2009**, *131*, 4622–4627.

(68) Smith, S. J.; Du, K.; Radford, R. J.; Tezcan, F. A. Functional, Metal-Based Crosslinkers for α-Helix Induction in Short Peptides. *Chemical Science* **2013**, *4*, 3740.
(69) Smith, S. J.; Radford, R. J.; Subramanian, R. H.; Barnett, B. B.; Figueroa, J. S.; Tezcan, F. A. Tunable Helicity, Stability and DNA-binding Properties of Short Peptides with Hybrid Metal Coordination Motifs. *Chemical Science* **2016**, 7, 5453–5461.

(70) Fischer, N.; Tóth, A.; Jancsó, A.; Thulstrup, P.; Diness, F. Inducing α-Helicity in Peptides by Silver Coordination to Cysteine. *Chemistry – A European Journal* **2024**, *30*, e202304064.

(71) Richardson-Matthews, R.; Velko, K.; Bhunia, B.; Ghosh, S.; Oktawiec, J.; Brunzelle, J. S.; Dang, V. T.; Nguyen, A. I. Metal-α-Helix Peptide Frameworks. *Journal of the American Chemical Society* **2025**, 147, 17433–17447.

(72) Monticelli, L.; Tieleman, D. P.; Colombo, G. Mechanism of Helix Nucleation and Propagation: Microscopic View from Microsecond Time Scale MD Simulations. *The Journal of Physical Chemistry B* **2005**, *109*, 20064–20067.

(73) Acharyya, A.; Ge, Y.; Wu, H.; DeGrado, W. F.; Voelz, V. A.; Gai, F. Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study. *The Journal of Physical Chemistry B* **2019**, *123*, 1797–1807.

(74) Lin, M. M.; Shorokhov, D.; Zewail, A. H. Dominance of Misfolded Intermediates in the Dynamics of α-Helix Folding. *Proceedings of the National Academy of Sciences* **2014**, *111*, 14424–14429.

(75) Li, P.; Merz, K. M. J. MCPB.Py: A Python Based Metal Center Parameter Builder. *Journal of Chemical Information and Modeling* **2016**, *56*, 599–604.

(76) Hanwell, M. D.; Curtis, D. E.; Lonie, D. C.; Vandermeersch, T.; Zurek, E.; Hutchison, G. R. Avogadro: An Advanced Semantic Chemical Editor, Visualization, and Analysis Platform. *Journal of Cheminformatics* **2012**, *4*, 17.
(77) Neese, F. Software Update: The ORCA Program System—Version 5.0. *WIREs Computational Molecular Science* **2022**, 12, e1606.

(78) Talmazan, R. A.; Podewitz, M. PyConSolv: A Python Package for Conformer Generation of (Metal-Containing) Systems in Explicit Solvent. *Journal of Chemical Information and Modeling* **2023**, 63, 5400–5407.

(79) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S. et al. All-Atom Empirical Potential for Molecular Modeling and Dynamics Studies of Proteins. *The Journal of Physical Chemistry B* **1998**, 102, 3586–3616.

(80) Chermette, H. Density Functional Theory: A Powerful Tool for Theoretical Studies in Coordination Chemistry. *Coordination Chemistry Reviews* **1998**, 178–180, 699–721.

(81) Mayne, C. G.; Saam, J.; Schulten, K.; Tajkhorshid, E.; Gumbart, J. C. Rapid Parame-
terization of Small Molecules Using the Force Field Toolkit. *Journal of Computational
Chemistry* **2013**, 34, 2757–2770.

(82) de Hatten, X.; Cournia, Z.; Huc, I.; Smith, J. C.; Metzler-Nolte, N. Force-Field De-
velopment and Molecular Dynamics Simulations of Ferrocene–Peptide Conjugates as
a Scaffold for Hydrogenase Mimics. *Chemistry – A European Journal* **2007**, *13*, 8139–
8152.

(83) Filippini, G.; Goujon, F.; Bonal, C.; Malfreyt, P. Energetic Competition Effects on Thermodynamic Properties of Association between β-CD and Fc Group: A Potential of Mean Force Approach. *The Journal of Physical Chemistry C* **2012**, *116*, 22350–22358.

(84) Mayaan, E.; Moser, A.; MacKerell Jr, A. D.; York, D. M. CHARMM Force Field Parameters for Simulation of Reactive Intermediates in Native and Thio-Substituted Ribozymes. *Journal of Computational Chemistry* **2007**, *28*, 495–507.
(85) Pavlova, A.; Gumbart, J. C. Parametrization of Macrolide Antibiotics Using the Force Field Toolkit. *Journal of Computational Chemistry* **2015**, *36*, 2052–2063.

(86) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. *Journal of Computational Chemistry* **2012**, *33*, 580–592.

(87) Zhang, J.; Lu, T. Efficient Evaluation of Electrostatic Potential with Computerized Optimized Code. *Physical Chemistry Chemical Physics* **2021**, *23*, 20323–20328.

(88) Marcus, Y. Ionic Radii in Aqueous Solutions. *Chemical Reviews* **1988**, *88*, 1475–1498.

(89) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. *The Journal of Chemical Physics* **1983**, *79*, 926–935.

(90) Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O. MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations. *Journal of Computational Chemistry* **2011**, *32*, 2319–2327.

(91) Gowers, R.; Linke, M.; Barnoud, J.; Reddy, T.; Melo, M.; Seyler, S.; Domański, J.; Dotson, D.; Buchoux, S.; Kenney, I. et al. MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations. Python in Science Conference. Austin, Texas, 2016; pp 98–105.

(92) Abraham, M. J.; Murtola, T.; Schulz, R.; Páll, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High Performance Molecular Simulations through Multi-Level Parallelism from Laptops to Supercomputers. *SoftwareX* **2015**, *1–2*, 19–25.

(93) Bussi, G.; Donadio, D.; Parrinello, M. Canonical Sampling through Velocity Rescaling. *The Journal of Chemical Physics* **2007**, *126*, 014101.

(94) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. *Journal of Applied Physics* **1981**, *52*, 7182–7190.
(95) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. *Journal of Molecular Graphics* **1996**, *14*, 33–38.

(96) Hénin, J.; Lopes, L. J. S.; Fiorin, G. Human Learning for Molecular Simulations: The Collective Variables Dashboard in VMD. *Journal of Chemical Theory and Computation* **2022**, *18*, 1945–1956.

(97) Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V. et al. Scikit-Learn: Machine Learning in Python. *Journal of Machine Learning Research* **2011**, *12*, 2825–2830.

(98) Hinton, G. E.; Salakhutdinov, R. R. Reducing the Dimensionality of Data with Neural Networks. *Science* **2006**, *313*, 504–507.

(99) Chen, W.; Ferguson, A. L. Molecular Enhanced Sampling with Autoencoders: On-the-fly Collective Variable Discovery and Accelerated Free Energy Landscape Exploration. *Journal of Computational Chemistry* **2018**, *39*, 2079–2102.

(100) He, K.; Zhang, X.; Ren, S.; Sun, J. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. *arXiv:1502.01852 [cs.CV]* **2015**,

(101) Wehmeyer, C.; Noé, F. Time-Lagged Autoencoders: Deep Learning of Slow Collective Variables for Molecular Kinetics. *The Journal of Chemical Physics* **2018**, *148*, 241703.

(102) Tschannen, M.; Bachem, O.; Lucic, M. Recent Advances in Autoencoder-Based Representation Learning. *arXiv:1812.05069 [cs.LG]* **2018**,

(103) Ceriotti, M.; Tribello, G. A.; Parrinello, M. Demonstrating the Transferability and the Descriptive Power of Sketch-Map. *Journal of Chemical Theory and Computation* **2013**, *9*, 1521–1532.

(104) Paszke, A.; Gross, S.; Chintala, S.; Chanan, G.; Yang, E.; DeVito, Z.; Lin, Z.; Desmaison, A.; Antiga, L.; Lerer, A. Automatic Differentiation in PyTorch. 31st Conference
on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA. 2017; p 4.

(105) Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L. et al. PyTorch: An Imperative Style, High-Performance Deep Learning Library. *Advances in Neural Information Processing Systems* **2019**, 12.

(106) Kingma, D. P.; Ba, J. Adam: A Method for Stochastic Optimization. arXiv:1412.6980 [cs] 2017,

(107) Srivastava, N.; Hinton, G.; Krizhevsky, A.; Sutskever, I.; Salakhutdinov, R. Dropout: A Simple Way to Prevent Neural Networks from Overfitting. *J. Mach. Learn. Res.* **2014**, *15*, 1929–1958.

(108) E, W.; Ren, W.; Vanden-Eijnden, E. Finite Temperature String Method for the Study of Rare Events. *The Journal of Physical Chemistry B* **2005**, *109*, 6688–6693.

(109) Vanden-Eijnden, E.; Venturoli, M. Revisiting the Finite Temperature String Method for the Calculation of Reaction Tubes and Free Energies. *The Journal of Chemical Physics* **2009**, *130*, 194103.