Single-layer MoS2 solid-state nanopores for coarse-grained sequencing of proteins

Proteins are essential biological molecules to use as biomarkers for early disease diagnosis. Therefore, their detection is crucial. In recent years, protein sequencing has become one of the most promising techniques. In particular, solid-state nanopores (SSNs) are powerful platforms for single biological molecule sensing without any labeling and with high sensitivity. Atomically thin two-dimensional (2D) materials with nanometer-sized pores, such as single-layer MoS₂, represent the ideal SSN because of their ultimate thinness. Despite the benefits they offer, their use for protein sequencing applications remains very challenging since the fast translocation speed provides a short observation time per single molecule. In this work, we performed extensive molecular dynamics simulations of the translocation of the 20 proteinogenic amino acids through single-layer MoS₂ nanopores. From ionic current traces, we characterized peptide-induced blockade levels of current and duration for each of the 20 natural amino acids. Using clustering techniques, we demonstrate that positively and negatively charged amino acids present singular fingerprints and can be visually distinguished from neutral amino acids. Furthermore, we demonstrate that this information would be sufficient to identify proteins using the coarse-grained sequencing technique made of only three amino acid categories depending on their charge. Therefore, single-layer MoS₂ nanopores have great potential as sensors for the identification of biomarkers.

1 Introduction

Single-molecule protein sequencing has been very recently identified as one of the seven technologies “to watch” in the coming year (Eisenstein, 2023). It is due to the fact that the proteome, which represents the complete set of proteins made by a cell or organism, contains information about health and disease. However, it remains extremely challenging to characterize. Compared to DNA, single-molecule protein sequencing is crucial for early disease diagnosis due to the fact that DNA sequencing of living cells does not fully define human diseases (Cressiot et al., 2020). For instance, protein sequencing technologies could be used to identify tumor biomarkers, which can help to determine the presence, absence, or evolution of cancer (Borrebaeck, 2017). Still, the protein ensemble is by far more complex than the DNA ensemble. First, to sequence a protein, it necessitates the recognition of 20 naturally occurring (proteinogenic) amino acids, compared with the four nucleotides forming the building blocks of DNA molecules, which results in a much larger chemical diversity (charge, hydrophobicity, polarity, etc.). Moreover, the proteome includes proteins with post-translational modifications (Stierlen et al., 2023), e.g., phosphorylation, which may alter the location, the function, and even the folded state of a protein (Bah et al., 2015). Finally, in contrast to the negatively uniformly charged double strands of nucleotides, which are the common shared structure of DNA molecules, proteins occur in many different folded structures with various heterogeneous charge states. Nowadays, single-molecule sensors inspired by the techniques used for DNA that could sequence proteins in an electrolyte sample could be a major breakthrough on the horizon. Among existing technologies, nanopore sequencing has immense potential due to the fact that this technology presents a high sensitivity since single molecules can be detected. Nonetheless, there are still considerable challenges to overcome (Bandara et al., 2022; Nicolaï and Senet, 2022; Yang and Dekker, 2022).

Solid-state nanopores (SSNs), fabricated from stimuli-responsive materials, have been widely studied in the past decade for the detection and characterization of single proteins (Lee et al., 2018; Luo et al., 2020; Xue et al., 2020). The physical principle behind SSN sensing experiments is the measurement of the ionic current variations when charged molecules, initially immersed in an electrolyte, translocate through a nanometer-sized channel in response to an external voltage applied across the membrane (Figure 1A). Therefore, as the passage of the single molecule through the nanopore is driven by an electric field, an appropriate control of the total charge of the molecule of interest is required (Nicolaï and Senet, 2022). During that time, the ionic current is monitored to detect the passage of single molecules through the pore at a sub-microsecond temporal resolution. By analyzing the features of the ionic current trace, one can extract crucial structural information about the biological molecule, including its primary structure, i.e., its sequence. In comparison with biological nanopores, such as α-hemolysin (Song et al., 1996) or aerolysin (Strack, 2020), SSNs are mechanically robust and durable in time, with tunable pore sizes, geometries, and chemistry (Pérez-Mitta et al., 2019), and compatible with various electronic or optical measurement techniques. However, they particularly suffer from critical limitations, such as the high translocation speed (Fragasso et al., 2020), the low spatial resolution, and the stochastic motion of biological molecules, which remain as challenges for accuracy and sensitivity (Meyer et al., 2021) or the non-specific interaction between proteins and the walls of the SSN, which can clog the pore and block the translocation of other molecules (Eggenberger et al., 2019).

FIGURE 1

FIGURE 1. (A) Structure of the MoS₂ nanopore sensor simulated in the present work. The membrane is shown in ball and stick (Mo, blue and S, yellow) plus surface (gray) representations. The peptide is shown in red (cartoon), with the positions of the center of mass of each amino acid represented by spheres. The electrolyte is represented by transparent spheres, the water molecules being not represented for more clarity. (B) Model peptide sequences X_K7 studied in the present work. The 20 proteinogenic amino acids are grouped by family: positively (blue) and negatively charged (red), polar neutral (violet), hydrophobic aromatic (cyan) and non-aromatic (green), and special cases (orange).

Two-dimensional (2D) SSNs, such as graphene (Garaj et al., 2010; Merchant et al., 2010; Schneider et al., 2010), hexagonal boron nitride (Liu et al., 2013; Zhou et al., 2013), transition-metal dichalcogenides MoS₂ and WS₂ (Liu et al., 2014; Feng et al., 2015; Danda et al., 2017), or MXenes (Mojtabavi et al., 2019) nanopores, have been extensively studied experimentally for DNA sequencing (Arjmandi-Tash et al., 2016; Qiu et al., 2021). Nevertheless, protein sequencing using 2D SSNs is much less advanced, particularly compared with silicon nitride SSNs (Kennedy et al., 2016; Dong et al., 2017; Kolmogorov et al., 2017). To the best of our knowledge, only few theoretical and one experimental studies about MoS₂ SSNs for protein sequencing applications have been reported (Barati Farimani et al., 2018; Chen et al., 2018; Nicolaï et al., 2020; Wang et al., 2023). Among those, a very recently published experimental work demonstrates the identification of amino acids with sub-1-Dalton resolution using MoS₂ nanopores (Wang et al., 2023). The authors present the use of 41 different sub-nanometer-engineered pores, with effective diameters ranging from sub-nm to 1.6 nm to directly identify 16 out of 20 types of natural amino acids. Among the 20 natural amino acids, 18 were negatively charged by controlling the pH of the electrolyte. However, using such heterogeneous sub-nm pores and electrolyte properties might be an obstacle for protein sequencing applications, particularly for the threading of polypeptides through the nanopores. In this case, the use of larger pores ($>1$ nm) and polycationic charge carriers is one solution (Nicolaï and Senet, 2022). Moreover, one of the major challenges for protein sequencing using 2D SSNs is that the fast translocation speed of the biological molecule through the nanoporous membrane of ultimate thickness provides only a short sensing period, i.e., dwell time, per single molecule (Nicolaï and Senet, 2022). It makes the assignment of fingerprints to each of the 20 proteinogenic amino acids from ionic current time series measurements very challenging. For example, several distinct features in the recorded ionic current time series can be detected within a blockade event, and algorithms in pattern recognition and machine learning can be very helpful to identify specific fingerprints associated with the single molecule detected (Barati Farimani et al., 2018; Misiunas et al., 2018; Farshad and Rasaiah, 2020; Meyer et al., 2020; Nicolaï et al., 2020; Taniguchi, 2020; Arima et al., 2021; Diaz Carral et al., 2021; Tsutsui et al., 2021; Xia et al., 2021; Mittal et al., 2022; Taniguchi et al., 2022; Jena and Pathak, 2023). Finally, in addition to signal analysis techniques, molecular dynamics (MD) is also a very powerful tool to help: i) understanding the origin of these features and ii) assigning these features to amino acid properties (chemical, charge, hydrophobicity, etc.) since, from MD, the positions of all the atoms of the system are known at each time step, which is an additional crucial information for single biological molecule sensing, compared to experiments.

In the present work, we performed extensive unbiased all-atom MD simulations for a total duration of 250 μs for the translocation of 20 proteinogenic amino acids through a single-layer MoS₂ nanopore of an effective diameter of D = 1.3 nm (Figure 1A). Individual amino acids were chemically linked to a short polycationic charge carrier, lysine heptapeptide (Figure 1B), allowing transport of the peptide through the nanopore. This probe was designed to guide the target peptide toward MoS₂ nanopores (Nicolaï et al., 2019). It allows us to control peptide translocation through solid-state nanopores and relate protein characteristics with nanopore readouts. Furthermore, this probe has also been used experimentally (arginine heptapeptide) using biological nanopores to distinguish among uniformly charged homopeptides and to assign signature ionic currents to the charged homopeptides. A transient current blockade is then induced by the passage of the peptide, whereby the characterizations of relative residual current and blockade duration are used to reveal the identity of the linked amino acid (Ouldali et al., 2020). Moreover, as performed in real-life experiments, the peptide is initially placed above the membrane in the cis compartment to simulate its complete translocation through the nanopore to the trans compartment using a transverse electric field (no other bias). From the ionic current time series extracted from MD, we show that each amino acid presents a large diversity of ionic current blockade levels and duration. Nevertheless, by applying unsupervised machine learning (clustering) to the segmentation of translocation events, specific fingerprints dependent on the charge of the amino acids were identified. Hereafter, we demonstrate that both positively and negatively charged amino acids present well-distinguishable distributions of blockade levels of ionic current and duration compared to all the other amino acids. Finally, ideal fingerprints associated with each of the 20 proteinogenic amino acids are presented, some of them being characteristic of more than one amino acid. These promising findings may offer a route toward protein sequencing using MoS₂ solid-state nanopores via the identification of coarse-grained sequences of proteins, from the detection of the position of charged amino acids in the primary structure, the average coarse-grained sequence identity being around 10% only.

2 Materials and methods

2.1 Atomistic modeling of MoS₂ SSNs

SSN sensors simulated in the present work are composed of three distinct elements: a single-layer MoS₂ membrane and a biological peptide, both immersed in a KCl electrolyte solution (Figure 1A). The atomic structure of the full system comprised around 100,000 atoms in total. Initially, MoS₂ membranes were constructed using 2H-MoS₂ orthorhombic unit cell lattice vectors $\vec{a}=(3.1,\mathrm{0,0})$ Å and $\vec{b}=(\mathrm{0,5.4},0)$ Å, comprising six atoms, two Mo, and four S. The Mo–S bond length was taken as d_Mo−S = 2.4 Å, and the S–S distance was taken as d_S−S = 3.2 Å. It corresponds to the geometrical thickness h of the membrane, the effective thickness h* being around 0.7 nm (Nicolaï et al., 2019; Nicolaï et al., 2020). The pores of cylindrical shape were drilled at the center of the membrane by removing atoms whose coordinates satisfy x² + y² < R², where R is the radius of the pore. We consider MoS₂ membranes with dimensions of 7.5 × 7.5 nm² and pores of diameter D = 1.3 nm. Last but not least, the membrane is considered globally neutral, with atomic partial charges q_i for Mo and S computed from the charge equilibration algorithm (Rappe and Goddard, 1991; Nakano, 1997) in vacuum using ReaxFF, available in the LAMMPS software package (Ostadhossein et al., 2017). Partial charges, on average, are around +0.42 for Mo atoms and −0.21 for S atoms, and the distribution of partial charges relative to the center of the pore is shown in Supplementary Figure S1. As expected, partial charges are strongly influenced by the presence of the pore (vacancies) at the center of the membrane, with a decrease of partial charges for S atoms at the mouth of the pore and a decrease or increase for Mo atoms partial charges depending on their S environment (see Supplementary Figure S1). The modeling of partial charges is essential for a better description of electrostatic interactions between the peptide, the electrolyte with membrane atoms belonging to the edge of the nanopore.

Biological peptides were built using the AmberTools software. From the sequence of amino acids defining the peptide, the module leap creates the all-atom structure from a database. The initial structure of the peptide created that way does not exhibit a particular 3D shape and is linear (Figure 1A). During MD simulations, the structure of the peptide is fully relaxed and can adopt any conformation. However, during the translocation process, the peptide is elongated in the nanopore due to its small diameter. In this work, we study the translocation of 20 distinct peptide sequences made of a lysine heptapeptide plus one of the twenty natural amino acids (Figure 1B). This methodology, based on the number of charge carriers added, and its impact on the ionic current traces measured during MD simulations has been discussed in a previous work (Nicolaï et al., 2019). Other techniques have been tested theoretically, such as applying a hydrostatic pressure gradient (Chen et al., 2018) or modifying the chemical potential of the membrane (Luan and Zhou, 2018). The total charge of the peptide is +7 for neutral amino acids (A, G, I, L, P, V, F, W, Y, S, T, C, M, N, and Q), +8 for positively charged amino acids (R, K, and H), and +6 for negatively charged amino acids (E and D). Peptides are initially placed at a distance of 2.5 nm above the membrane to avoid a common biased threading when the peptide is originally placed inside the pore, and it allows us to simulate the complete translocation process (five steps) as shown in Supplementary Figure S2, i.e., i) diffusion in bulk electrolyte, ii) diffusion on the top surface, iii) passage through the pore, iv) diffusion on the bottom surface, and v) diffusion in bulk electrolyte. Finally, water molecules, potassium K⁺ and chloride Cl⁻ ions (1 M) were added to the simulation box using GROMACS (Abraham et al., 2018).

2.2 Molecular dynamics simulations

All-atom classical MD simulations in explicit solvent were carried out using the GROMACS software package (Abraham et al., 2018) (version 2018.2 in double precision). Peptide translocation was enforced by imposing a uniform electric field directed normally to the nanoporous membrane (z-direction) to all atomic partial charges in the system. The corresponding applied voltage simulated is V_bias = −EL_z, where L_z = 15 nm is the length of the simulation box in the z-direction. No other biases were applied in the present simulations, as done in other works (Barati Farimani et al., 2018), and we performed the simulation of the full translocation process of the peptide through the membrane, i.e., from the bulk solvent compartment above the membrane to the bulk solvent compartment below the membrane (Figure 1A). The MoS₂ nanoporous membrane was modeled using the harmonic potential for Mo–S bonds plus S–Mo–S and Mo–S–Mo angles (Sresht et al., 2017). As mentioned earlier, atomic partial charges q_i for Mo and S were computed from charge equilibration in vacuum using ReaxFF. Finally, LJ parameters (ϵ_i and σ_i) for Mo and S atoms were adapted from the work of Gu et al. (2017). Peptides were modeled using the AMBER99sb*-ILDN-q force field (Best et al., 2012). The water model used in the present work is TIP3P (Jorgensen et al., 1983). Potassium chloride K⁺ and Cl⁻ ion non-bonded parameters (q_i, ϵ_i, and σ_i) were taken from the work of Joung and Cheatham (2008), where specific parameters were developed for the TIP3P water model. Neighbor searching was performed with a pair list generated using the Verlet method (particle-based cut-offs) as implemented in GROMACS (Abraham et al., 2018). The neighbor list was updated every five steps (10 fs), with a cut-off distance for the short-range neighbor list of 1.0 nm. Moreover, electrostatic interactions were computed using a Coulomb potential and van der Waals interactions using the Lennard–Jones (LJ) potential plus arithmetic mixing rules. Technically, the particle–particle particle–mesh (PPPM) method (Isele-Holder et al., 2012) was used to describe long-range electrostatic interactions with a Fourier spacing of 0.16 nm and a PME order of 4. A cut-off of 1.0 nm was applied to both Coulomb and LJ potential for non-bonded interactions. Finally, a long-range analytical dispersion correction was applied to the energy and pressure. Similar MD parameters have been used in other works (Heiranian et al., 2015; Barati Farimani et al., 2018; Chen et al., 2018; Thiruraman et al., 2018; Nicolaï et al., 2019; Nicolaï et al., 2020; Barrios Pérez et al., 2019; Shankla and Aksimentiev, 2020; Zhao et al., 2021).

For each NEMD run, the simulation box built from the modeling procedure was first minimized using the steepest-descent algorithm with a force criterion of 1,000 kJ/mol/nm. Then, the minimized structure was equilibrated in the NVT ensemble for 100 ps (δt = 1 fs) using the V-rescale thermostat (Bussi et al., 2007) at T = 300 K (τ_T = 0.1 ps), and position restraints were applied to the membrane and the peptide. The NVT equilibrated structure was then equilibrated in the NPT ensemble for 500 ps (δt = 1 fs) using a Parrinello–Rahman barostat (Parrinello and Rahman, 1981; Nosé and Klein, 1983) at P = 1 bar (τ_P = 1.0 ps), and position restraints were applied to the peptide. Finally, the NPT equilibrated structure was simulated at V_bias = 1 V for 500 ns (production run) with a time step δt = 2 fs with constraints applied on chemical bonds involving H atoms using the LINCS algorithm (Hess et al., 1997). During production runs, xyz-coordinates of all the atoms of the simulation box were saved every 10 ps.

In total, 12.5 μs of MD simulations were performed for each of the 20 proteinogenic amino acids, i.e., 250 μs simulation time in total. It represents more than 10 million hours of CPU time, performed on AMD EPYC 7302@3 GHz (2 processors, 16 cores/processor) with a scaling of 150 ns per day on 256 cores.

2.3 Data analysis

2.3.1 Effective free-energy profiles and surfaces

From MD, we probed the position of the amino acid of interest X in peptides X_K7 by computing the cylindrical coordinates (ρ, z) of the center of mass of the amino acid side chain at each time step, as performed in a previous work (Nicolaï et al., 2020). Effective free-energy profiles V_z and surfaces V_ρ,z were computed by using the following formula:

$V_z=-kT\log \frac{P_z}{P_z^{max}};V_{\rho ,z}=-kT\log \frac{P_{\rho ,z}}{P_{\rho ,z}^{max}},(1)$

where k is the Boltzmann constant, T is the temperature, P_z and P_ρ,z are the 1D and 2D probability density functions (PDFs) of the normal z and both radial ρ and normal z-coordinates, respectively, and $P_z^{max}$ and $P_{\rho ,z}^{max}$ are the maximum values of P_z and P_ρ,z, respectively. PDFs were computed using the cylindrical coordinates time series (1,250,000 points) extracted from concatenated MD trajectories for each of the 20 proteinogenic amino acids, as shown in Figure 1B.

2.3.2 Ionic current

Ionic current time series were computed from MD production runs using z-coordinates of K⁺ and Cl⁻ ions as a function of time:

$I\left(t\right)=\frac{1}{\mathrm{\Delta }t{L}_z}\sum _{i=1}^{N_{\text{ions}}}{q}_i\left[z_i\left(t+\mathrm{\Delta }t\right)-z_i\left(t\right)\right],(2)$

where Δt is the time between MD snapshots chosen for the calculations (1 ns), L_z is the dimension of the simulation box in the z-direction, which is the direction of the applied electric field, N_ions is the total number of ions in the electrolyte, q_i is the charge of the ion i (+1 or −1), and z_i(t) is the z-coordinate of the ion i at time t. In addition, ionic current time series were filtered in order to remove high-frequency fluctuations by computing the moving mean of the ionic current over T = 1,000 samples.

2.3.3 Detection of peptide-induced blockade events

The detection of peptide-induced blockade events from ionic current time series was performed using a two-threshold method, as applied elsewhere (Ouldali et al., 2020). First, a threshold th₁ is applied to identify possible blockade events. The threshold th₁ was defined as th₁ =< I₀ > − 4σ₀, where $<I_0>$ is the mean value of open-pore ionic current and σ₀ is its standard deviation. In the case of single-layer MoS₂ nanopore of diameter D = 1.3 nm, the corresponding values are $<I_0>=3.55$ nA and σ₀ = 0.25 nA (Barrios Pérez et al., 2019). A possible blockade event always starts when the ionic current decreases below th₁ and ends when the ionic current first increases above th₁ (see Supplementary Figure S4). The advantage of this threshold is to eliminate the overwhelming majority of the open-pore ionic current fluctuations monitored during translocation experiments. Second, from ionic current values below th₁ for a given possible blockade event, we computed the corresponding probability distribution P(I), and a Gaussian distribution was then fitted to the data. If the mean value of the Gaussian fit $<I_b>$ is below th₂ =< I₀ > − 5σ₀, the event is considered a peptide-induced blockade event.

2.3.4 Structural break detection and clustering analysis

Structural break detection was performed using the Chow test, an algorithm used when a potential structural break in the time series may be recognized a priori. The principle is to evaluate the parameter stability, namely, to determine if the underlying regression model parameters have remained unchanged. In this case, peptide-induced blockade event ionic current data were split by one point in time, getting two different datasets. The null hypothesis of the Chow test asserts that true coefficients in two linear regressions on these two datasets are equal. Structural changes take place in points where the null hypothesis is rejected (Aronov et al., 2019; Sun and Wang, 2022).

Clustering was performed using the Gaussian mixture model (Reynolds, 2009) (GMM) for which Gaussian free parameters (π_k, μ_k, and Σ_k) representing the weight, the means, and the covariances, respectively, were estimated from the expectation–maximization (EM) algorithm (Dempster et al., 1977). To do so, we used scikit-learn, which is an open-source machine learning Python library. In addition, to estimate the number of sub-populations for each amino acid, we used the Bayesian Information Criterion (BIC) score to estimate the proper number of components K to GMM (Schwarz, 1978) (Supplementary Figure S13). In addition, full and tied covariances were set as a parameter of the model for 1D and 2D clustering, respectively. Finally, the convergence threshold used was 0.001, which means that when the lower bound average gain falls under this limit, EM iterations will end. From GMM clustering outputs, i.e., cluster means $<\mathrm{\Delta }{I}_b>$ and $<{\tau }_b>$, we computed 2D probability densities P(< ΔI_b >, < τ_b >) using 20 and 30 bins, respectively. The convergence of GMM clustering techniques applied to 1D (Figure 3) and 2D probability densities (Figure 4) as a function of input data is presented in Supplementary Figure S14.

3 Results and discussion

3.1 Translocation of the 20 proteinogenic amino acids through MoS₂ nanopores

In translocation simulations, a nanoporous membrane made of single-layer MoS₂ with a pore of diameter D = 1.3 nm separates the two compartments, cis and trans, which contain a 1M KCl electrolyte solution (Figure 1A). In the cis compartment, a biological peptide X_K7, with X being one of the 20 proteinogenic amino acids (Figure 1B), is initially placed above the membrane at a vertical distance of around 2.5 nm. The translocation simulation starts by applying an external voltage of 1 V across the membrane. After diffusing in bulk electrolyte for a few ns, the peptide starts diffusing on the top surface of the membrane and then translocates through the nanopore (Supplementary Figure S2). Once the translocation happens, the peptide diffuses on the bottom surface of the membrane in the trans compartment and detaches at some point to go back to the bulk electrolyte. This latter step is not observed in all translocation simulations, and sometimes, only a partial translocation is achieved (Supplementary Figure S2).

From MD, we computed the sensing time T_S of each amino acid X belonging to the peptide X_K7. As shown in Figure 2A, negatively charged amino acids E and D present a T_S one order of magnitude higher than that of the neutral amino acids and two orders of magnitude larger than that of the positively charged amino acids. It means that the charge property of the amino acids mainly dictates the sensing characteristics of the amino acids in MoS₂ nanopores using MD. Within a family, sensing time T_S are very similar, except for: i) K in the positively charged family, which presents a T_S 3–4 times larger than H and R; ii) S and Q in the polar neutral family, which present a T_S 3–4 times larger than T and N; and iii) C in the special cases family, which presents a T_S 2–3 times larger than G and P. In addition, from the position of the center of mass of each amino acid side chain, we computed the effective free-energy profiles V_z along the normal coordinate z in order to estimate the barrier for the passage of each amino acid through the nanoporous membrane. Figure 2B shows the effective free-energy profiles V_z (FEPs) for R (positively charged), E (negatively charged), S (polar neutral), W (hydrophobic aromatic), V (hydrophobic non-aromatic), and G (special cases). The other FEPs are available in Supplementary Figure S3. From MD and independently of the amino acid characteristics, the FEPs along the normal coordinates present an asymmetry due to the presence of the electric field and share two similar features: i) a local minimum in the cis compartment (z ∼ 0.5 nm) corresponding to the diffusion of the peptide on the top surface of the membrane and ii) a global minimum in the trans compartment (z ∼ − 0.5 nm) corresponding to the diffusion of the peptide on the bottom surface of the membrane after translocation. However, the behavior of negatively charged amino acids (E and D) shows some differences compared to the others. In the cis compartment, there are two local minima centered around z ∼ 0.0 and z ∼ 1.0 nm. This happens because negatively charged amino acids interact with the electric field in the opposite direction of translocation, and even after the full translocation of the peptide, these amino acids can go back individually to the pore during the diffusion process. It means that the free-energy barriers for all amino acids except the negatively charged ones correspond to the full translocation, whereas for negatively charged amino acids, it corresponds mainly to the exit of the pore, for which the barrier of the entrance is much smaller (Figure 2B; Supplementary Figure S3A). For comparison, the profiles for cations K⁺ and anions Cl⁻ are symmetrical and flat in the bulk region. The free-energy increases when approaching the MoS₂ surface and being maximum (saddle point) at z ∼ 0 nm.

FIGURE 2

FIGURE 2. (A) Sensing time T_S (in ns) as a function of amino acids. The color code is the same as in Figure 1. (B) Effective free-energy profiles V_z (in kT unit, T = 300 K) along the normal coordinate z of the amino acid side chain center of mass. Gray rectangles represent the position of the MoS₂ nanoporous membrane. (C) Effective free-energy barriers ΔV_z (in kT unit) as a function of the amino acid volume (in ${\mathring{\mathrm{A}}}^3$). (D) Effective free-energy surfaces V_ρ,z (in kT unit) as a function of the radial and normal coordinates of the amino acid side chain center of mass inside the nanopore (ρ < R = 0.65 nm and |z| < h/2 = 0.16 nm). The colormap is terrain, from blue (0 kT) to green (2.5 kT) to yellow (5 kT) to brown (7.5 kT) to white (≥10 kT). The red and yellow circles represent the global and local minima within 1 kT, respectively. (E) Effective free-energy profiles V_z along the normal coordinate z of the ions. (F) Effective free-energy surfaces V_ρ,z (in kT unit) as a function of the radial and normal coordinates of the ions inside the nanopore.

From the 1D FEPs V_z, we estimated the effective free-energy barrier for the translocation of each amino acid X. As shown in Figure 2C, the free-energy barriers ΔV_z are correlated with the volume of the amino acids (Pearson correlation $\sim 0.7$). This is particularly clear for amino acids with volumes below 150 ${\mathring{\mathrm{A}}}^3$, and even for larger amino acids $(>150{\mathring{\mathrm{A}}}^3)$, the tendency is increasing, although other properties may influence the translocation, the charge property being one of them, as shown by comparing amino acids with similar volumes and different charge properties, i.e., E and V or K and L in Figure 2C. The correlation of free-energy barriers ΔV_z with the amino acid number of atoms is similar to the one with the volume of amino acids (Pearson correlation $\sim 0.7$, Supplementary Figure S3B). For comparison, the free-energy barriers for the passage of K⁺ and Cl⁻ ions are 4.9 and 4.4 kT, respectively (Figure 2E).

Finally, we computed the effective free-energy surfaces V_ρ,z (FESs) of each amino acid during their passage inside the MoS₂ nanopore. First, the FESs explored by the 20 proteinogenic amino acids are very heterogeneous (Figure 2D; Supplementary Figure S3C). However, some observations must be highlighted. For instance, all three positively charged amino acids, K, H, and R, translocate through the pore far away from the vertical edges located at ρ ∼ R. It is also the case even if it is less pronounced for hydrophobic non-aromatic amino acids, such as V, I, L, and M. The opposite behavior is observed for negatively charged amino acids E and D, which reside inside the nanopore closer to the vertical edges due to the presence of Mo atoms in the pore throat, with their global minimum being inside the pore, as explained earlier from FEPs V_z. It is also the case for serine (S), which is characterized by the presence of an oxygen atom at the extremity of its side chain, as it is the case for E and D. For comparison, free-energy surfaces of K⁺ and Cl⁻ ions present the same behavior, i.e., cations translocate in a narrower channel than anions due to the presence of positively charged Mo atoms at the mouth of the pore. However, compared to the amino acids, the translocation landscape of ions is more flat and spread over the entire pore channel. Second, as shown in Figure 2D, some amino acids present a wide, extended basin in their FESs, such as H, N, W, and G, whereas some of them present a narrower translocation channel, such as R, Q, A, and P. It is not surprising for G since it is characterized by the smallest side chain, i.e., an H atom. Nevertheless, it is surprising for W amino acid, which is the largest amino acid in terms of volume. It comes from the different orientations of the aromatic rings observed during MD. Therefore, hydrophobic aromatic amino acids W and Y present multiple minima in the radial direction ρ during their passage inside the nanopore. In the wider translocation channel (H, N, W, and G), FESs are quite flat, with only small barriers between the existing multiple local minima. In the narrower channel, the barriers are much larger, with uphill profiles inside the pore to enter it (K and Q) or exit it (M, C, V, and T).

3.2 Detection of peptide-induced blockade events

Figure 3A shows ionic current variations monitored during MD and representing the translocation of the 20 different proteinogenic amino acids through MoS₂ nanopores. The data are grouped according to the family to which amino acid X belongs, i.e., positively charged (blue), negatively charged (red), polar/neutral (violet), hydrophobic aromatic (cyan), hydrophobic non-aromatic (green), and a special case (orange). In the absence of peptide inside the nanopore, a steady ionic current of mean value I₀ = 3.55 ± 0.25 nA flows through the pore. The threading of the peptide into the nanopore induces transient blockades of the ionic current, each ionic current blockade corresponding to the presence of an individual peptide in the nanopore (Nicolaï et al., 2020). From ionic current time series, peptide-induced blockade events were extracted using a two-threshold method (Supplementary Figure S4) in order to proceed in a very similar way as performed in experiments (Ouldali et al., 2020). Each peptide-induced blockade event is characterized by a blockade ionic current trace I_b(t) of duration τ_b (Figure 3B). The total sensing duration per amino acid, which corresponds to tens of translocations, varies from 10% (T) to 25% (V) of the total simulation time per amino acid (12.5 µs), with an average of around 17%. As shown in Figure 3B and as observed experimentally, there is a very large variability of blockade ionic current traces that can be visually observed for all amino acids (Supplementary Figures S5–S8). On the one hand, for a given amino acid, some events with similar duration τ_b are characterized by deep ionic current blockades, and some traces are characterized by slight ionic current blockades, as shown in Figure 3B for N and I amino acids. On the other hand, some events maintain fairly constant blockade current traces, and others show switching levels and bumps, as shown in Figure 3B for R and F amino acids, depending on the radial position of the peptide in the pore (Nicolaï and Senet, 2022). Finally, some blockade traces are characterized by very short duration (a few ns), whereas others are relatively long (a few hundred of ns), as shown in Figure 3B for D and C amino acids. To better characterize this variability of traces detected from translocation simulations, we computed probability densities of blockade ionic current P(I_b) and compared them between the 20 proteinogenic amino acids.

FIGURE 3

FIGURE 3. (A) Ionic current (in nA) as a function of time (in μs) recorded during MD simulations of the translocation of the 20 amino acids through MoS₂ nanopore. Dashed lines represent the average open-pore value $<I_0>$. The gray area represents the threshold used to detect peptide-induced blockade events (see Materials and methods). For each amino acid, the same color code is used as in Figure 1B. (B) Examples of peptide-induced blockade ionic current traces I_b(t) recorded during translocation simulations. Depth ΔI_b ≡ 1 − I_b/ < I₀ > (in %) and duration τ_b (in ns) are indicated. The color code is the same as in (A). (C) Probability densities P(I_b) computed using a bin of 0.1 nA. The color code is the same as in (A).

3.3 Probability densities of blockade ionic current traces

Figure 3C shows the probability densities P(I_b) for each amino acid grouped per family. Overall, the superimposed densities do not exhibit well-separated populations between the amino acids within a family, as measured experimentally for biological nanopores (Ouldali et al., 2020). Nevertheless, some notable exceptions are observed and discussed in the following text. In the present work, P(I_b) densities present multiple peaks for each amino acid, i.e., sub-populations, which means that different fingerprints of blockade current exist during translocation simulations through MoS₂ nanopores. Per amino acid, the number of sub-populations in the data was assessed by using the Gaussian mixture model (GMM) clustering technique associated with the Bayesian Information Criterion (BIC, see Materials and methods). In total, we identified two (P), three (H, R, D, W, V, I, L, M, C), four (K, E, S, T, Q, F, Y, A, G), or five (N) sub-populations per amino acid (Supplementary Table S1), corresponding to four ranges of blockade current I_b: first, the range (0, 1.0) nA, corresponding to depths ΔI_b larger than around 70% of the open pore signal; second, the range (1.0, 1.5) nA, corresponding to depths ΔI_b between around 60% and 70%; third, the range (1.5, 2.0) nA, corresponding to depths ΔI_b between 40% and 60%; and fourth, the range (2.0, 2.5) nA, corresponding to depths ΔI_b smaller than 40%. The two-threshold method imposed here does not permit the detection of depths ΔI_b lower than 30% of the open-pore current.

For all 20 proteinogenic amino acids, the major sub-population of P(I_b) is between 1.7 nA (depth ΔI_b of 50%) for W amino acid and 1.9 nA (depth ΔI_b of 45%) for P amino acid, which is close to be easily distinguishable (Figure 3C). The associated weights of each sub-population (see Supplementary Table S1) range from 34% (N) to 80% (P). Per family, for positively charged amino acids, 3 (H and R) and 4 (K) fingerprints of blockade current are detected, with major sub-populations centered around 1.7–1.8 nA. The main differences between the three positively charged amino acids are observed for K, which presents a minor sub-population at 0.4 nA (depth ΔI_b of 90%) compared to H and R, and for H, which presents a minor sub-population around 0.9 nA (depth ΔI_b of 70%). For negatively charged amino acids, 4 (E) and 3 (D) fingerprints of blockade current are detected, with major sub-populations centered around 1.7 nA, these values being slightly smaller than the ones for positively charged amino acids. The main differences between E and D are observed for larger blockade ranges (depth ΔI_b > 60%), with minor sub-populations centered around 1.3 and 0.6 nA for E and around 1.0 nA for D.

For polar/neutral amino acids, 4 (S, T, Q) and 5 (N) fingerprints of blockade current are detected, with major sub-populations centered between 1.7 and 1.8 nA. These values are comparable with charged amino acids, S and T closer to (K, H, and R) and (N and Q) closer to (E and D), as shown in Figure 3C. However, for minor sub-populations, polar/neutral amino acids present much more dissimilarities between them than charged amino acids. For instance, T amino acid shows a singular minor sub-population centered around 1.3 nA. In addition, singularities are also observed for N and S amino acids, which show a minor sub-population at 2.0 and 1.5 nA, respectively.

For hydrophobic/aromatic amino acids, 3 (W) and 4 (F and Y) fingerprints of blockade current are detected, with major sub-populations centered around 1.7 nA (F and W) and 1.8 nA (Y). For Y amino acid, a minor sub-population close to the major one at 1.5 nA is detected, which is not the case for F and W amino acids. Moreover, compared to W and Y, F amino acid presents a minor sub-population centered at 0.7 nA, which corresponds to a depth ΔI_b of 80% (75% at maximum for W and Y). For hydrophobic/non-aromatic amino acids, 3 (V, I, L, and M) and 4 (A) fingerprints of blockade current are detected, with the major sub-population centered around 1.7 nA with values being extremely close. Among all the amino acid families, the hydrophobic/non-aromatic is the one showing the least differences between amino acids except for L, which shows a singular behavior with two major sub-populations of similar weight at 1.8 and 1.1 nA. To a lesser extent, M amino acid shows the same sub-population at 1.1 nA but with a smaller weight, 20% vs. 40% for L (Supplementary Table S1).

Finally, for the special case amino acids, 2 (P), 3 (C), and 4 (G) fingerprints of blockade current are detected, with the major sub-populations being centered around 1.7 nA for C and G, and 1.9 nA for P, which is the largest value detected. Visually, the special case family is the one that reveals the largest dissimilarities with a major sub-population for P amino acid that is very wide compared with not only G and C but also all the other amino acids. Moreover, C amino acid presents a second well-separated sub-population at 1.2 nA (depth ΔI_b of 65%) compared to G and P. Last but not the least, surprisingly, G amino acid, which is the smallest amino acid with an H atom as a side chain, presents a sub-population at 0.4 nA (depth ΔI_b of 90%) as observed for K amino acid. This confirms that the volume of the amino acids (Perkins, 1986) is not the only physical mechanism underlying the dependence of blockade ionic current on the amino acid type through MoS₂ solid-state nanopores (Supplementary Figure S9). In fact, only tryptophan (W) amino acid, which is the largest amino acid in volume (228 Å³), presents the largest major sub-population of blockade ionic current among all the 20 proteinogenic amino acids. On the contrary, glycine (G), which is the smallest amino acid in volume (60 Å³), presents a minor sub-population in the same range as W (same weight), with a value centered at 0.35 nA for G compared to 0.94 nA for W.

Compared to the experimental work mentioned in the introduction (Wang et al., 2023), we identified more sub-populations per amino acid. For SSNs with diameters comparable to the size of the amino acids being detected (0.6 nm), the experimental distributions of the current trace are bimodal, whereas in the present work, it can vary from 2–5 sub-populations. It is due to the fact that we consider a single device here, compared to 41 experimental devices, with a pore diameter of 1.3 nm compared to sub-nm (0.6–0.8 nm) to 1.6 nm in experiments and the time scale of microseconds in MD compared to seconds in experimental measurements. However, the overlap between the probability distributions P(I_b) of the different amino acids is similar between our theoretical work and the experimental one, but the separation of the maximum peaks is more important in the latter than the ones presented in Figure 3C and in Supplementary Table S1. Finally, the correlation between the means of blockade current and the volume of the amino acid is well established experimentally for SSNs with diameters comparable to the size of the amino acids being detected, whereas in our simulations with larger pore diameters, other mechanisms, such as the orientation of the side chains, are important, as already demonstrated in a previous work (Nicolaï et al., 2020). This mechanism is also observed experimentally for positively charged amino acids (Wang et al., 2023).

To conclude, among the 20 proteinogenic amino acids studied here, peptides containing K, T, N, G, P, or L amino acids produced distinct minor blockade sub-populations of ionic current compared to the other amino acids, whereas the major blockade sub-populations of ionic current are very similar to be differentiated. Therefore, additional information from blockade traces of ionic current is required to improve their recognition using MoS₂ SSNs. A first guess is to include, in the clustering analysis, a better description of the depth and duration of the blockade traces of ionic current detected from translocation simulations.

3.4 Clustering of blockade levels from ionic current traces

To quantify the depth ΔI_b and duration τ_b of each level of ionic current observed during peptide-induced blockade events and extracted from the time series shown in Figure 3A, we applied a structural break detection algorithm (see Materials and methods). It allows us to convert raw signals of blockade current traces into simplified step-wise signals, as shown in Figure 4A. It leads to: i) a better characterization of blockade events compared to the traditional methodology, i.e., using the mean values of ionic current during the associated blockade event, considering the events to be constant as a function of time, and ii) an increase of the statistics of blockade event data. For instance, it reduces by a factor of 3 the mean-squared errors between the raw and the step-wise model signals compared to the constant model signal (Supplementary Figure S10). In addition, it increases by a factor of 6 the statistics of blockade event data, which is crucial for machine learning applications.

FIGURE 4

FIGURE 4. (A) Structural break detection applied to ionic current blockade traces. The raw signal is converted into a step-wise signal, and each level of blockade ionic current is characterized by its duration τ_b and depth ΔI_b. (B) Blockade level duration τ_b (in ns) vs. blockade level depth ΔI_b (in nA). The data are grouped by amino acid family using the same color code as in Figure 1. (C) 2D Probability density functions of cluster means $<\mathrm{\Delta }{I}_b>$ and $<{\tau }_b>$. Yellow circles represent the extrema. (D) Similarity matrix between 2D PDFs shown in (C). (E) Ideal representation of a blockade ionic current trace made of the 20 proteinogenic amino acids and extracted from extrema shown in (C).

Figure 4B represents the duration τ_b vs. depth ΔI_b of blockade levels of ionic current extracted from structural break detection. First, ΔI_b is between 1.0 and 3.5 nA, which represents depths from 30% to 100% of the total open-pore conductance. Second, duration τ_b is between a few hundreds of picoseconds to a few hundreds of nanoseconds. The visual comparison of 2D maps (ΔI_b, τ_b) per amino acid family is complex due to the existing overlap between blockade level characteristics. However, we can observe some major differences between positively and negatively charged amino acids. For example, E and D amino acids present blockade levels with larger depths, whereas K, H, and R present blockade levels with shorter durations. Moreover, the hydrophobic/non-aromatic amino acid family (A, V, I, L, and M) shows similarity with the positively charged amino acid family. Finally, for G amino acid, which presented a non-negligible sub-population of depth ΔI_b 90% blockade in its probability density P(I_b) (Figure 3C), we can observe in its 2D map (ΔI_b, τ_b) that only three very long blockade levels among the hundreds detected are, in fact, responsible for this behavior (Figure 4B).

To extract duration τ_b and depth ΔI_b fingerprints of blockade events associated with the 20 proteinogenic amino acids for further sequencing applications, we applied unsupervised learning (clustering) to the 2D maps presented in Figure 4B. The GMM algorithm was employed repeatedly to detect a single cluster per amino acid by modifying the data taken into account to initialize each cluster mean (see Materials and methods). As input data of GMM algorithm, each blockade level k was characterized by the three following features $({\mathrm{a}.\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{b}\mathrm{e}\mathrm{l}}^k,{\mathrm{\Delta }{I}_b}^k,{{\tau }_b}^k)$. As output data of the GMM algorithm, the cluster means of duration $<{\tau }_b>$ and depth $<\mathrm{\Delta }{I}_b>$ were extracted for each amino acid and 2D probability densities P(< ΔI_b >, < τ_b >) were computed. As shown in Figure 4C, the application of the clustering technique to the depth and duration of blockade levels provides crucial information for the identification of the 20 proteinogenic amino acids using MoS₂ SSNs. First, negatively charged amino acids E and D show very similar fingerprints within each other and very low similarity compared to all the other amino acids (except for T, W, F, I, and C with medium similarities, Figure 4D and Supplementary Figure S11). In addition, they both present two distinct extrema (Figure 4C; Table 1), which correspond to the two relevant blockade levels of current that can be associated with them. These two distinct fingerprints are not present for medium similarity amino acids (T, W, F, I, and C), for which only the levels having the smallest depths are observed. Second, a comparable observation can be made for positively charged amino acids K, H, and R. They present the same number of fingerprints (2 extrema, Table 1) and show distinct fingerprints compared to all the other amino acids except with M, which is extremely similar to K. Moreover, the comparison between positively charged and neutral Histidine (Supplementary Figure S12) confirms that the presence of a second extremum at a smaller duration τ_b is specific to positively charged amino acids. On the other hand, H and R present fingerprints with very high similarities within each other and with P, but with a different number of extrema (2 vs. 1). Compared to E and D, the two fingerprints observed for K, H, and R are characterized by different durations for smaller depths (Figure 4E).

TABLE 1

TABLE 1. Characteristics of extrema per amino acid (a. a.) extracted from 2D PDFs of cluster means $<\mathrm{\Delta }{I}_b>$ and $<{\tau }_b>$ shown in Figure 4C. N_e corresponds to the number of extrema per a. a.

Overall, in addition to charged amino acids, which present specific characteristics and can be easily identified, T and L amino acids also present singular behavior with 4 and 3 fingerprints (Table 1), respectively. These two amino acids can also be easily identified visually from clustering of levels duration and depth of blockade events. Within each amino acid family, starting with the polar/neutral family, only S and Q show high similarity, while all the others present very low similarity within each other. It is noticeable that N amino acid, although being characterized by a single fingerprint as many other neutral amino acids (80% of them), differs by possessing the smallest and relatively short level of blockade current among all the amino acids. Then, for hydrophobic amino acids, only F and W present very similar fingerprints, as well as A and V. Finally, for the special cases family, only G and P present medium similarity. To summarize and as shown in Figure 4E, only two families of amino acids can be visually identified from their blockade levels of ionic current recorded from their translocation through single-layer MoS₂ nanopores: the positively charged amino acids on one side and the negatively charged amino acids on the other side. For neutral amino acids, T and L can also be identified, presenting singular fingerprints. This result is crucial to demonstrate the feasibility of using 2D MoS₂ nanopores for protein sequencing applications.

4 Conclusion

In the present work, we demonstrated the ability of single-layer MoS₂ nanopore sensors to differentiate positively and negatively charged amino acids from neutral ones using classical MD and unsupervised machine learning-based models. From the large variability of ionic current traces monitored during translocation simulations and shown in Figure 3B and Supplementary Figures S5–S8, we developed a methodology to extract relevant blockade levels of ionic current based on multiple translocations (readouts) of a given amino acid. We used structural break detection applied to the different traces. Then, 2D clustering of blockade depth (drop) and duration (dwell) allows us to statistically identify relevant discrete blockade levels, hereafter called fingerprints specific to each amino acid. From this methodology, we showed that both positively and negatively charged amino acids are characterized by two fingerprints, while most of the neutral amino acids are characterized by a single one (except T, L, and M). In addition, the similarity between amino acids fingerprints is very low, with 60% of the similarities between pairs of amino acids being below 30%, with 30% being between 30% and 70%, and 10% larger than 70%. From the present conclusion, we propose the use of Coarse-Grained SEQuences (CGSEQs) of proteins for their identification. CGSEQs are made of three motifs A, B, or C, A being positively charged amino acids (K, H, and R), B being negatively charged amino acids (E and D), and C being neutral amino acids. For example, the CGSEQ of the KTKEGV sequence, which is a specific motif of the protein α-synuclein, a biomarker of Parkinson’s disease (Dettmer et al., 2015; Nicolaï et al., 2020), is ACABCC.

As a proof of concept, we tested the CGSEQ protein sequencing hypothesis by using the protein sequences available from the ASTRAL database (Brenner et al., 2000), which provides representative subsets of proteins after the elimination of doublons and sequence identity larger than 95%. It corresponds to a total of 13,000 protein sequences instead of 35,000 available. For each pair of sequences of the same length, we computed the CGSEQ percentage identity as the normalized dot product between simplified sequences by assigning value 1 for the product of two identical symbols and 0 otherwise. For example, the dot product of ACAB with BCAA is (0 + 1 + 1 + 0)/4 = 0.5. As shown in Figure 5A, the average percentage of CGSEQ identity, computed considering at least 10 protein sequences of the same length for each length available, varies from 9.0% to 21.6%, with an average score of 13%, which is very low. By comparison, the average percentage identity using the full sequence of amino acids is 6% (values range between 5.4% and 17.2%). In addition, if we consider one of the largest ensembles of protein sequences of the same length, i.e., N = 99 amino acids, we observe that 6% of CGSEQ identities are exactly zero (Figure 5B). Moreover, 35% and 92% of the CGSEQ identities are below 10% and 20%, respectively (Figure 5C). Therefore, the present results and the CGSEQ identity analysis demonstrate that the differentiation of positively charged, negatively charged, and neutral amino acids using MoS₂ nanopores would allow the identification of proteins from their sequences. This is a major finding for further protein sequencing applications as it seems that the goal of detection of every amino acid of a polypeptide for its identification is not necessary.

FIGURE 5

FIGURE 5. (A) Average CGSEQ percentage identity (left y-axis) as a function of the sequence length computed from protein sequences available in the ASTRAL database. Green and red dots indicate the identity values using the full sequence and the coarse-grained sequence, respectively. Blue dots indicate the number of sequences as a function of the sequence length from the database (right y-axis). (B) CGSEQ identity matrix computed between protein sequences of length N = 99 available in the ASTRAL database. (C) Histogram of CGSEQ identity computed between protein sequences of length N = 99 available in the ASTRAL database.

Data availability statement

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Author contributions

AUH: data curation, formal analysis, software, validation, and writing–original draft. PD: data curation and writing–review and editing. CG: methodology and writing–review and editing. AN: conceptualization, data curation, formal analysis, methodology, supervision, validation, writing–original draft, and writing–review and editing. PS: conceptualization, funding acquisition, project administration, supervision, and writing–review and editing.

Funding

The authors declare financial support was received for the research, authorship, and/or publication of this article. This work is part of the project SEPIA supported by the EIPHI Graduate School (contract ANR-17-EURE-0002), the Conseil Régional de Bourgogne-Franche-Comté, and the European Union through the PO FEDER-FSE Bourgogne 2021/2027 program.

Acknowledgments

The simulations were performed using HPC resources from DSI-CCuB (Université de Bourgogne).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors declare that they were editorial board members of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fnano.2023.1296454/full#supplementary-material

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