## Introduction

In recent years, nanopore-sequencing technology has matured to an extent where it is now used in the industry (e.g., Oxford Nanopore, Genia) as a long-read, single base resolution, and label-free detection platform. The parallel use of thousands of pores and the ability to read a chain of DNA thousands of times empower the sequencing technology with single base resolution. Specifically, with the advances in data alignment, machine learning and data processing, the fast and long-read sequencing features obtained from the nanopore-sequencing technology have become practicable since multiple readings and statistical learning can alleviate the problem of noise in detection.1,2,3,4,5 Ionic current and residence time (signal bandwidth) of each base in the nanopore are the primary detection signatures, which are used as features in data classification.6,7,8 However, the fact that these signals overlap with each other for different DNA bases, has inspired scientists to propose other signal types or to functionalize the existing nanopores and discover new materials for improved signal resolution.9,10 The conventional Si3N4 pore and other solid state nanopores have a thickness of several nanometers2 limiting the single base recognition of biological molecules.3,6 The thickness of these membranes results in the encapsulation of multiple DNA/amino acid bases/residues, making it difficult to decompose the signal associated with each base.11,12,13,14,15

A single-layer molybdenum disulfide (MoS2) which is a 2-dimensional (2D) material with a three-atom thick lattice of Mo and S atoms has an appropriate bandgap for use as an electronic transistor.16 Recent experimental17,18 and computational19 work has shown that a MoS2 nanopore has a high signal-to-noise ratio for DNA base detection making it an attractive material for biological sensing. In addition, the stickiness of the biological molecules to the mouth of MoS2 nanopore can be significantly lowered by irradiation of sulfur atoms creating a molybdenum dominated pore.18 Compared to other 2D materials (graphene and boron nitride), MoS2 nanopores can operate without degradation for an extended duration of time.18,20

Many diseases including cancer, diabetes and digestive disorders are caused by malfunctioning of ribosomes (Ribosomopathies).21 As a result, the amino acid chain might have a faulty transcription from DNA. Therefore, identification of an amino acid chain is necessary for diagnostic purposes and early stage of cancer/other disease detection.22 In fact, the data acquired from proteomic fingerprints can be more trustworthy in defining the health status of humans than the genome; but it is important to note that acquiring and analyzing such data is more difficult.23

Recent work has used graphene nanopores for protein identification using molecular dynamics (MD) simulations where stepwise translocation of polypeptides has been shown. These results make interpretation of ionic current signal feasible.24 Kolmogrov et al.25 used machine learning (random forest and support vector machines) to process the ionic current signals obtained from solid-state nanopore sequencing of a polypeptide chain. They showed that the signals obtained using a sub-nanometer pore is sensitive enough for the detection of protein sequence.

Given the significance of amino acids identification in health diagnostics and the potential of MoS2 material, we characterized the ionic current and residence time associated with the 20 standard amino acids by translocating them through a single-layer MoS2 nanopore using extensive simulations. Supervised and unsupervised machine learning and classification techniques were used to classify and detect signals with a high prediction accuracy of up to 99.6%.

## Results and discussion

By performing detailed MD simulations, we demonstrate that a single-layer nanoporous MoS2 can identify individual amino acids with high accuracy. Figure 1 shows the schematic of a typical simulation box consisting of a single-layer MoS2 membrane (with the pores considered), an amino acid chain (16 identical residues), water and ions. The water molecules are not shown in the figure.

### Ionic currents and residence times

To characterize the ionic current characteristics for different pore sizes and validate the simulations against experimentally known properties (e.g., conductance), we performed MD simulations with a bare pore (with no amino acid chain in the system) applying both positive and negative biases. The I-V curves for different sizes of the nanopore in MoS2, in the absence of the polypeptide chains, show an Ohmic behavior (Fig. 1d). The conductance (G) is computed to be 2.69, 4.96, and 10.64 nS for the 1.35, 1.85, and 2.52 nm diameter pores, respectively. These conductance values are in good agreement with the experimentally measured conductance of MoS2 nanopores with similar pore diameters.26 In addition, the conductance values obtained from the model developed by Wannanu et al.27 are comparable to the values computed in the simulations.

The amino acids are translocated through the nanopore using an external force under a constant bias of 200 mV. All the production simulations were performed for the pore with a diameter of 1.85 nm. The average values of ionic currents and residence times for all the amino acids are tabulated in Fig. 2. The largest ionic current values (with 55–65% blockade) are observed for the amino acids (G, A, S, T, C) in the first row of Fig. 2. G, A, S, T, C are among the smallest amino acids based on the combined vdW radii.28 G, A and S exhibited a very fast translocation with an average residence time per amino acid of 33.02, 64.52, and 23.10 ps, respectively. Of all the amino acids in Fig. 2, Methionine exhibits an inconsistent ionic current of −18.21 pA. We investigated this anomaly by probing further into the components of the current (anion and cation contributions). We observed an intermittent anion binding to the thiol groups of Methionine resulting in a strong negative ionic current due to the fact that the Methionine is pulled by the external forces and drags the anions in the direction of the electric field (see the supporting information).

In Fig. 3a, the residence time and ionic current statistics for all the 20 amino acids are shown. L, V, E, M, P, and I amino acids show similar ionic current and residence time statistics. Their residence time is between ~100 and ~1000 ps and their ionic current is between ~13 and ~50 pA (except for the anomalous negative current of M amino acid). These amino acids have both smaller sizes and higher residence times compared to G, A, S, T, and C amino acids. The common feature among this class of amino acids is their hydrophobic nature (Fig. 3b). A 3D scattered plot of the vdW volume of each amino acid (vdW volumes are taken from ref. 28) as a function of its residence time and ionic current is shown in Fig. 3c (a similar plot is available in the supporting information for the mass of amino acids). The obvious trend in this data is the correlation of the volume of amino acids (or mass) with their ionic current, and residence time (higher volume (or mass) mostly leads to higher residence time and lower current). We find that the residence time (TR, ps) and the mass ($$\bar M$$, Da) are related by a power law relation, $$T_R = 4.66\left( {10^{ - 9}} \right)\bar M^{5.339}$$ (supporting information).

Larger amino acids such as W, Y and F have larger residence times (~1500 ps < TR < ~4000 ps) and low ionic currents (<10 pA, where the bare pore current is 571 ± 2.1 pA). W, Y, and F have a phenyl group that occupies most of the pore (the phenyl group alone has a vdW diameter of 7.5 Å) and the blockade is higher (see the supporting information) for these amino acids. Specifically, W contains an α-amino group, an α-carboxylic acid group, and a side chain indole, making it the largest amino acid. W’s ionic current (1.8 pA, with 99.9% pore blockade) depicts the larger size of this amino acid (Fig. 3c). In the supporting information, we compared the blockade of the MoS2 nanopore in different configurations of ALA (A) and TRP (W) inside the pore.

Glutamate (E) and Tryptophan (W) have the lowest and highest standard deviation (STD) of both ionic currents and residence times among all amino acids, respectively. Amino acids N, H, D and also Q, K and R have both intermediate ionic current and residence time (~50 pA < Ic < ~200 pA and ~500 ps < TR < ~2000 ps). For these amino acids with intermediate residence time and ionic current, the common feature is their polar behavior (Fig. 3b). Based on the Ic and TR values, we classified the amino acids into very small (G, A, S, T, C: very low TR and High Ic), very big with phenyl groups (F, W, Y: very high TR and very low Ic), small and hydrophobic (L, V, P, M, E, I: low TR and low Ic) and polar (N, H, D, Q, K, R: intermediate Ic and intermediate TR) as shown in Fig. 3b.

It is noteworthy that these simulations are for short homopeptides. In protein identification platforms with different amino acids in a sequence, the relative distance between the cluster centers can also be used to identify an amino acid. To this end, we can use ML with extrapolative properties.

### Machine learning (ML)-based prediction

In practice, the data acquired from amino acid translocation through a MoS2 nanopore is unlabeled and a priori information is not available on the sensing ability (i.e., identifying the type of amino acid) of the nanopore. Here, we employ ML-based models to predict the amino acid type if the ionic current and residence time are known from nanopore detection. In addition, we also attempt to identify the most accurate and predictive ML model. To estimate the accuracy of amino acid class (or type) prediction of each model, the Monte Carlo Cross Validation (MCCV) algorithm is used. The MCCV randomly splits the dataset into test (unlabeled) and train sets (labeled). We split the dataset keeping 80% of it for training and the rest for testing the prediction by the trained models. In the training process, we used three ML models, namely, k-nearest neighbor, logistic regression and random forest, available in the Scikit-learn machine learning package in Python.29 Initially, using each model, the training was performed with the labeled data from all 20 amino acids having 100 data points each for the current and residence time. The details on the three ML models and the optimization technique to determine the parameters are described in the supporting information. To identify and predict the class of a future reading (amino acid translocation data from the nanopore), we generated a grid with mesh size 0.5 × 0.5 (pA, ps) with the upper and lower bounds of the current (along x-axis) and residence time (along y-axis). The upper and lower bounds of ionic current and residence time (current: −45–330 pA, residence time: 0.1–3800 ps) can be obtained from Fig. 3a. To account for data at the boundaries, we extended the upper and lower limits by 2 pA and 2 ps. A total number of 2,885,714 grid squares were generated in current/residence time space. Each grid square can be thought of as a hypothetical sensor reading. Many of these grid squares in the top right corner of the current/residence time plot are beyond the scope of the available data; therefore, the practical number of hypothetical readings is lower in actuality. The amino acid class/type of each grid square is predicted using all the three ML models. The prediction landscapes are shown in Fig. 4. The prediction is denoted by different colors for different amino acid types. The mean values of the labeled data (from Fig. 3a) are marked on each figure to compare with the prediction. The prediction of amino acid class regions with k-nearest neighbor is affected by different scales of ionic current (two orders of magnitude variation) and residence times (three orders of magnitude variation) (Fig. 4a). Since the scale of residence time is higher than that of ionic current, the prediction of the region associated with each amino acid is dominated by the residence time data (Fig. 4a). Logistic regression shows smooth and straight decision boundaries (Fig. 4b) whereas random forest shows flexible and mixed decision boundaries (Fig. 4c). The accuracy of logistic regression, k-nearest neighbor and random forest is 72.45, 94.55, and 99.6%, respectively. From these results, we can conclude that random forest and k-nearest neighbor are the best models for the prediction. Random forest exhibits the best accuracy (up to 99.6%) in the regions where training data (labeled data) is populated.

### Heterogeneous chain of amino acids

The ML classification is used to predict the type of amino acids in a practical amino acids chain. As the actual proteins do not typically contain chains of polypeptides, a chain of mixed type amino acids has been translocated in 10 different long-time simulations (each ~100 ns) in which a smaller force per residue of 0.4516 pN is applied. The ionic current as a function of translocation time is plotted for one of the simulations (Fig. 5a). The chain consists of 16 amino acids as shown in Fig. 5b. To alleviate the challenge of noise, the ionic current and residence time of each amino acid are averaged over the 10 simulations (Table 1). The resulting currents and residence times are then used as unlabeled data by the polypeptides trained classification models in Fig. 4. Since a smaller force per residue is applied, the residence times are much larger than that of the polypepties. Therefore, to use the classification from the training on the polypeptipes, which are based on larger forces, the currents and residence times of both polypepties and mixed amino acids chain are normalized by the maximum values of current and residence time, respectively (Table 1). The type of each amino acid in the mixed chain is predicted and the accuracy of prediction for logistic regression, k-nearest neighbor and random forest is found to be 31.25, 43.75, and 62.50%, respectively. The lower accuracy is due to the large noise in the chains of mixed amino acids. The noise is expected to be much lower in experiments where the translocation times of each residue are much longer.

### MoS2 pore sensitivity

To characterize the sensitivity of MoS2 pore with regard to its size, another set of simulations for two pore sizes of d = 1.85 nm and d = 2.52 nm were performed (d = 1.35 nm pore is not used as it is too small to accommodate a residue of a large amino acid). We selected two amino acids (W and Y) having similar ionic currents and residence times (Fig. 3a). A force of 0.7643 pN was applied. We performed 100 simulations with an applied transmembrane bias of 200 mV for each amino acid (200 simulations in total). All other simulation parameters were kept the same except for the pore size. The ionic current and residence time data represent different patterns and values for the two pore diameters (Fig. 6). For d = 1.85 nm, TYR (Y) and TRP (W) show quite distinguishable residence times with the mean values of ionic current and residence time (5.83 pA, 1787 ps) and (2.23 pA, 2866 ps), respectively (these values are for 100 samples per each pore diameter and the average values differ slightly from the data in Fig. 2). For d = 2.52 nm, the ionic current and residence times clusters overlap and does not exhibit the distinguishability of the 1.85 nm pore (Fig. 6). The mean values of ionic current and residence time are (TYR: 1125.91 pA, 645.84 ps) and (TRP: 964.92 pA, 786.92 ps). The inter cluster distance (reported as a dimensionless number and computed by treating each unit of current and time as one unit) between TYR and TRP, for the pore diameters of 1.85 nm and 2.52 nm is 1079 and 51.9, respectively. Based on this data and inter cluster distances, it can be inferred that the pore with a smaller diameter (d = 1.85 nm) is 20 times more sensitive compared to the 2.52 nm pore (the ratio of the distance between cluster means of 1.85 nm pore to 2.25 nm pore is ~20). In general, as the diameter increases, the sensitivity decreases significantly. Our conclusion is consistent with the experimental result of Feng et al.18 for DNA identification in different MoS2 pore sizes. It is also notable that there is a lower limit to the nanopore size for the translocation of biomolecules. For DNA, pore sizes smaller than 2.0 nm will cause a permanent blockade of pore due to the large size of bases and the presence of deoxyribose. For amino acids, it can be as small as ~1.80 nm.

In summary, we have proposed a single-layer MoS2 nanopore for amino acid detection using ionic current, residence time and machine learning-based predictive models. We demonstrated that the acquisition of current-residence time (with at least 1000 reads per amino acid type) would yield an accuracy of up to 99.6% for amino acid detection assisted with machine learning. The 20 amino acids, each with 16 units, were categorized into different classes based on the similarity of current-residence time data. We found that the W, Y, and F residence times are significantly higher than those of A, C, G, S, and T. However, their ionic current data has an inverse relationship with the residence time (i.e., higher residence time, less current and more blockade). We also found that the polar characteristics of K, Q, R, N, H, and D give rise to intermediate current levels and residence times. The hydrophobic amino acids, in spite of their small size, exhibit very low currents and intermediate residence times. We also employed and compared different machine learning classification techniques to predict the amino acid type based on the current-residence time training data.

## Methods

Molecular Dynamics simulations were performed using the LAMMPS package.30 Each simulation box consists of a single-layer MoS2 membrane, an amino acid chain (16 identical residues), water and ions (Fig. 1.a). The MoS2 membrane, amino acids, water molecules and ions were generated using visual molecular dynamics.31 A nanopore is created in MoS2 membrane by removing the unwanted atoms in the center of the MoS2 lattice. The MoS2 pore has both Mo and S atoms at its edge to replicate the most probable pore architecture in experiments. The system has dimensions of 6 × 6 × 10 nm in x, y, and z, respectively. The membrane is fixed in the xy plane at z = 0 and the amino acid chain is initially placed just above the nanopore center along the of the pore (Fig. 1.a). The box containing the membrane and the polypeptide is solvated with water molecules with a padding of ~3 nm in z. Then the resulting box is ionized with a molarity of ~1 M (sodium and chloride). A typical simulation box contains about 32,000 atoms. A snapshot of proline chain translocating through the MoS2 pore is depicted in Fig. 1b. The pore (diameter = 1.85 nm) used in the production simulations has an accessible area of 156.9 Å2. The pore diameters are computed using the method in ref. 32. To characterize the size-dependent pore sensitivity of MoS2 and study the I-V curves, we created two other pores with an average diameter of 1.35 and 2.52 nm (Fig. 1c).

The TIP3P water model was used and the SHAKE algorithm was employed to maintain the rigidity of the water molecules. The CHARMM27 force field33 was used for water molecules, ions and polypeptides. For MoS2, the non-bonded interactions were modeled by the combination rule to obtain the Lennard-Jones (LJ) parameters.34 The LJ cutoff distance was 12 Å. The long range electrostatic interactions were computed by Particle-Particle-Particle-Mesh.35 Periodic boundary conditions were applied in all the three orthogonal directions.

For each simulation, the energy of the system was minimized for 30,000 steps. Next, to reach the equilibrium water density (1 g/cm3), the system was simulated in NPT ensemble for 2 ns at a pressure of 1 atm and a temperature of 300 K. Then, the system is further equilibrated in NVT ensemble for 2 ns. Temperature was maintained at 300 K by using the Nosè-Hoover thermostat with a time constant of 0.1 ps.36,37 The production simulations were performed in NVT ensemble for up to 40 ns depending on the translocation speed of polypeptides. In each simulation, a constant bias of 200 mV was applied in the z-direction. Since only 4 out of 20 amino acids are charged, an external force per residue was needed to pull the polypeptide chain through the nanopore. Different forces were applied in the range of 0.4169–1.1811 pN to find the common applied force that can successfully translocate all twenty amino acids (see supporting information for translocation history vs. different applied forces). For residence times, we ran 100 simulations per amino acid type (total 2000 trajectories) with an applied force of 0.7643 pN, but we used different external forces for ionic current calculations to better mimic the experimental conditions. During all the simulations, the MoS2 atoms were held fixed in space (See supporting movie for Proline translocation through a MoS2 nanopore).

We monitored the time-dependent ionic current, I (t), in the pore. We computed the ionic current through the nanopore by using the definition of current, I (t) = dq/dt, as $$I\left( t \right) = \frac{1}{{L_z}}\mathop {\sum}\limits_{i = 1}^n {q_i} \left[ {\frac{{z_i\left( {t + \delta t} \right) - z_i\left( t \right)}}{{\delta t}}} \right]$$, where the sum is for all the ions, δt is chosen to be 5 ps, and z i and q i are the z-coordinate and charge of ion i, and n is the total number of ions, respectively.10 To get less noisy ionic current, we skip the first and last 10% of the trajectory of the translocation. For all the trajectories used in the post-processing analyses, the presence of amino acids is checked frame by frame inside the pore. The frames, where amino acids are absent, are discarded. The residence time per residue is computed by dividing the total translocation time of the polypeptide chain translocated through the nanopore by the number of residues.

To achieve statistically meaningful data, we ran 4283 simulations in parallel (4103 translocation simulations, 80 I–V characteristic simulations, 100 pore sensitivity simulations). For each amino acid, at least 200 replica trajectories are used (out of 4103 simulations, 103 simulations were discarded because of no translocation event). This resulted in an aggregate data of 2 TB as well as a total combined simulation time of 66 µs (see the supporting information for details on all the simulation sets.). We used Python Numpy for post-processing the data.38 After collecting the ionic currents and residence times for the 20 amino acids, we created two sets of unlabeled and labeled (by the names of acid types) data for machine learning analyses. In the labeled data, we have three columns consisting of ionic currents (Ic), residence times (TR) and amino acids labels (e.g., THR, TYR, ALA, …). In the unlabeled data, we removed the third column with amino acid labels. Both the unlabeled and labeled data are available as supporting information (Amino_acid_IR.xlsc).

### Supporting Information Available

Machine Learning parameter selection and optimization technique, pore blockade for ALA and TRP for different conformations inside the pore, effect of mass of amino acids, translocation history of residues versus different applied forces, and Methionine thiol binding to anions.

### Data availability

The data related to the findings of this work are available from the corresponding author subject to a reasonable request.