A Physics-Augmented Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Authors: Cailong Hua
Sivaraman Rajaganapathy
Rebecca A Slick
Joseph Vavra
Joseph M. Muretta
James M. Ervasti
Murti Salapaka
Venue: ICML 2025 poster (2025)
Keywords: Single molecule force spectroscopy
protein unfolding
experimental datasets
application in single molecule identification
physics-augmented deep learning framework
physics-based Monte Carlo simulation
Primary area: applications->chemistry_physics_and_earth_sciences

Abstract: Deciphering protein folding and unfolding pathways under tension is essential for deepening our understanding of fundamental biological mechanisms. Such insights hold the promise of developing treatments for a range of debilitating and fatal conditions, including muscular disorders like Duchenne Muscular Dystrophy and neurodegenerative diseases such as Parkinson's disease. Single molecule force spectroscopy (SMFS) is a powerful technique for investigating forces involved in protein domains folding and unfolding. However, SMFS trials often involve multiple protein molecules, necessitating filtering to isolate measurements from single-molecule trials. Currently, manual visual inspection is the primary method for classifying single-molecule data; a process that is both time-consuming and requires significant expertise. Here, we both apply state-of-the-art machine learning models and present a novel deep learning model tailored to SMFS data. The proposed model employs a dual-branch fusion strategy; one branch integrates the physics of protein molecules, and the other operates independently of physical constraints. This model automates the isolation of single-molecule measurements, significantly enhancing data processing efficiency. To train and validate our approach, we developed a physics-based Monte Carlo engine to simulate force spectroscopy datasets, including trials involving single molecules, multiple molecules, and no molecules. Our model achieves state-of-the-art performance, outperforming five baseline methods on both simulated and experimental datasets. It attains nearly 100\% accuracy across all simulated datasets and an average accuracy of $79.6 \pm 5.2$\% on experimental datasets, using only $\sim$30 training samples, surpassing baseline methods by 11.4\%. Notably, even without expert annotations on experimental data, the model achieves an average accuracy of $72.0 \pm 5.9$\% when pre-trained on corresponding simulated datasets. With our deep learning approach, the time required to extract meaningful statistics from single-molecule SMFS trials is reduced from a day to under an hour. This work results in SMFS experimental datasets from four important protein molecules crucial to many biological pathways. To support further research, we have made our datasets publicly available and provided a Python-based toolbox (https://github.com/SalapakaLab-SIMBioSys/SMFS-Identification).

A Physics-Augmented Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Cailong Hua Sivaraman Rajaganapathy? Rebecca A. Slick Joseph Vavra Joseph M. Muretta
James M. Ervasti Murti V. Salapaka"
Abstract
involving single molecules, multiple molecules, and no molecules. Our model achieves state-of- the-art performance, outperforming five baseline methods on both simulated and experimental datasets. attains nearly 100% accuracy across all simulated datasets and average accuracy of 79.6 = 5.2% on experimental datasets, using only ~30 training samples, surpassing baseline methods by 11.4%. Notably, even without expert annotations on experimental data, the model achieves an average accuracy of 72.0 + 5.9% when pre-trained on corresponding simulated datasets. With our deep learning approach, the time required to extract meaningful statistics from single-molecule SMFS trials is reduced from a day to under an hour. This work results in SMFS experimental datasets from four important protein molecules crucial to many biological pathways. support further research, we have made our datasets publicly available and provided Python- based toolbox com/ 5a
Deciphering protein folding and unfolding pathways under tension is essential for deepening our understanding of fundamental biological mechanisms. Such insights hold the promise of developing treatments for range of debili- tating and fatal conditions, including muscular disorders like Duchenne Muscular Dystrophy and neurodegenerative diseases such as Parkinson's disease. Single molecule force spectroscopy (SMFS) is powerful technique for investigating forces involved protein domains folding and unfolding. However, SMFS trials often involve multiple protein molecules, necessitating filtering to isolate measurements from single-molecule trials. Currently, manual visual inspection is the primary method for classifying data; a process that is both time-consuming and requires significant expertise. Here, we both apply state-of-the-ar machine learning models and present novel deep learning model tailored to SMFS data. The proposed model employs dual-branch fusion strategy; one branch integrates the physics of protein molecules, and the other operates independently of physical constraints. This model automates the isolation of single-molecule measurements, significantly enhaneing data processing efficiency. To train and validate our approach, developed physics-based Monte Carlo engine to simulate force spectroscopy datasets, including trials
moleccle
SMFS Irrs-Iddetiiiiaatii
1. Introduction
Many biological processes depend on controlling mechani- cal forces achieved via the folding and unfolding of domains in molecules like titin (Rief al., 1997; 1998; Oberhauser et al., 2001), dystrophin and its homologue utrophin (Raja- ganapathy et al., 2019; Ramirez et al., 2023), neurotoxic pro- teins (Hervás et al., 2012), and extracellular matrix protein tenascin (Oberhauser et al., 1998). For example, dystrophin and utrophin work as molecular shock absorbers that limit myofiber membrane damage when undergoing reversible unfolding upon muscle stretching and contraction (Ervasti, 2007). Evidently, studying mechanical properties of single molecules can provide vital insights into mechanisms of debilitating diseases. Instruments such as optical tweezers (Ashkin et al., 1986) and atomic force microscopes (AFMs) (Binnig et al., 1986) have enabled single molecule force spectroscopy (SMFS), where molecular forces in the femto
Deearrmeet of Electrical and Computer Engincering, Uni- versity of Minnesota Twin Cities, Minncapolis, MN 55455 'Department of Artificial Intelligence and Informatics, Mayo Clinic, Rochester, MN 55905 DDepartment of Biochemistry, Molecular Biology and Biophysics, University of Minnesota Twin Cities, Minneapolis. MN 55455. Correspondence to: Cai- long Hua <hua00023 umn.edu>, Murti V. Salapaka <mur- tis udu.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
to nano-Newton range, over sub-nanometer to micrometer distances, can be measured and studied. In SMFS ex- periment, measurements from force probe are recorded while it is made to interact with molecules of interest. Since the size of a typical force probe is orders greater than a typical bio-molecule, the probe may come in contact with one or more molecules. Measurements obtained from in- teractions involving more than one molecule confound the interpretation of results and are significant challenge in characterizing the behavior of single molecules. How to identify and isolate measurements and data that result from a single-molecule is an important objective for SMFS.
volves purifying protein molecules from expression systems (either bacterial or insect), preparing samples with the target protein molecules, and setting up the AFM to automatically perform multiple pulls to obtain numerous SMFS trials. Sub- sequent to obtaining trial data, an expert manually filters which curves correspond to single molecules. Each session typically involves approximately 2,000-5,000 trials, requir- ing the expert to meticulously sift through the data to filter out curves that not from single molecules. This process can take between 12 and 24 hours. To ensure reliable as- sessment, the molecule is expected to be expressed at least thrice, with each expression resulting in multiple sessions, making the cumulative time investment significant. This article aims to reduce this time to less than one hour.
The use of chemical functionalization of probes, along with molecular fingerprints has emerged as an approach for iden- tifying single molecule trials ( (Yang et al., 2020a). Chemical functionalizatton modifies the surface of the force probe and substrate to enable site-specific attachment of molecules, where fingerprints are well-characterized molecules that yield distinct unfolding patterns. Here fingerprints in the trials can be leveraged to discern single molecule trials from trials that result from multiple molecules. However, surface chemical functionalization is time-consuming, often taking at least 6 hours (Zimmermann et al., 2010), and demands careful handling and practice. Moreover, advanced filtering techniques, informed by an understanding of all molecules involved in the complex, are essential for effectively identi- fying single molecule trials (Yang et al., 2020a).
In this work, we introduce state-of-art machine learning models and present a novel deep learning model that aug- ments the unfolding physics of protein molecules to accu- rately classify SMFS data into three classes: 1) no molecule, 2) single molecule, and 3) multiple molecules. The model employs a dual-branch fusion strategy, one branch incor- porating the physics of protein molecules and the other operating independently of physical constraints. To train and validate our approach, we present the first publicly ac- cessible datasets, both simulated and experimental, obtained from non- non-specific pulling of multi-domain molecules: titin, utrophin, and dystrophin (Hua et al., 2024). The simulated datasets, comprising of SMFS trials that originate from a single molecule, multiple molecules, or no molecules, are created with a novel physics- based Monte Carlo engine. Ex- tensive evaluations on these datasets, in comparison with five state-of-the-an baseline models, demonstrate efficacy of our proposed model. Specifically, our model achieves nearly 100% accuracy on the simulated datasets, outperforming baselines by 6%. When testing on experimental datasets, our model achieves average accuracies of 79.6 + 5.2%, surpass- ing baselines by 11.4%, with only approximately 30 training samples. Even without expert annotations on experimen- tal data, our model can still achieve average accuracies of 72.0 +.9% when pre-trained with corresponding simulated datasets. With this deep learning approach, the time required to extract meaningful statistics from single-molecule SMFS trials is reduced from a day to under an hour. is expected that this pilot effort will stimulate significant activity with associated impact of ML methods on the understanding of protein folding and unfolding that emphasize mechanical properties.
In contrast, conducting experiments without functionalizing probes and introducing fingerprints into the native molecule has significant advantages. Probes without functionaliza- tion are easier and less expensive to manufacture, and bio- molecules without fingerprints engineered into their struc- ture are easier to synthesize. Moreover, there is greater confidence that the experimental data characterizes the un- altered native bio-molecule without any confounding ef- feets introduced by fingerprints. Despite these advantages, when there are no fingerprints, distinguishing data that re- sult from single molecules and multiple molecules is more challenging. Currently, prevalent accepted method for dis- tinguishing the data is based on visual inspection, which is a cone-con process that demands a high level of expertise (Bornschlögl & Rief, 2011; Lyubchenko, 2018). Additionally, trials need to be collected from a large num- ber of experiments, not only to ensure statistical confidence but also because the molecule concentration is generally lowered to minimize the possibility of involving multiple molecules (Ramirez et al., 2023; Oberhauser et al., 2001). These factors hinder obtaining precise statistics of single molecular trials without functionalization and the genera- tion of large, annotated dataset suitable for training deep learning models.
2. Related work
Single molecule classification A ID convolutional neu- ral network trained using triplet loss function (Hoffer & Ailon, 2015) was utilized classify force curves into single, multiple, or no molecule classes, with reported accuracy
A typical traditional workflow for SMFS experiments in-
2

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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
b
No molecule
Single molecule
Multiple molecules
Cantilever
Deflection
(1)
(2)
(4)
d
(6)
(3)
Cantilever
substrate distance
Extension
Folded
domains
Substrate
d
No molecule
Single molecule
Multiple molecules
300
300
Unfolding Events
300
250
250
200-
200-
Force [pN]
Force [pN]
Force [pN]
150
150
150-
100-
100
100-
50
50
-50
200
400
600
800
-50
50
100
150
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-50
100
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500
Extension [nm]
Extension [nm]
Extension [nm]
Figure 1. Illustration of AFM based SMFS. Schematic showing the desirable of single protein molecule with four folded domains under tension between the tip of the AFM cantilever and the substrate. The deflection d and the separation between the cantilever and the substrate measured. The tensile force the protein molecule computed from the deflection d. Depictions of possible scenarios, categorized into three classes: (I) no molecule present between the tip and substrate, (2-3) single molecule or a section of a single molccule present between the tip and the substrate, and (4-6) multiple molecules sections multiple molccules between the tip and the substrate. (c-e) Show example force curves representative of the three different classes, with blue circles highlighting unfolding events.
ranging from 65 - 70% (Waite et al., 2023). Moreover, a machine learning workflow was proposed to iteratively clas- sify different unfolding pathways of single molecule curves (Doffini et al., 2023). However. these two datasets were collected with chemically functionalized probes and finger- prints. The chemical functionalization process is dependent on the specific molecule and thus cannot be made agnos- tic to the molecule under investigation. Moreover, in the first dataset, each single molecule curve contains only one unfolding event (Waite et al., 2023), simplifying the classifi- cation problem; the second dataset comprises images rather than time series data (Doffini et al., 2023), which introduces redundancy given that force curves inherently time series data. There are currently time series datasets available, which are from non-specings non-specific pulling of multi-domain pro- tein molecules; most naturally occurring protein molecules have multiple domains. Here, we construct such datasets for classification purposes.
time series classification (TSC) algorithms, including both non-deep learning methods (Bagnall et al., 2017) and deep learning methods (Fawaz et al., 2019; Wang et al., 2017), are present in prior-art. Although more than 80 different datasets from the University of California, Riverside (UCR) time series classification repositories (Dau al., 2019) evaluated with these methods, none of these datasets include SMFS data. Methods that do not use deep learning become computationally intensive and impractical to execute on large-scale datasets (Bagnall al., 2017; Fawaz et al., 2019). In this article, we focus on deep learning methods to classify our SMFS datasets.
3. Problem formulation
We first describe an atomic force microscope (AFM) based SMFS setup. Here, a microcantilever with a sharp tip is pressed against a substrate on which the protein molecules under study are deposited. Under applied force, parts of more protein molecules non-specifically attached
Time series classification (TSC) More than hundreds of
3

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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
to the cantilever tip; characterized by stochastic adhesion event (Leite et al., 2012). Upon retraction of the cantilever from the surface, sections of the protein molecules between the tip of the cantilever and the substrate experience a ten- sile force. The record of the force F experienced by the cantilever (and therefore the molecule) versus molecule ex- tension x known as force curve, as depicted in Figure Ic-e. If only one protein molecule is present between the cantilever tip and substrate, the force curve unveils impor- tant mechanical properties of the protein molecule. We illustrate such scenario in Figure la, where a single pro- tein molecule with four folded domains is attached between the substrate and the tip of the cantilever. As the cantilever retracts, the molecule experiences mechanical tension, even- tually causing a folded domain to unfold. The applied force drops abruptly when domain unfolds, as highlighted by the blue circles in Figure 1d. This process continues until either all domains are unfolded or the connection between the cantilever and the substrate is broken (Rief et al., 1997), producing a saw-tooth pattern of force curves (Figure Id).
to one of the three classes Given a dataset of samples, D ( y (F(m), x(m), y())], the goal is to design an effective deep learning model capable of ac- curately predicting the class label of a force curve.
4. Proposed model
We introduce Polymer Elastic Models Neural Networks (PemNN), a novel deep learning model designed clas- sify force curves originating from no molecule, single molecule or multiple molecules. PemNN contains two branches, the force trace branch, which uses the force data F(i, and the physics- based branch, which incorporates polymer elastic models (Section 4.1) with both extension and force data, Features extracted from these branches are fused using either early fusion (depicted in Figure 2) or late fusion strategies (see Section 4.2).
Both branches pass through convolutional block, compris- ing I I-Dimensional convolutional layer, batch normaliza- tion layer (Ioffe & Szegedy, 2015) and a Rectified Linear Unit (ReLU) (Nair & Hinton, 2010) activation layer. Convo- lutional layers have demonstrated compelling performance and efficiency in time series classification (Wang et 2017; Fawaz et al., 2019; Karim et al., 2019; Pham et al., 2022; Zhang et al., 2020; Zheng et al., 2016; Foumani et al., 2021). Then features from the first convolutional block of both branches are fused with one of four methods detailed in Section 4.2. The fused output undergoes two additional convolutional blocks, and a Global Average Pooling (GAP) layer is applied reduce parameters by averaging across the time dimension (Wang et al., 2017; Fawaz et al., 2019).
In practice, the force curves can be categorized into one of three classes- 1) No molecule: where no molecule is present between the tip and substrate, 2) Single molecule: when section of single molecule
only a single molecule is present, or 3) Multiple molecules: where multiple molecules or sections of multiple molecules are present between the tip and substrate. Example experimental force curves corresponding to the three classes are depicted in Fig- ure 1c, 1d, and le respectively. The force curves originating from multiple molecules typically exhibit larger unfolding forces than those with a single molecule (Figure Ie) and have mixture of unfolding events that cannot be traced back to a specific protein molecule (Fig. lb (4-6)), con- founding useful interpretation. Here, excluding force curves with no molecule and multiple molecules is necessary to obtain accurate and interpretable data from SMFS. The iden- tification of the single molecule force curves is challenging due to number of reasons: 1) large number of force curves (2000-5000) need to be collected in single experi- ment since protein molecule capture success rates are kept at 1-5% (Oberhauser et al., 2001; Ramirez et al., 2023). 2) the study of a specific protein molecule involves at least three replications for confidence on results, 3) the force curves are corrupted from instrument measurement noise and intrinsic thermal noise of the molecules, and 4) often the protein molecules under investigation have no prior char- acterization, which makes the adjudication time consuming and difficult even for domain experts.
To further enhance temporal encoding, a long short-term memory (LSTM) (Hochreiter & Schmidhuber, 1997; Sun- dermeyer et al., 2012) layer is applied to each branch, fol- lowed by a dropout layer (Srivastava et al., 2014) to mitigate overfitting (Karim et al., 2019). Earlier studies have shown that augmenting convolutional layers with LSTM signifi- cantly improves performance in time series classification with only a modest increase in the number of parameters (Karim et al., 2019; Zhang et al., 2020; Hewamalage et al., 2021).
The outputs of the GAP and L.TT layers are concatenated and fed into a fully connected layer with three neurons, corresponding to the three classes: 1) no molecule, 2) single molecule, and 3) multiple molecules. A softmax activation function is used in the final fully connected layer, and the model is trained with categorical cross-entropy loss:
The i-th force curve, of length T0) consists of force data F I F(i) .... F(2 and extension data ( =
L(F()x(0) = r log
(o (P)),
(1)
Ix x x Each force curve (F(1), (0) is as- sociated with a class label Y. E (0, 1,2), corresponding
where L(F(),, (00) represents the loss for classifying the
force curve (F((), (Z()) Here, y/(1) is the label for class j
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
LSTM
Drapout
Polymer elartic
Contour length
BatchNorm
models
filter
Conv 1D
SMFS Force Curves
Physics-based
branch
Fusion Module
Concatenate
Conv 1D
BatchNorm
ReLU
Conv 10
BatchNorm
RelL
Global average pooling
Softmax
Extension
branch
trace
Preprocessing module
Conv 1D
BetchNomm
ReLU
Drapout
LSTM
Figure 2.
The overall architecture of the Polymer Elastic Models Neural Networks (PemNN) comprises rryysics-based branch and force trace branch, illustrated with the early fusion approach (the fusion approach shown Figure in Appendix).
of i-th force curve (2(()) E {0, 11), and (0 is predicted probability for class j of i-th force by the neural network.
maps along the filter dimension, followed by a convolution with a kernel size 1.
With late fusion method (depicted in Figure the Ap- pendix), features from the first convolutional block are inde- pendently processed through two additional convolutional blocks for each channel, with shared parameters. GAP lay- ers are applied to the outputs of both branches, and their results are fused using one of the following methods (see Appendix B): (i) Late-Concale directly concatenates the out- puts of GAP layers; and (ii) Late-Gating (Liu al., 2021) Concatenates GAP layer outputs with learnable weights.
4.1. Polymer elastic models
Polymers (proteins included) exhibit entropic elasticity that is well described by the worm-like chain (WLC) model (Bustamante et al., 1994) given by:
KBT Lp
T
F =
4
Le
4
where, F and represent the force and extension respec- tively, kg is the Boltzmann constant, 7 is temperature, Le is the contour length, and Tp is the persistence length. The con- tour length L. represents the maximal length of physically possible extension and the persistence length Lp quantifies the bending stiffness of the polymer. Other widely used polymer elastic models are described in Appendix A.1.
5. Datasets
Datasets from four different protein molecules are employed. Out of these four protein molecules, only Titin 1270 (Athena Enzyme Systems an engineered protein molecule com- posed of eight repeats of the Ig 27 domain that serves as meth-
reference protein for calibrating and validating ods. The other three protein molecules come from natural proteins with considerable variations in their sequence and structure, dystrophin and utrophin. Dystrophin is protein molecule expressed primarily at the muscle cell membrane, or sarcolemma, striated muscle tissue. Deficiencies of this protein molecule lead severe muscle wasting disorder like Duchenne muscular dystrophy (DMD), a fatal disease occurring in out of 4000 male births (Mendell al., 2012). Structurally, dystrophin is composed of four major domains: an amino terminal (NT) actin-binding domain (ABDI), large central rod domain with 24 triple helical spectrin-like repeats (SLRs) interspersed with 4 hinge domains, includ- ing second tinding domain (ABD2). cysteine-rich (CT) domain (Figure 3a).
In the physics-based based branch, the contour length Lega) is estimated each force-extension pair ,r/"), (x(()) using the WLC model with fixed persistence length Lp- A subsequent filtering step selects /' samples with Lep [0, .M), where M is the filter threshold. If the number of qualified data points is less than P, sampling is performed with replacement.
4.2. Fusion module
The early fusion approach contains four methods: (i) Early- Sum: sums convolutional feature maps; (ii) Early-Max: selects the maximum value at each element from convolu- tional feature maps, (iii) Early-Wor Wavg: computes a weighted sum of convolutional feature maps with learnable weights; and (iv) Early-Conv: concatenates convolutional feature
domain and a carboxy-termine Utrophin (Figure 3b) is a fetal homologue of dystrophin and is under active investigation dystrophin replace-
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Table J. Details of experimental datasets
NUMBER CURVES
PULLING SPEEDS [rem/s]
DATASET
LENGTHS
DIFFERENT DAYS
PER CLASS
DDRs (WAITE ET AL.,, 2023)
[102,102,136]
400
NA
2000 500, 1000, 2000 500, 1000, 2000, 5000 500. 1000, 2000
TITIN 1270
[181,164,191
736-4859
5
BACT UTRN-R3 (HUA ET AL., 2024)
[181,181,178]
957-9974
10
INSECT UTRN-R3 (HUA ET AL., 2024)
[175.166,200]
1777-8890
11
DYSN-R3 (HUA ET AL., 2024)
[191,185.177]
1659-4814
6
500. 1000. 2000
ment therapy for DMD. We include dystrophin and utrophin fragments encoding the NT through SLR 3 domains, re-
2. For the experimental data, as previously described in (Rajaganapathy et al., 2019; Ramirez et al., 2023; Hua et al., 2024), force curves were collected on different days and at various pulling speeds, as outlined in Table 1. As a result, the lengths of the force curves are different, and substantial variations exist even within the same class. Annotation is performed through visual inspection of the unfolding force curves.
ferred to as DysN-R3 (Fig. 3c) and UuN-R33 (Fig. 3d), respectively. Previous studies have demonstrated that the mechanical properties of UtrN-R3
influenced by the expression system used, such insect or bacterial cells (Ramirez et al., 2023; Hua et al., 2024). Consequently, we further categorize UtrN-R3 into insect UtrN-R3 and bact UtrN-R3 to reflect these variations. In summary, our four real protein molecules are: Titin 1270, bact UtrN-R3, insect UtrN-R3, DysN-R3. Additionally, we include the Discoidin Domain Receptors (DDRs) dataset (Appendix D.1) (Waite al., 2023) to compare the performance of different deep learning methods.
6. Results and Discussion
The performance of our proposed model, PemNN, is eval- uated in this section. We outline the evaluation setup in Section 6.1, followed by comparison of PemNN's clas- sification performance against baseline models in Section 6.2. Next, we analyze the functionality of the force trace branch and physics- bassed branch Section 6.3. Finally, we assess performance under limited training data, a scenario frequently encountered in SMFS applications, in Section 6.4, and apply it to AFM data analysis through comparison to non non-machine learning methods in Section 6.5.
ABD1
ABD2
DgBD
Dystrophin
Utrophin
:000:
ABD
DgBD
6.1. Evaluation setup
UtrN-R3
DysN-R3
We evaluate our proposed model, PemNN, against five base- lines: 1) Triplet network (Triplet) (Waite et al., 2023): The model designed for analyzing SMFS specific pulling data. 2) Fully convolutional neural networks (FCN) and 3) the residual networks (ResNet): Two of the highest performing deep neural networks on the UCR time series classification archive (Fawaz et al., 2019). 4) InceptionTime: The current state-of-the-an deep learning model on the UCR archive (Is- mail Fawaz et al., 2020). 5) LSTMFCN: It outperforms FCN and ResNet on the UCR time series classification archive and demonstrates robust performance on multivariate time series classification (Karim et al., 2018; 2019). Further details about these baselines are provided in Appendix C.
Figure Diagrams of dystrophin and utrophin. (a) Full-length dystrophin. (b) Full-length utrophin. (c) UtrN-R3 construct (d) DysN-R3 construct. The ovals are spectrin- like repeats (SLRs); the diamonds are hinge domains; NT is the N terminus: CT is the C terminus; CR is a cysteine-rich domain; ABDI & 2 are actin-binding domains; DgBD is the dystroglycan binding domain. Figure courtesy of previous study (Ramirez et al., 2023)
For each protein molecule, we have two datasets, one is simulation dataset generated with our physics-based Monte Carlo simulation engine described Appendix A, and one experimental dataset that is obtained from physical ex- periments conducted via AFM on real protein molecule samples. The simulation dataset, comprising 600 force curves, is generated for three classes; Class 0 has no protein molecule between the substrate and cantilever tip, Class 1 has one protein molecule, and Class has two protein molecules attached. Different protein molecules are dis- tinguished by different model parameters listed in Table
The baselines were implemented using default parameters from sktime (Löning al., 2019), which is python frame- work for ML with time series data. For PemNN, the default configuration incorporates the WLC model, LSTM layers in both branches, and Early-Conv fusion method. An abla- tion study of PemNN's architecture is presented in Section
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
D.2, and additional implementation details provided in Appendix C.2.
For each dataset, 20% of the data was used for training, and the remaining 80% was reserved for testing, as adjudication a time-consuming task that requires significant expertise. Stratified resampling was applied to maintain class distri- butions. Each train-test split was seeded for reproducibility. Identical resamples were applied to all models within single run, and performance was evaluated using overall accuracy of the test data across five runs.
Accuracy
0.8
0.6
0.4
Insect UnN-R3
LiNN-RS
DysN-R3
Simulated datasets
1000 mm
pm
1,0
6.2. PemNN classification performance
4000
RuB
pm
20000 pm
Per each dataset, evaluated all models on testing data and ranked them based on their mean classification accuracy over five runs, assigning rank of to the most accurate model and 6 to the least accurate. The average ranking is then computed across all datasets, including both simu- lated and experimental testing sets for all protein molecules. These average rankings are summarized in the critical dif- ference diagram (Demšar, 2006), as presented in Figure 4. PemNN achieves the lowest ranking of 1.4167, indicating that our model is more accurate than baseline models.
16000 pmrs
1024000
30
3000
64000 mm
256000 LSTMFON
500
FON
Triplt
Inceplionimme
Figure 5. a) The average accuracy of all models across the four simulated datasets, with error bars indicating the standard devia- tions over five runs. b) The average accuracy across four simulated datasets over five runs as the contour length threshold varies, de- picted in a radar chart where longer radii indicate higher accuracy. c) The average accuracy across four simulated datasets over five runs as the persistence length changes.
InceptionTima gow Trilti 2.00
PamNN LSTMFON
FCN 220r
ReeNet
models, was evaluated by comparing PemNN (using both force trace and physics- based branches) to baselines that only utilized the force trace branch. As shown in Figure 5a, PemNN achieves near perfect accuracy (98.9 1.9 %) across four simulated datasets, significantly outperforming the bascline. The largest performance gap is in the Titin 1270 simulated dataset, where PemNN outperformed base- lines by 15%; the smallest gap occurs in the insect UINN-33 dataset, with PemNN maintaining a 6% higher accuracy.
Figure 4. Critical difference diagram different deep learning models across the simulated and experimental testing sets of all protein molecules hased on average accuracies. The most accu- rate model is assigned a rank of I, with thick horizontal line representing a group of classifiers that do not exhibit statistically significant differences in accuracy.
For statistical analysis, we employed the Wilcoxon signed- rank test with Holm correction as the post-hoc test following the Friedman test (Fawaz et al., 2019; Demsar, 2006). In Figure 4, thick horizontal lines represent groups of models that are not significantly different in terms of classification accuracy. Thus we conclude that PemNN is significantly more accurate than all baseline models. Among the base- lines, LSTMFCN has the lowest rank, with its performance statistically similar to ResNet and FCN, but significantly different from Triplet and Inception' Time.
Force trace branch Functionality Baselines were provided with the same input data as the physics-based branch to as- the contribution of the force trace branch. This was an- alyzed under two scenarios: one is changing contour length threshold in the filter, the other one is varying the persistence length Lp in the WLC model. Radar charts were employed to visualize model performance, with models represented by different transparent colors and higher radii indicating better accuracy. In Figure 5b, the contour length threshold is changed from 1, 1,000 1,024,000 nm in multiples of four, with "inf" denoting no threshold. PemNN maintained near- perfect accuracy for thresholds between 1,000 and 64.000 nm, range in which some baselines, such as LSTMFCN and ResNet, also perform well. However, as the threshold in- creases, baseline performance dropped sharply. In contrast, PemNN maintains robust performance, outperforming the
6.3. Functionality of two branches
This section evaluates the functionality of the force trace and based branches in PemNN using simulated datasets with known ground truths.
Physics-based branch functionality The importance of the physics-based branch, which integrates polymer elastic
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
baselines by at least 7% at threshold of 1,024,000 nm, with this margin growing to 25% when no threshold was applied. In Figure Sc, the persistence length Lp is varied logarithmi- cally from 0.3 to 30,000 pm. Both PemNN and baselines achieved near-perfect accuracy for Tup values between 30 and 30,000 pm. However, at 4p = 0.3 pm and 4, = 3 pm, baseline performance dropped significantly, whereas PemNN maintained least 3% and 10% higher accuracy, respectively. A more detailed discussion is provided in Appendix D.3. In conclusion, the physics-based branch en- hances performance by incorporating polymer elastic mod- els; the force trace branch increases robustness, ensuring reliable classification even when physics models are cor- rupted by parameter errors. By combining the strengths of both branches, PemNN consistently outperformed baselines in SMFS classification tasks, demonstrating its effectiveness under various conditions.
lated datasets generated using physies-based models and subsequently evaluating them on corresponding experimen- tal datasets. The pretraining strategy achieves comparable performance to models directly trained on experimental data, with an average accuracy of 72.0%, despite not utilizing any experimental data during its training. In our physics-based protein molecule unfolding model, we assume every pro- tein domain behaves identically. However, many protein molecules, including utrophin and dystrophin have folded domains that are significantly different from each other. De- spite being trained on simulation data using single double- well potential model for the domains, PemNN demonstrates the capability to classify the number of protein molecules involved in experiments with protein molecules exhibiting heterogeneous domains (See Appendix E for details).
6.5. Application to SMFS data analysis
Here, we apply both machine learning and non-machine learning methods to Titin 1270 data collected from one- day experiment (~ 3000 curves) (See Appendix D.5 for utrophin and dystrophin). Titin 1270 is a well-calibrated protein molecule with most probable unfolding force of 204 + 26 pN. In Figure 7, Raw includes all unfolding events. The Heuristic method, a non-machine learning ap- proach, filters data with the WLC model (Rajaganapathy et al., 2019; Ramirez et al., 2023) that requires manual ad- justments by experts to fine-tune parameters. PemNN was trained our Titin 1270 dataset and subsequently tested on the raw data to extract curves originating from single molecule. Notably, PemNN takes less than an hour to com- pute statistics, while the Heuristic method takes several hours, and RawData can take up to a full day.
6.4. Performance with limited data
In this section, we focus on experimental datasets and an- alyze model performance under limited training data. The testing data is fixed at 80% of the entire dataset, while the deep learning models are trained using varying propor- tions of the training dataset. When the training proportion ranges from 5% to 20% (approximately 30 to 120 samples), PemNN consistently outperforms baselines, achieving ac- curacies of 79.6% and 85.2% at training proportions of 5% and 20%, respectively (Figure 6). Among the baselines, LSTMFCN performs the best but remains 11 11.4% and 2.9%
less accuracy than PemNN at training proportions of 5% and 20%, respectively.
1.0
PemNN
LSTMFCN
RawData
Accuracy
0.8
0.25
Heuristic
ResNet
PemNN
0.6
FCN
Probability
0.20
Triplet
0.15
0.4
InceptionTime Time
0%
5%
10%
15%
20%
0.10
Training proportion
0.05
Figure 6. The performance of models trained with different pro- portions of experimental datasets (training proportion), with error bars indicating standard deviations across all experimental datasets over five runs.
0.00
100
200
300
400
500
Unfolding force [pN]
Figure 7. Application to SMFS data analysis of Titin 1270: Raw- Data the Baseline Method, Heuristic as non-machine learning method, and PemNN as the our proposed model.
At a training proportion of 0%, no experimental data is used during the training. Instead, a physics-guided pretraining strategy (see Appendix H) is used to eliminate the need for experimental labeling and mitigate human bias. In this approach, deep learning models are pre-trained on simu-
PemNN achieves a most probable unfolding force of 206.68 PN, closely aligning with the expected value (204 + 26 pN).
8

---

Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
In contrast, the Heuristic and RawData yield most probable unfolding forces of 217.41 PN and 192.21 pN, respectively (Table 5). Furthermore, the inclusion of data not originating from single-molecube events resulted in broader force distri- butions. We quantified the sharpness of these distributions using the interquartile range (IQR), as listed in Table 5, Our method, PemNN, achieved an IQR of 52.63, which is only a quarter of the IQR observed from the Heuristic or the Raw- Data effectively filtering out confounding factors. These results highlight that PemNN effectively analyzes AFM data by accurately capturing key statistical features while ef- fectively filtering out confounding factors from multiple molecules.
Impact Statement
Our deep learning model automates the classification of sin- gle molecule force spectroscopy (SMFS) data, effectively fil- tering out non-admissible data from experiments involving multiple molecules (as opposed to single molecule) without the need for expert knowledge. It also reduces the reliance on manual inspection, paving the way for faster and more consistent analysis of SMFS data. We expect the impact to be considerable on SMFS related research wherein laborious and tedious visual inspection can be automated. Addition- ally, this work provides SMFS experimental datasets from four important protein molecules, crucial many biologi- cal pathways, which are made publicly available to support further research.
7. Conclusions
Single-mon moleclee force spectroscopy (SMFS) data of pro- tein molecules are time and resource intensive to collect. Currently, manual visual inspection remains the primary method for classifying force curves resulting from single molecules. This process typically requires a full day per experimental iteration of specific molecule, with multiple iterations being standard practice in the field. These fac- tors make it challenging to obtain precise statistics of single molecular force curves and to generate large, annotated dataset appropriate for training deep learning models.
References
Ashkin, A., Dziedzic, J. M., Bjorkholm, J. E., and Chu, S. Observation of a single-beam gradient force optical trap for dielectric particles. Optics letters, 11(5):288-29) 1986.
Bagnall, A., Lines, J., Bostrom, A., Large, J., and Keogh, E.
The great time series classification bake off: a review and experimental evaluation of recent algorithmic advances. Data Mining and Knowledge Discovery, 31(3):606 2017.
We developed a novel deep learning model that fuses a physics model based branch with another that does not em- ploy physics to efficiently classify SMFS data as originating from no molecules, single molecules, multiple molecules. We also applied state-of-the-art machine learning models (including ResNet, FCN, InceptionTime, and LSTMFCN) to SMFS data. Experimental datasets, obtained from four molecules (Titin 1270, bact UtrN-R3, insect UtrN-R3, and DysN-R3) are used to test and train the deep learning model. Monte-Carlo engine, based on the physics of proteins, is developed and employed to provide simulated data. The pre- sented approach achieves superior performance compared to tfate-of-the-art baseline methods on all simulated or ex- perimental datasets. Remarkably, strong performance on experimental data even when trained solely on simulated data is corroborated. Furthermore, the model surpasses non-machine learning approaches in SMFS data analysis, demonstrating its effectiveness and reliability, while reduc- ing processing time from a day under an hour.
Binnig, G., Quate, C.F., and Gerber, C. Atomic Force Microscope. Physical Review Letters, 56(9):930-935 1986.
Bornschlögl, and Rief, M. Singlc-Molecule Protein Un- folding and Refolding Using Atomic Force Microscopy. In Peterman, E. J. G. and Wuite, G. J. L. (eds.), Single Molecule Analysis, volume 783, pp. 233-250. Springer, 2011.
Bustamante, C., Marko, J. F., Siggia, E. D., and Smith, S. Entropic Blasticity of -Phage DNA. Science, 265(5178): 1599-1600, 1994.
Chen, Y., Xie, H., and Shin, H. Multi-layer fusion tech- niques using a CNN for multispectral pedestrian detec- tion. IET Computer Vision, 12(8): (148):11799) 1179-11777 2018.
Dau, H. A., Bagnall, A., Kamgar, K., Yeh, C.-C. M., Zhu, Y., Gharghabi, S., Ratanamahatana, C. A., and Keogh, E. The UCR time series archive IEEE/CAA Journal of Automatica Sinica, 6(6): 1305, 2019.
Acknowledgements
This project was supported by funding from NIH A5401AR)
Demšar, J. Statistical comparisons of classifiers over mul- tiple data sets. Journal of Machine learning reseurch, 7 (Jan):1-30, 2006.
Doffini, V., Liu, H., Liu, Z., and Nash. M. A. Iterative Machine Learning for Classification and Discovery of

---

Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Single-Molecule Unfolding Trajectories from Force Spec- troscopy Data. Nano Letters,
Huang, L.,, Zhang, C., and Zhang. H. Self-adaptive training: beyond empirical risk minimization. Advances in neural information processing systems, 33:19365-19376, 2020.
2023.
Dudko, O. K., Hummer, G., and Szabo, A. Intrinsic rates and activation free energies from single-molecule pulling experiments. Physical Review Letters, 96(10):18810) 2006.
loffe, S. and Szegedy, C. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International conference machine learning, pp. 448- 456. pmlr, 2015.
Dudko, O. K., Hummer, G., and Szabo, A. Theory, analysis, and interpretation of single-molecule force spectroscopy experiments. Proceedings of the National Academy of Sciences USA, 105(41): 2008.
Ismail Fawaz, H., Lucas, B., Forestier, G., Pelletier, C.,, Schmidt, D. F., Weber, J., Webb, G. I., Idoumghar, L.., Muller, P.-A., and Petitjean, F. InceptionTimee Finding AlexNet for time series classification. Data Mining and Knowledge Discovery, 34(6):1936-196,, 2020.
Ervasti, J. M. Dystrophin, its interactions with other pro- teins, and implications for museular dystrophy. Biochim- ica et Biophysica Acta (BBA)- MMoleclar Basis of Disease, 1772())108-117,, 2007.
Israelachvili, J. N. Intermolecular and surface forces. Aca- demic press, 2011.
Fawaz, H. I., Forestier, G., Weber, J., Idoumghar, L., and Muller, P.-A. Deep learning for time series classification: review. Data Mining and Knowledge Discovery, 33(4): 917-963, 2019.
Jobst, M. A., Schoeler, C., MMlinowska, K., and Nash, M. A. Investigating Receptor-ligand Systems of the Cel- lulosome with AFM-based Single-molecule Force Spec- troscopy. Journal of Visualized Experiments, (82):50950, 2013.
Foumani, S. N. M., Tan, C. W., and Salehi, M. Disjoint-cnn for multivariate time series classification. In 202/ Interna- tional Conference on Data Mining Workshops (ICDMW), pp. 760-769. IEEE, 2021.
Karim, F., Majumdar, S., Darabi, H., and Chen, S. LSTM Fully Convolutional Networks for Time Series Classifica- tion. IEEE Access, 6:1662-1669, 2018
He, K., Zhang, X., Ren, S., and Sun, J. Deep residual leamn ing for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778, 2016.
Karim, F., Majumdar, S., Darabi, H., and Harford, Multi- variate LSTM-FCNs for time series classification. Neural Networks, 116:237-245, 2019.
King, W. Su, M., and Yang, G. Monte Carlo simulation of mechanical unfolding of proteins based on a simple two-state model. International Journal of Biological Macromolecules, 46(2):159-166, 2010.
Hervás, R., Oroz, J.. Galera-Prat A., Goñi, O., Valbuena, A., Vera, A. M., Gómez-Sicilia, Losada-Urzias F., Uversky, V. N., Menéndez, M., Laurents, D. V., Bruix, M., and Carrión- Vázquez, M. Common Features at the Start of the Neurodegeneration Cascade. PLoS Biology, 10(5): e1001335, 2012.
Kingma, D. Adam:
method for stochastic optimization. arXiv preprint 1rXiv:/412.6600 2014.
Hewamalage, H., Bergmeir, C., and Bandara, K. Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions. International Journal of Forecasting, 37(1):388 427, 2021.
Leite, F. L., Bueno, C. C., Da Róz, A. L., Ziemath, E. C., and Oliveira, O. N. Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy. International Journal of Molecular Sciences, 13(12) 2012.
Hochreiter, and Schmidhuber, Long short-term memory. Neural computation, 9():1133--180, 1997.
Liu, M. Ren, S., Ma, S. Jiao, J., Chen, Y., Wang, Z., and Song, W. Gated transformer networks for multivariate time series classification. arXiv preprint arXiv:2 103. 14438, 2021.
Hoffer, F. and Ailon, N. Deep metric learning using triplet network. In Similarity-based pattern recognition: third in- ternational workshop. SIMBAD 2015, Copenhagen, Den- mark, October 12-14, 2015. Proceedings 3, pp. 92. Springer, 2015.
Liu, Z., Liu, H., Vera, A. M., Bernardi. R. C., Tinnefeld, P., and Nash, M. A. High force catch bond mechanism of bacterial adhesion in the human gut. Nature Communica- tions, 11(1):432,, 2020.
Hua, C., Slick, R. A., Vavra, J., Muretta, J. M., Ervasti, J. M., and Salapaka, M. V. Two operational modes of atomic force microscopy reveal similar mechanical properties for homologous regions of dystrophin and utrophin. bioRxiv, 2024.
Livadaru, L., Netz, R. R., and Kreuzer, H. J. Stretching Response of Discrete Semiflexible Polymers. Macro- molecules, 36(10))3733-3744 2003.
10

---

Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Lyubchenko, Y. L. Nanoscale Imaging: Methods and Pro- tocols. Springer, 2018.
Salapaka, M. V., and Ervasti, J. M. Phosphorylation alters the mechanical stiftness of a model fragment of the dystrophin homologue utrophin. Journal of Biological Chemistry, (99(2):10284) 2023.
Löning, M., Bagnall, A., Ganesh, S., Kazakov, V., Lines, J., and Király, F. sktime: unified interface for machine learning with time series. arXiv preprint 2019.
Rief, M., Gautel, M., Oesterhelt, F., Fernandez, J. M., and Gaub, H. E. Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM. Science, 276(5315)) 1109-1112, 1997.
Mendell, J. R., Shilling, C., Leslie, N. D., Flanigan, K. M., al-Dahhak, R., Gastier-Foster, J., Kneile, K., Dunn, D. M., Duval, B., and Aoyagi, A. Evidence- baaend path to new- born screening for Duchenne muscular dystrophy. Annaly of neurology, 71(3):304-3122 2012.
Rief, M., Gautel, M., Schemmel, A., and Gaub, H. E. The Mechanical Stability Immunoglobulin and Fibronectin III Domains in the Muscle Protein Titin Measured by Atomic Force Microscopy. Biophysical Journal, 75(6): 3008-3014, 1998.
Nair, V. and Hinton, G. E. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th international conference on machine learning (ICML-I0), pp. 807-814, 814, 2010.
Rief, M., Pascual, J., Saraste, M., and Gaub, H. E. Single molecule force spectroscopy of spectrin repeats: low un- folding forces in helix bundles. Journal of Molecular Biology, 286(2):553-611, 1999.
Oberhauser, A. F., Marszalek, E., Erickson, H. P., and Fernandez, M. The molecular elasticity of the extracel- lular matrix protein tenascin. Nature, 393(6661):1881-1)) 1998.
Schoeler, C., Malinowska, K. H., Bernardi, R. C., Milles, L. F., Jobst, M. A., Durner, E., Ott, W., Fried, D. B., Bayer, E. A., Schulten, K., Gaub, H. E., and Nash, M. A. Ultrastable cellubosome--dhhesion complex tightens under load. Nature Communications, 5(1):5635, 2014.
Oberhauser, A. F., Hansma, P. K., Carrion- Carrion-Vazquez, M.,
and Fernandez, M. Stepwise unfolding of titin under force-clamp atomic force microscopy. Proceedings of the National Academy of Sciences, 98(2):468-477 2001.
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., and Salakhutdinov, R. Dropout: simple way to prevent neural networks from overfitting. The journal of machine learning research, 15(1):1929-1958 2014.
ISBN: 0027-8424 Publisher: The National Academy of Sciences.
Ortiz, C. and Hadziioannou, G. Entropic Elasticity of Single Polymer Chains of (olhmmethaerylic acid) Measured by Atomic Force Microscopy. Macromolecules, 32(3):780- 787, 1999.
Summers, C. and Dinneen, M. J. Improved mixed- example data augmentation. In 2019 JEEE winter conference on applications of computer vision (WACV), pp. 1272-1270.
IEEE, 2019. ISBN 1 1-7281-1975-8.
Otten, M., Ott, W., Jobst, M. A., Milles, L. F., Verdorfer, T., Pippig, D. A., Nash, M. A., and Gaub, H. E. From genes to protein mechanics chip. Nature Methods, 11(11):
Sundermeyer, M., Schlüter, R., and Ney, H. LSTM neural networks for language modeling. In Interspeech 2012, pp. 194-197, ISCA, 2012.
1127-1130, 2014.
Tavenard, R., Faouzi, J., Vandewiele, G., Divo, F., Androz, G., Holtz, C., Payne, M., Yurchak, R., Rußwurm, M., Kolar, K., and Woods, E. Tslearn, Machine Learning Toolkit for Time Series Data. 2020.
Pham, T.-A., Lee, J.H and Park, C.-S. MST-VAE: Multi- Scale Temporal Variational Autoencoder for Anomaly Detection in Multivariate Time Series. Applied Sciences, 12(19): 2022.
Tokozume, Y., Ushiku, Y., and Harada, T. Learning from between-class examples for deep sound recogni- tion. arXiv preprint arXiv:
Puchner, E. M., Franzen, G., Gautel, M., and Gaub, H. E. Comparing Proteins by Their Unfolding Pattern. Biophys- ical Journal, 95(1) 4324:444,,4,, 2008
2017.
Tokozume, Y., Ushiku, Y., and Harada, T. Between- Class Learning for Image Classification. In 2018 IEFF/CVF Conference on Computer Vision and Pattern Recognition, pp. 5486-5494, Salt Lake City, UT, 2018. IEEE
Rajaganapathy, S., McCourt, J. L., Ghosal, S., Lindsay, A., McCourt, M., Lowe, A., Ervasti, J. M., and Salapaka, M. V. Distinet mechanical properties in homologous spectrin-like repeats of utrophin. Sei. Rep., 9(1):2210, 2019.
Waite, J. R., Tan, S. Y., Saha, H., Sarkar, S., and Sarkar, A. Few-shot deep learning for AFM force curve character- ization of 100672, 2023.
Ramirez, M. P., Rajaganapathy, S., Hagerty, A. R., Hua, C., Baxter, G. C., Vavra, J., Gordon, W. R., Muretta, J. M.,
interactions. Patterns, 4(1):

---

Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Wang, L., Zhang, J., Liu, Y., Mi, J., and Zhang, J. Mul- timodal Medical Image Fusion Based on Gabor Repre- sentation Combination of Multi-CNN and Fuzzy Neural Network. IEEE Access, 9:67634-678 6764777747, 2021.
Wang, Z., Yan, W., and Oates, T. Time series classification from scratch with deep neural networks: A strong base- line. In 2017 International joint conference neural networks (IJCNN), pp. 1578-158.. IEEE, 2017.
Yang. B., Liu, H., Liu, Z., Doenen, R., and Nash, M. A. Influence of Fluorination on Single-Molecule Unfolding and Rupture Pathways of a Mechanostable Protein Adhe- sion Complex. Nano Letters,
8950, 2020a.
Yang, B., Liu, Z., Liu, H., and Nash, M. A. Next Genera- tion Methods for Single-Molecule Force Spectroscopy on Polyproteins and Receptor- Ligand Complexes. Frontiers in Molecular Biosciences, 7:85, 2020b.
Zhang. S., Qian, H., Liu, Z., Ju. H., Lu, Z., Zhang, H.,, Chi, L., and Cui, S. Towards Unveiling the Exact Molecu- lar Structure of Amorphous Red Phosphorus by Single- Molecule Studies. Angewandte Chemie International Edition, 1656)1165-1 2019.
Zhang, X., Gao. Y., Lin, J., and Lu, C.-T. TapNet: Multi- variate Time Series Classification with Attentional Pro- totypical Network. Proceedings of the AAAI Conference on Artificial Intelligence, 34(04):6845-66 66552, 2020.
Zheng. Y., Liu, Q., Chen, E., Ge, Y., and Zhao, L. Exploit- ing multi-channels deep convolutional neural networks for multivariate time series classification. Frontiers of Computer Science, 10(1):96-118 112, 2016.
Zimmermann, L., Nicolaus, T., Neuert, G., and Blank, K. Thiol-based, site-specific and covalent immobilization of biomolecules for mingle-molecule experiments. Nature Protocols, 5(6):975-984 2010.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
A. Simulating protein unfolding
Monte Carlo Simulation based methods are used widely in the SMFS studies, yielding results that closely align with experimental data (Liu al., 2020; King al., 2010). However, prior simulation frameworks are restricted to the idealized case of force curves arising from single molecule. To build comprehensive training dataset, we incorporate the real cases of force curves generated by molecule and multiple molecules. Additionally, we model the cases where only partial sections of molecules are present as well as the stochastic adhesion and detachment events, of the cantilever to the protein, to better approximate experimental data.
Algorithm Monte Carlo Simulation
Require: 2, L ()) AL ALP No. Art, AGI, N, D
Initialization: { 0, ( + 0
1: for + 0: At: : T do
2: I = 2 + r
3: Solve (3) for extension æ
4: for 1: :N do
5: Calculate p())
WLC using (4)
6: Compute kofs WLC using (13)
Compute p (FW.c) using (5)
7:
8:
Draw (8) M(..))
if 17) < p (1 then
9:
I + Le + ALe, Lp +- (1) + ALp
10:
11:
UG) t (1() +1
12:
end if
13:
Draw Ná
(4) Mo.1)
U()
D and nl (LC) then
(1) (
15:
T. Le + Cla T.p t- I.p + CCp
16:
end if
17: end for
end for
For the simulations, N proteins considered with i-th protein having (*) folded domains attached between the substrate and the force probe. The base of the cantilever probe is moved away a constant speed here the position of the base of the cantilever z is initialized at zero and is updated every At seconds. The protein extension is determined by solving the equation,
kid =
(() L 100 1.)
where ke is the spring constant of the cantilever, and d is the deflection (Fig la). Here, (2, F00
( 1.4 is the worm-like chain (WLC) model that relates the force applied to the extension of i-th protein (See Appendix A.1), given by (Rief et al., 1999),
KnT
F F (z, 1 (1) =
(4)
( Lp
L
4
136
where Kg is the Boltzmann constant, T' is temperature, and L and L,) are the contour length and the persistence length of the i-th protein, respectively. For the i-th protein, the probability of domain unfolding during the time interval At is found by
p( ( (L (D - - Koss Fors WLe)
(5)
where U+() the number of unfolded domains which is initially set to zero, and koss (F()) is the transition rate that can be determined with the Setioo-Hummer-SaAae model (Dudko al., 2008) (See Appendix A.2).
13

---

For determining unfolding events of i-th protein, a random number (7()) is generated uniformly from 0 to 1 and is compared to the unfolding probability p (F(i) WLC). No unfolding event is triggered if the random number is larger than P!u) (F WL): the simulation will continue to the next time slot by adding time interval At. Otherwise, one the domains unfolded, Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
leading to a increase in the number of unfolded domains, U by 1, and the simulation continues to the next unfolding event if folded domains still exist after updating contour length and persistence length via adding increments ALC AL? respectively.
Once all domains in i-th protein unfold, the protein detaches from either the cantilever tip or substrate based on the detachment probability,
F2 Fia 10 F<a
Ca
Pa(F)
(6)
where Ca is a constant and Fia is a random number sampled from the Gaussian distribution, denoting the threshold at which the detection of detachment begins. Upon detachment of the i-th protein, its WLC force is reduced to zero by adding large
constants (CLe and CLp) to contour length L and persistence length (5) respectively. To better replicate experimental force curves, we introduce Gaussian noise to the WLC force immediately after its calculation at line 5 of Algorithm 1. The
adhesion force (see Appendix A.3) is added at the end of the simulation process.
A.1. Polymer elastic models
Various polymer elasticity models have been developed to model the force-extension (F- x)) behavior. The widely used models are the worm-like chain (WLC) model (Bustamante et al., 1994), the freely jointed chain (FJC) model (Ortiz & Hadziioannou, 1999), and the freely rotating chain (FRC) model (Livadaru et al., 2003).
The force-extension relationship for each model is given by the following equations:
The WLC model: model:
KBT F
1
(7)
Lp
2
Le
4
where kg is the Boltzmann constant, T is temperature, Le is the contour length, and Lp is the persistence length.
The FJC model:
FLN, KBT
KgT
cothl
(8)
Le
FLx
where Lg is the Kuhn length.
The FRC model:
KBT
(9)
Lc
2F
where La is the bond length.
In these models, the contour length L. is a robust statistical parameter representing the maximal length of physically possible extension given folding state. (Puchner et al., 2008) first proposed solving for contour length Le using each data point, rather than fitting each loading region with polymer model. This approach has been widely adopted in SMFS studies (Liu et al., 2020; Yang al., 2020b; Jobst al., 2013; Otten al., 2014; Zhang al., 2019; Schoeler al., 2014). Given the physically relevant constraints (L. > 0, x > 0, F > 0, < Le) and fixed values for the persistence length Lp. Kuhn length Lx. and the bond length La, the contour length L,, can be calculated using the following equations for three polymer elasticity models:
The WLC model (Jobst et al., 2013):
L
WLC T
+ 4u +
9 3u + 4u²
+ +s(w))
(10)
6u
g(u)
where
FL, and y(u) (27 F
27
+ 36
8
3/3 2
V uu² [[1u - 3)3 - -108)
1/3
2
14

---

Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
The FJC model:
LC
(11)
coth FLe Kn
knT FL
Thee FRC model, assuming bonds are connected by a fixed angle y (Livadaru al., 2003; Liu et al., 2020):
Bark T
for FL
La
Fa
kn n
<
P
for knT
La <
FL
P
Le
PRC
Lta
(12)
2F
for L.
<
kgT
FLa
where Lb (I-c0s7)coe(1//) is the Kuhn length and
Lb
cos(1/2) [m(cos))]
is the persistence length.
A.2. The Dudko-Huummrr-salh model
The Dudko-Hummer-Szale (DHS) model (Dudko et al., 2008) provided an expression find the force-dependent transition rate (F))(F) by,
kofs(F) = ki (1 *FAx1
b-1
BaGt
uPAs! 1-(11
1/0 aGt
(13)
AGI
where ko is the intrinsic transition rate, Ax is the distance to energy barrier, AG is the energy barrier height, and / kaT and y = 1/2 or 2/3, representing the cusp-like or linear-cubic energy landscape. Here ku, Ax and AG are defined the absence of external force. The parameters for Titin 1270 are reported by (Dudko et al., 2006), while those for UuN-R3 and DysN-R3 are reported by (Hua al., 2024).
Table 2. The DHS model parameters
DHS v = 1/2
MOLECULES
In(ko)
Ar [am]
AG [kg2]]
TITIN 1270 (DUDKO AL., 2006)
99.1
0.40
20.00
BACT UTRN-R3 (HUA ET AI.., 2024)
6.50
0.85
14.50
BACT DYSN-R3 (HUA ET AL., 2024)
-4.50
0.60
11.50
INSECT UTRN-R3 (HUA ET AL.. 2024)
-2.50
0.41
9.80
A.3. Adhesion force model
The adhesive force be composed of various components like der Waals force, capillary force, and chemical forces, which depend on environmental conditions such as roughness, interacting angles, and wetness (Leite al., 2012; Israelachvili, 2011). I). However, quantifying these environmental conditions is challenging, and they can vary significantly between experiments. Consequently, we adopt straightforward yet versatile method to model adhesive force rather than a more intricate approach,
Fad
0 1 <hh t1 < t < t2
F.(1) =
t- Fad
(14)
12
else
where the adhesive force increases linearly in the interval [0, (1) reaching the adhesive force threshold Fod at (1, then adhesion between the cantilever tip and the substrate begins to disconnect at & and vanishes at tg. The vanishing phase [t,, should much faster than the adhesive phase j0, t,), with common choice being to set 12 close to f,, for example, t2 = 1.1t1. To introduce stochasticity and enhance generality, we assume both Fad and f to be Gaussian distributed random variables with user-specified mean and standard deviation.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
LSTM
Dripoout
Shared parameters
shared parameters
Polymer clatte
Contout longah
medtls
Conv tD
Batchtorm
Conv 1D
BatchNorm
ReeU
Come to
Batchoorm
ReLL
everegg Sooling Grod
SMSS Force Curves
Physics-based
Rusion Module
Concatenate
Pregra Propracssing modulks
Secemin 200)
Conv 10
Batchterm
RaLU
Conv 10
BarchNerm
ReLU
Cone to
BetchNorm
BaLL
Dataa Danttatin
Reference data
Dropout
LSTM
Figure 8. Overall architecture of the PemNN model with late f'usion strategy. The data augmentation block is not enabled by default but is utilized through mhysics-guided pretraining strategy described Appendix
B. PemNN fusion methods
PemNN contains two branches: the force trace branch T and the physics-based branch P. To uniquely identify block, we use the notation pos), where C E {P.T. PT} specifies the channel with PT representing the fusion of two branches, and pos E {pre - module, CNN1, BNI, RELUI, C2N2, fusion, GAP,.. indicates the name. For example, (T, CN) identifies the first convolutional layer in the force trace branch. We use fc,pos denotes the output of a block, PemNN supports two fusion strategies- late fusion and early seioo-whiich differ based on the dimensionality of the features being fused.
early fusion module is applied to fuse outputs of layers (T, (T,RELU1) and (P, RELU) (Figure 2). We discuss four different methods as follows:
Farly-Sum:
EEarly- fusion (F(), x(0) = fT.RELUI(F()) + f fr.RELUI(FF)) (F( x(0))
(15)
which sums convolutional feature maps across branches.
Early-Max:
S'rryy fusion (0))) ) = max (FT,RERZ((F(O), JERREL (F x100)
(16)
where the maximum value at each element selected.
Early-Wavg:
Ctarly-fueion (000)(00) aT NETUT.RELU((F()) + aE x(0) s.t. tap
(17)
which computes weighted sum of feature maps with coefficients aT, ap learned during optimization.
Early-Conv: The three methods described above require consistent output shapes for the layers (T,REL11) and (P, RELU1). The (i.j) element of fusion (F((), x(() derived from the corresponding (i.j) elements of fT. (RELUI(F()) and fR.RELU2(FF)) x())), without any information exchange across different branches. To exchange information across branches, we propose using convolution with set of filters w Early-com of length of
Eariy- fusion (F() x(0)) = (JT.RELUI(FR (F (F10) (F(0, 30 Eorly-cone
where 2 is the convolution operator, and the vertical concatenating operator is defined as 2/ U1 " "² given e; = (Vo, Va, .,..., ) and U, = (Ujo, Uy....., "jn)".
(Uso, orl...., Vins .. ..p....00
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Late-fusion strategy, where the fusion module is applied after the GAP layers, as depicted in Figure 8. Two methods considered:
Late-Concat:
Jaate-fusion fusion (F()) ,x())) =raao()))))l x(0)
where GAP layers are concatenated directly.
Late-Gating:
fLate- (F(), (F(),((1)) (OTTT.CAP(Z(1)) (IPfr.CAP(Z()) x(10)
where GAP layers are concatenated with learnable weights. The gating weights 9T.9P are calculated as
(gT.9p) (W.. (FF.FFr..r (Fr.car(F")) (z()))))))))))) +b).
where W and b are the weights and bias of fully connected layer and (-) is softmax activation function.
In multivariate time series classification, the widely used approach is late fusion, which directly concatenates features extracted from Global Average Pooling (GAP) layers. For example, (Karim et al., 2019) concatenated the GAP layer of a convolutional block with output of LSTM layer, (Zheng al., 2016) concatenated GAP layers of convolutional blocks originated from different input branches, (Zhang al., 2020) integrated both L.STM and GAP features from different branches, and (Liu et al., 2021) not only concatenated features from two transformer encoders but also introduced a gating mechanism to assign weights to these features. Unlike late fusion, early fusion focuses on combining convolutional feature maps from multiple branches. Examples includes (Wang et al., 2021), which employed an element-level maximum operator for feature fusion in image classification; (Chen et al., 2018), which summed feature maps for image detection; and (Pham et al., 2022), which concatenated feature maps extracted with different kernel sizes for anomaly detection.
C. Baselines and implementation
C.1. Baselines
The triplet network (Hoffer & Ailon, 2015) takes three samples: the anchor the positive sample x+, and the negative sample r= Here, is the sample under classification, xt comes from the same class as and x is of different class. All three samples are passed through the same network architecture, where the weights are shared, to learn representations in the embedding space. The triplet loss is employed,
Triplet
Ltriplet = (0, || Net(2))l ||Nett==) (o((==")>Ne(==)1)) Net(2))1 m),
(18)
where || denotes the L2 norm, and represents the margin parameter that controls the separation between positive and negative samples in the embedding space. The objective is to minimize the distance between the anchor and the positive sample while maximizing the distance between the anchor and the negative sample in the embedding space. Subsequently, the resulting embeddings are fed into the MLP described earlier to learn classification. The embedding network adopts the ResNet structure, which will be elaborated on below.
FCN
Fully convolutional neural networks (FCN) (Wang al., 2017) is composed of three convolutional blocks followed by Global Average Pooling (GAP) layer and softmax layer. Each convolutional block includes ID convolutional layer, batch normalization, and Rectified Linear Unit (RELU) activation layer. The output of the final convolutional block is passed through a GAP layer, followed by fully connected softmax layer. A stride of 1 with zero padding is used to preserve the length of time series data. The filter sizes and kernel sizes of the three convolutional layers are {128, 256, 128) and {8, 5, 3), respectively.
ResNet The ResNet (He al., 2016) extends neural networks to very deep structures by incorporating shortcut connections. These connections enable the gradient flow directly through the network, easing the training of deeper models. Our Residual Network (ResNet) comprises three residual blocks followed by a GAP layer and softmax layer. Each residual block contains three convolutional blocks similar to those in the FCN architecture. The output of the last convolutional block is added to the input of the residual block before proceeding to the next layer. The kernel size for the three convolutional layers in each residual block remains consistent with FCN architecture, set as (8,5,3) 3). The number of filters is the same within the same residual block, with filter sizes specified as {64, 128, 128] for three residual blocks, respectively.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Inception Time InceptionTime (Ismail Fawaz al., 2020) ensembles the predictions of several InceptionNet models, each with different initializations, overcome the high variance across different runs. The InceptionNet model consists of two residual blocks, followed by global average pooling (GAP) layer and softmax layer. Within each residual block are three Inception modules. Each Inception module begins with a bottleneck layer that reduces dimensionality while preserving the original sequence length through a kernel size and stride of 1. Subsequently, 1D convolutions with varying kernel sizes are applied to the bottleneck output, capturing patterns across different scales, Additionally, a max pooling layer, followed by another bottleneck layer, is applied to the original time series.
LSTMECN LSTMFCN (Karim et al., 2019) employs the augmentation an LSTM layer and CNN layers along with a qquezz--add-exciattoo block to generate feature maps, followed by a softmax layer for time series classification. The three convolutional layers in LSTMFCN are configured with filter sizes of {128, 256, 128} and kernel sizes of {8,5, 3), respectively. The LSTM layer has a hidden dimension of 8, followed by dropout layer with rate of 0.8.
C.2. Implementation details
In PemNN, the CNN blocks contains {128, 256, 128} filters with kernel sizes of (8,5,3). respectively; the LSTM layers are configured with hidden dimension of 8, followed by a dropout layer with rate of 0.8 to mitigate overfitting. The contour length threshold is set to 1000 nm, the persistence length 4p = 300 pm, Kuhn length LA = 300 pm, and bond length L, = 150 pm by default. The batch size is 16 for all models except for InceptionTime with 64, and the number of training epochs are kept at 200 epochs for all models. All models are trained with Adam (Kingma, 2014) with the learning rate 0.001, 31 0.9, 32 0.999 and c = 8. The best-performing model, determined by achieving the lowest training loss, is then selected and evaluated the testing data. These models are trained with Apple MI Pro, which has 10-core CPU and 16-core GPU.
C.3. Data preprocessing
In both single molecule and multiple molecule cases, the force curve typically consists of two parts, separated by the detachment of the event. Our interest lies in the region before detachment, where unfolding events occur. Here, the force curves are trimmed to retain the region before detachment by identifying the detachment point. This trimming process is illustrated in the transition from Figure 9a to Figure 9b. In the force trace branch, data is resampled using linear interpolation 4=
to default of 400 points, followed by min-max normalization, Iscated Zmar and maximum values of the data x. This ensures the models focus on learning shapes rather than magnitudes, as shown in the transition from Figure 9b to Figure 9c. In the physics-based branch, 400 samples are extracted from the trimmed force curve by default, and the countour length Le is calculated using polymer elastic models, illustrated in Figure 9d. We utilize tools from the publicly available time series library Tslearn (Tavenard et al., 2020) implement the two preprocessing steps: resampling and normalization.
Fumin
where Umin and Umaz are minimum
a
b
d
1.0
Force
300
300
800
Normalized Force
0.8-
Force [pN], Lc[nm]
Lc
WWw
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Force [pN]
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bpschnseppli
Apple
0
0
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200 Extension [nm]
250
0
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t
Extension [nm]
Figure 9. Data preprocessing example. (a) The original force curve. (b) The force curve after trimming. (c) The force data after normalization and resampling in the force trace branch. (d) The foree curve with calculated Le in the physics-based branch.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
D. More Results
D.I. Results of the Discoidin Domain Receptors (DDRs) dataset
The DDRs dataset contains unfolding curves of interaction forces between DDRs and its ligand, collagen, measured by AFM at the single molecule level (Waite al., 2023). The dataset contains three classes: 1) no molecule, 2) single molecule, and 3)multiple molecules. However, force curve collection standardized have equal lengths for each sample. However, method, PemNN, is not applicable extension data is not provided. Instead, compare the performance of the remaining deep learning methods.
conducted single pulling speed, and the dataset is
All deep learning models. except the Triplet model, were trained using 80% of the total dataset as the training dataset and tested on the remaining dataset. Their performance is compared to that of the triplet model reported in (Waite et al., 2023), as presented Table The dataset was pre-processed as proposed in (Waite et al., 2023), which involves applying numerical first-order derivative, followed by moving average filter with a window size of 13, and finally min-max normalization. Among the models, Inception Time demonstrated the best performance, achieving approximately 20% higher overall accuracy and F1 score compared to the Triplet model.
Table 3. Overall accuracy, class accuracy, and Fi-score of DDRs dataset for Triplet, MLP, FCN, ResNet, and Inception Time are presented format of average (standard deviation) from runs. Among these models, Inception Time demonstrates superior performance compared to the others.
CLASS ACCURACY (%)
MODELS
OVERALL ACCURACY (%)
F1-SCORE(%)
CLASS
CLASS 1
CLASS 2
TRIPLET (WAITE AL., 2023)
66.70
73.30
63.30
63.30
66.70
FCN RESNET LSTMFCN INCEPTIONTIME
77.10(5.15)
81.22(4.96)
77.49(13.59)
73.48(10.06)
77.30(5.32)
79.03(4.84)
81.90(10.52)
83.97(4.74)
70.92(7.44)
79.02(4.88)
73.81(3442)
70.91(2.49)
88.24(4.16)
71.30(9.02)
76.17(3)32)
85.48(1.14)
97.14(2.61)
84.00(8.94)
72.50(12.96)
85.26(1.02)
D.2. Ablation study of model architecture
In this section, we explore the architectures of our model, PemNN, in greater detail to provide insights into optimizing model designs for SMFS classification. We examine 1) different fusion strategies, 2) the inclusion exclusion of LSTM layers, and different polymer elastic models.
10
9
Bact Uti--33
PamNN_FRRC PenNN WWC
Incepption
1.0
Tripial
Lice
Pambbt E-Mee Pamblli E-Sum
DysN-R3
1270
ReatNal
Lice
PamNN L-Gating
0.6
InceptlonTime sje
Triplet
1863 PemMNN 1Pg
23185 PomNN. F1Pt
Insect UbNeR3
0.4
Sim Titin 1270
ResNet sibe
1 PomNN_F0P0
LS5 TMF CN
Inception Time
PomNN FRC PomNiN FJC
Bact UtrN-R3
Sim Insect UtrN-R3
Triplet
Auesi
ReaNet Soess
LSTMFON
Sim DysN-R3
Figure 10. Ablation study of PemNN architecture. a) Critical diagram comparing various fusion strategies, where 'E-" and 'I.-' denote early fusion and late fusion strategies, respectively. b) Critical diagram evaluating the incorporation of LSTM layers, with "FIPI' indicating LSTM layers included both the force trace physics-base based branches. с) Critical diagram different polymer clastic models, d) Performance of PemNN across datasets with three distinct polymer elastic models.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Fusion Strategies Figure 10a presents results of various fusion strategies. Our model, PemNN, consistently outperforms the baselines regardless of the fusion strategy used. Moreover, all early fusion methods exhibit superior performance compared to late fusion methods. For late fusion methods, the GAP layers from the last convolutional blocks are concatenated, leading to significant information loss since each element in the GAP layer represents a single channel from the convolutional block. In contrast, early fusion methods directly integrate branches from first convolutional blocks, preserving more information. Among the early fusion strategies, the Early-Conv strategy stands out, likely due to its use of filters to effectively process information across branches.
LSTM Layers Figure 10b shows the impact of incorporating LSTM layers into the two branches of PemNN. Regardless of the specific use of LSTM layers, PemNN consistently outperforms the baselines, with all models showing statistically significant improvements over the baselines, except for LSTMFCN. Including LSTM layers in both the trace and physics- based branches achieves the best overall performance, with the average ranking of 2.4167.
Different polymer elastic models Regardless of the chosen polymer clastic model, PemNN consistently outperforms the baselines, as shown in Figure 10c. Furthermore, employing the FRC and FJC models improves performance compared to the WLC model. Figure 10d presents the performance of the three polymer elastic models across simulated and experimental datasets using radar chart. Even though the WLC model is used to generate the simulated datasets, PemNN with the FRC and FJC models performs comparably, with differences in averaged accuracy remaining within 3%, For real experimental datasets, PemNN maintains this robustness, with accuracy differences across the three models limited to within 3% for all four protein molecules.
These results highlight the consistent performance PemNN classification tasks, regardless of fusion methods, the incorporation of LSTM layers, or the choice of Polymer elastic models, and its ability to consistently outperform baselines.
D.3. Closer look force trace branch functionality
In Section 6.3, we demonstrate that our model, PemNN, is robust to variations in physical parameters, specifically the contour length threshold and persistence length. Here we provide a detailed discussion.
Force
Lp 0.3
Lp
Force [pN], Lc [nm]
10
Lp
Lp 300
10
Lp 3000
Lp 30000
2
x
100
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10"
160
140
10
20
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xp [nm]
120
125
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[nm)
Figure 1.. Contour length calculations using the WLC model with varying persistence lengths (Lp)), visualized with a simulated force curve of Titin 1270.
Contour length threshold Contour lengths typically span the micrometer scale. However, factors such as signal noise or deviations from the polymer elastic models can lead to exaggerated contour length values, potentially degrading model performance. Despite these challenges, PemNN exhibits robust performance even when datasets include such extreme values.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Persistence length The persistence length Lp quantifies the bending stiffness of polymer. When Lp underestimated, the polymer appears excessively flexible, causing the contour length Le be overestimated. Conversely, when Tp is overestimated, the polymer appears stiffer, and Le approaches the extension Figure 11 illustrates the relationship between Lp and Le using the WLC model applied to force curve from the Titin 1270 dataset. At Lp 300, contour length Le remains consistent within unfolding events, indicating a correctly chosen L.p. Underestimated Tp (0.3-30) results in large and inconsistent Le leading to performance degradation. When Lp is overestimated (3000, 30000), L. becomes linear with x, converging toward an identity function (red line the inset Figure I1).
D.4. Performance under varying train/test splits
We evaluated our model and baseline methods using a range of train/test split ratios on experimental datasets. Table 4 reports the mean accuracy (with standard deviation parentheses) across all experimental datasets over five independent runs. Our model consistently outperforms baseline methods, particularly under low-data conditions, achieving least 11.4% higher average accuracy when trained only 5% of the data. As the training data increases, our approach maintains superior accuracy while exhibiting smaller standard deviations.
Table 4. Model performance experimental datasets with varying train/test split ratios. Values represent mean accuracy (%) with standard deviations over five runs in parentheses.
TRAIN/TEST RATIO
5/80
40/60
60/40
80/20
PEMNN
79.61
86.82(4.86)
88.50(5.09)
88.54(5.68)
LSTMFCN
68.26(12.12)
85.12(7.49)
85.51(6.87)
87.66(7.66)
RESNET
37.47(6.33)
81.01(9.13)
84.62(7.13)
84.47(9.26)
FCN
35.88(7.37)
75.50(8.92)
75.48(13.15)
79.43(10.18)
TRIPLET
55.58(10.17)
66.78(12.06)
69.15(12.26)
66.92(11.45)
INCEPTIONTIME
35.32(3.97)
80.78(12.78)
81.35(9.07)
84.76(11.58)
D.5. Application to SMFS data analysis
In Section 6.5, we examined the unfolding force distributions of Titin 1270 using three methods: RawData as the baseline, Heuristic as non-machine learning approach, and PemNN, our proposed model. Expanding on this analysis, we provide additional details for utrophin and dystrophin molecules, as illustrated Figure 12.
Unfolding force distributions are visualized using violin plots, where black stars indicate the values with the highest probability. The violins depict data distributions with kemell density estimation (shown as black lines either side), and the width of each curve represents the relative frequency of data points. For each protein molecule, Titin I270, bact UtrN-R3, insect UtrN-R3, and DysN-R3, the unfolding distributions generated by PemNN are significantly more concentrated compared to those from RawData and Hewristic, as quantified by the interquartile range (IQR) listed in Table 5. Furthermore, the most probable forces obtained with PemNN differ from those achieved by the Heuristic method by no more than 10 pN. These results highlight that PemNN effectively analyzes AFM data by accurately capturing key statistical features while effectively filtering out confounding factors from multiple molecules.
Table The most probable forces (in pN), along with the interquartile range (IQR) in parentheses, for all four protein molecules analyzed using different methods during AFM data analysis.
TITIN 1270 HEURISTIC 217.41(270.46)
BACT UTRN-R3 HEURISTIC 72.84(66.55)
RAWDATA 192.21(234.52)
PEMNN 206.68(52.63)
RAWDATA 60.50(63.22)
PEMNN 70.40(36.97)
INSECT UTRN-R3 HEURISTIC 90.58(80.57)
DYSN-R3 HEURISTIC
RAWDATA 81.41(85.29)
PEMNN 84.66(39 98)
RAWDATA 63.76(53.18)
PEMNN 72.54(26.79)
74.38(53.10)
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
500
RawData
Heuristic
Unfolding force [pN]
400
PemNN
300
200
100
0
Titin 1270
Bact UtrN-R3 molecule
Insect UtrN-R3
DysN-R3
Figure Application PemNN AFM Data Analysis: RawData as Baseline Method, Heuristic as non machine learning method. and PemNN as the proposed model. Unfolding force distributions are depicted using violin plots, where black stars signify the positions of values with highest probability, with values detailed Table 5. violins illustrate data distributions using kemel density estimation black lines each side, with the width of cach curve indicating the relative frequency of data points.
E. Physics-guided pretraining strategy
Given the challenge of constructing a large, well-annotated dataset using SMFS experimental data and to eliminate experimental labeling and human bias, we employed physics-guided pretraining strategy. In this approach, deep learning models are pre-trained on simulated datasets generated using physics-based models and subsequently evaluating them on corresponding experimental datasets.
E.1. Pretraining deep learning models with the physics protein unfolding
By utilizing simulation data, we effectively incorporate the underlying physics of protein unfolding into our analysis. Our simulation (Appendix A) carried out using the WLC model. The WLC model encapsulates the physics of the protein unfolding, accurately describing the entropic spring like behavior of the protein between two unfolding events the protein, which is also corroborated by experimental data. Subsequently, test the performance of these pre-trained deep learning models using experimental data.
Data augmentation via linear combinations of examples from different classes is shown to be effective in image classification (Summers & Dinneen, 2019; Tokozume et al., 2018; Huang et al., 2020) and sound recognition (Tokozume et al., 2017). Here, we incorporate M E IN reference data into the force trace branch of PemNN to augment the force data under classification (Figure 8). The reference data are randomly sampled simulated force data from the training dataset. Each reference data F(O) is augmented with the force data F=()) via the difference (J(i) - ()) as additional channels, resulting in total of M + channels. The force data FF(() can be either a simulated or experimental force curve undergoing classification. This augmented input through the force trace branch.
F(0, F(0
F(0) M
comprising the force data and the reference data, then passed
E.2. Physies-guided pretraining strategy performance
first evaluate the data augmentation block discussed Appendix E. by empirically testing three methods for selecting reference data:
random balanced: Reference data are randomly selected while maintaining an equal number of samples from each class for every input data.
random unbalanced: Reference data are randomly selected without class balance for every input data.
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
b
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0%
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Figure 1.3. Pretraining strategy results with PemNN. a)Critical difference diagram comparing different data augmentation methods. byThe physics-guided pretraining strategy (train size = 0%) slightly underperforms compared to direct training with experimental data (train sizes = 5% to 20%).
prefixed balanced: Reference data are fixed for all input data and are selected equally from each class.
Figure 13a presents the critical diagram comparing these selection criteria for different numbers of reference data M. Both the random balanced and random unbalanced criteria achieve higher rankings compared to the prefixed balanced criterion and the case where no reference data is used. Among these, the random balanced approach with M = 6 achieves the highest ranking and and is adopted for subsequent evaluations.
The physics-guide guided pretraining strategy demonstrates performance comparable to cases where the model is directly trained using experimental data, despite not utilizing any experimental data during its training. Specifically, the physics-guided pretraining strategy with PemNN achieves an average accuracy of 72.0% and an average ROC-AUC of 0.88 without invovling any experimental data (Figure 13). These metrics are only 13% and 0.07 lower, respectively, compared when 20% of the experimental data is incorporated during training.
E.3. Similarities between simulated and experimental data
We compared unfolding forces from experimental and simulated data based their most probable values and interquartile ranges (IQR) (see Table 6). Most probable values closely match, with differences from 1 pN (Titin 1270) to ~10 pN (10%) (Bact UtrN-R3, Insect UtrN-R3, DysN-R3), indicating reasonable simulation accuracy. The IQR discrepancy likely arises from using single double-well potential for domains in simulations. We note a key insight from our study; neural networks pre-trained on simulated data with homogeneous domains can effectively classify the number of proteins involved in experiments with hetcrogeneous protein domains.
Table The most prohahle forces (in pN), along with the interquartile range (IQR) in parentheses, for both experimental and simulated data across all four protein.
TITIN 1270
BACT UTRN-R3
INSECT UTRN-RR R3
DYsN-R3
EXPERIMENTAL
216.35(50.)) 17)
81.58(64.07) 85.38(22.28)
89.45(70.866 96.65(40.20)
91.25(65.66 644)
SIMULATED
217.75(36.17)
79.75(25.09)
E.4. Non-homogeneity introduces more challenges
The ROC curves (Figure 14) for PemNN generated using the One-vs-Rest strategy, where given class is regarded as the positive class and the remaining classes are regarded as the negative class as bulk. For Titin 1270, the ROC-AUC remains consistently high, above 0.85 in all cases, regardless of whether the training data is experimental or simulated (Figure 14a, Table 7). For both utrophin and dystrophin, the no-molecule class consistently performs well whether experimental data used for training or not. However, significant improvements are observed for the single-molecule and multiple-molesee moleccle classes when experimental data is used for training instead of simulation data with ROC-AUC of single-molecne class
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Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
increasing by least 0.2 for insect UtrN-R3, bact UtrN-R3, and DysN-RR3 (Figure 14b-d, Table 7). This suggests notable differences between simulation and experimental data for both utrophin and dystrophin.
Titin 1270
Insect UtrN-R3
Bact UtrN-R3
DysN-R3
1.00
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False Positive Rate
False Positive Rata
Trained with simulation data:
No molecule
Single molecule
Multi molecules
Trained with experimental data:
No molecule
Single molecule
Multi molecules
Chance level (ROC-AUC = 0.5)
Figure 14. ROC curves from single for four datasets, (a) Titin 1270, (b) Insect UtrN-R3, (c) Bact UtrN-R3 R3 and (d) DysN-R3 using PemNN. ROC curves are plotted using One-vs-Rest strategy, with no molecule, single molecule and multiple molecules classes depicted in yellow, red and blue, respectively. Solid lines represent results trained with simulation data, while dashed lines indicate results trained with experimental data. These ROC curves are generated using 80% of experimental data, with the corresponding ROC-AUC in Table
The ROC curves allow us to adjust the optimal probability threshold. We can achieve high precision but accept low sensitivity to ensure the reliability of single molecule data statistics. The probability threshold can be chosen to tune for minimum sensitivity or for a minimum specificity. For example, we have selected the thresholds to achieve an average of 93% of the positive identifications of single molecule are correct across four experimental datasets. Thus the method can effectively filter data such that inferences can be drawn from true single molecule experiments. Alternatively, we can aim for high sensitivity but accept low precision avoid losing data, given the scarcity and high cost of producing SMFS data (Appendix E.5).
We further investigated the possible reasons for the superior performances of Titin 1270 compared to insect UtrN-R3, bact UtnN-R3, and DysN-R3. Titin 1270 has identical domains whereas utrophin and dystrophin have heterogeneous domains. The simulation model we use assumes identical folded domains in a protein. model that can simulate a molecule with heterogeneous domains requires the model parameters for each domain. These parameters are not available for insect U3rN-R3, bact UtrN-R3, and DysN-R3. Thus, we hypothesize that when information about the molecular domains is missing in the simulation model, the usage of experimental data in training provides substantial improvements in performance. This is the case with molecules with heterogeneous domains.
Table ROC-AUC of ROC curves in Figure 14.
TRAINED WITH SIMULATION DATA
TRAINED WITH EXPERIMENTAL DATA
No
SINGLE MOLECULE
MULTIPLE MOLECULES
No
SINGLE MOLECULE
MULTIPLE
MOLECULE
MOLECULE
MOLECULES
TITIN 1270
0.98
0.86
0.90
1.00
0.95
0.96
INSECT UTRN-R3
0.92
0.61
0.75
0.99
0,81
0.84
BACT UTRN-R2 R3
0.97
0.67
0.82
1.00
0.92
0.93
DYSN-R3
0.97
0.61
0.77
1.00
0.88
0.90
E.5. Adjusting probability thresholds
The primary goal is identify single molecule force curves, we simplify the problem from multi-class to binary classification, focusing distinguishing force curves from single molecules versus those from no molecule and multiple molecules. By leveraging the ROC curve, which illustrates the true positive rates (TPR) against the false positive rates (FPR) by varying the probability threshold tp. we can choose the optimal probability thresholds top to classify these binary classes. The optimal probability threshold top is determined by maximizing the difference between TPR and FPR with a weight a E R on FPR.
top = argmar., (TPR - a FPR).
(19)
24

---

Deep Learning Framework for Classifying Single Molecule Force Spectroscopy Data
Subsequently, optimal thresholds with varying a are applied the binary classification task. The results, compared the original threshold, are presented in Figure 15 for ResNet. The models trained simulation data and then evaluated on experimental data.
1.0
0.8
0.6
0.4
Precision of single molcule
0.2
Recall of single molecule
0.0
w/o 0.2
0.5 1
5 10
Threshold
Figure 15, Performance of PemNN with varying probability thresholds for all four experimental datascts. The x-axis represents values of a, with 'w/o Threshold indicating no threshold used.
A larger weight a places greater emphasis on false positive, thereby increasing precision. For example, the precision of single molecule class improves to 0.93 when a = 10. However, this improvement comes with a trade-off in recall. This adjustment enhances the reliability single molecule data statistics, as we can be more confident that no-molecule and caatipple-ollculeee force curves are not misclassified as single-molecule class. Conversely, the preference is to accept some false positives rather than exclude any true positives the data are expensive and scarce, a 0.2 would be the choice achieve high recall, albeit with lower precision.
E.6. Discussion and limitations
significant insight of the study that we can perform the task of classification of data under no molecule, single molecule, and multiple molecules (for proteins with heterogenous domains) being pulled where the training is done based on simulation data, where single double-well potential model of the domains is employed. This implies that there is enough other information on the force-curves that allows discrimination between no, single, and multiple proteins-based force-curves. We emphasize that neural networks trained on simulated data using homogeneous domains have the capability to classify between the number of proteins being involved in the experiments of protein molecules with heterogeneous domains.
We identify the following limitations for the thysics-guided pretraining strategy. First, the simulation algorithm relies on energy landscape parameters, which are not straightforward obtain and typically necessitate experiments involving multiple pulling speeds or constant forces. Transforming our physics-guided pretraining strategy to be agnostic the energy landscape parameters is beyond the scope of this study. Second, in our physics-based protein unfolding model, assume every protein domain behaves identically. However, many proteins, including utrophin and dystrophin have folded domains that are significantly different from each other. Developing methods that can extract the individual energy landscapes of the different dissimilar domains in a protein is likely to aid identifying single molecule force curves arising from proteins with dissimilar domains. The development of techniques to extract distinct energy landscapes from a small amount of experimental data should be investigated in the future.
25


Reviews:
[{"review_id": "NJergiImAa", "reviewer": "Reviewer_tV21", "summary": "this work proposes a deep learning model to classify SMFS curves.\nthe model consists of two branch, one is \"based on physics\" and another is called \"force-trace\", followed by fusion modules.\ntheir experiments show improved accuracy.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful feedback. We have addressed your questions and concerns below. If there are any remaining issues, we would be happy to discuss them further. If there are no additional concerns, we would appreciate your consideration in raising our score.\n\nWe would like to emphasize that our article is the first to apply state-of-the-art machine learning models (ResNet, FCN, InceptionTime, and LSTMFCN) to Single Molecule Force Spectroscopy (SMFS) data. Additionally, we introduce PemNN, a novel model specifically designed for this domain, which outperforms baseline models. Furthermore, we provide a Monte-Carlo simulation engine and extensive datasets generated from atomic force microscopy experiments on a variety of proteins.\n\n1. *they claimed \"superior performance compared to sota baseline methods\" the results illustrated in Fig 6 however seems to question statistical significance, as indicated by overlapping error bars.*\n\n**Author response**: \n\nFigure 6 reports mean accuracy and standard deviations across all experimental datasets, with each dataset evaluated over five runs. PemNN outperforms ResNet, FCN, Triplet, and InceptionTime without overlapping error bars. While some overlap exists with LSTMFCN at training sizes 0.1, 0.15, and 0.2, PemNN maintains higher mean accuracy. To further assess the statistical significance, we conducted the Wilcoxon signed-rank test with Holm correction as the post-hoc test following the Friedman test [1,2]. The results are visualized in the Critical Difference (CD) diagram [1] in Figure 4, where thick horizontal lines indicate groups of classifiers that are not significantly different in terms of accuracy. In this diagram, our method is ranked significantly higher than the baseline methods.\n\n\n2. *the two-branch design seem to make sense to me, but it will be more convincing if the ablation study, e.g., one-branch vs two-branch, is presented.*\n\n**Author response**: \n\nThanks for your comment. Indeed, we have evaluated the efficacy of two branches (force trace branch and physics-based branch) vs a single branch in Section 6.3 (Page 7) of our submitted paper. We showed that the physics-based branch enhances performance by incorporating polymer elastic models. Furthermore, the force trace branch enhances robustness against parameter errors. By combining the strengths of both branches, PemNN consistently outperformed baselines in SMFS classification tasks, demonstrating its effectiveness under various conditions.\n\n3. *wondering what the broader community can learn from this work. I wish to see evidence that the architecture brings insights that can be applied not only on SMFS*\n\n**Author response**: \n\nSMFS is crucial in understanding protein folding and unfolding which is of vital importance for human biology and health; a cursory investigation on the internet can provide evidence of the journals and research in this area. Machine Learning has the potential to substantially revolutionize this area with public datasets and associated ML based methods, mirroring the impact that ML has already had across other scientific domains.\n\nThe many existing multivariate time-series classification models attempt to capture relationships across different input channels [3,4]. While biological data often exhibit an interdependency that can be modeled as nonlinear functions among multiple variables. Our method leverages the relationship between extension and force through the polymer elastic model in the physics-based branch. The exploration of cooperative features among biological data could extend beyond SMFS, offering a broader impact on multivariate time-series analysis in other biological domains; however, this is outside the scope of the present article.  \n\nAs alluded to earlier, our work provides (1) a new ML model, PemNN (2) a Monte-Carlo based simulation engine (3) SMFS experimental datasets for a variety of proteins (4) application of prior state-of-the-art ML models to SMFS data. We hope that the reviewer finds the scope of work, its innovations, and the potential avenues it opens for future research, convincing.\n\n[1] Demšar, Janez. \"Statistical comparisons of classifiers over multiple data sets.\" Journal of Machine learning research 7.Jan (2006): 1-30.\n\n[2] Ismail Fawaz, Hassan, et al. \"Deep learning for time series classification: a review.\" Data mining and knowledge discovery 33.4 (2019): 917-963.\n\n[3] Zheng, Yi, et al. \"Exploiting multi-channels deep convolutional neural networks for multivariate time series classification.\" Frontiers of Computer Science 10 (2016): 96-112.\n\n[4] Zhang, Xuchao, et al. \"Tapnet: Multivariate time series classification with attentional prototypical network.\" Proceedings of the AAAI conference on artificial intelligence. Vol. 34. No. 04. 2020.", "claims_and_evidence": "they claimed \"superior performance compared to sota baseline methods\"\nthe results illustrated in Fig 6 however seems to question statistical significance, as indicated by overlapping error bars.", "methods_and_evaluation_criteria": "the two-branch design seem to make sense to me, but it will be more convincing if the ablation study, e.g., one-branch vs two-branch, is presented.", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "looks good to me", "relation_to_broader_scientific_literature": "wondering what the broader community can learn from this work. \nI wish to see evidence that the architecture brings insights that can be applied not only on SMFS", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "see above (statistical significance, ablation study, broader impact)", "other_comments_or_suggestions": "see above", "questions_for_authors": "see above", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "c6P4tZMWNF", "reviewer": "Reviewer_sE8z", "summary": "The paper introduces Polymer Elastic Models Neural Networks (PemNN), a deep learning model designed to classify molecular force curves as originating from no molecule, single molecule or multiple molecules.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful feedback. We have addressed your questions and concerns below. If there are any remaining issues, we would be happy to discuss them further.\n\n1. *Figure 4: what do the numbers represent?*\n\n**Author response**: \n\nWe use classification accuracy as the metric to compare the performance of different models, including our model PemNN and five baseline models, across multiple datasets. Per each dataset, we evaluated all models on testing data and ranked them based on their mean classification accuracy over five runs, assigning a rank of 1 to the most accurate model and 6 to the least accurate. The average ranking is then computed across all datasets, including both simulated and experimental testing sets for all protein molecules. The average ranking for each model is presented in the critical difference diagram [1], as presented in Figure 4. PemNN achieves the lowest ranking of 1.4167, indicating that our model is more accurate than baseline models. \n\nTo assess statistical significance, we conducted the Wilcoxon signed-rank test with Holm correction as a post-hoc test following the Friedman test [1,2]. In Figure 4, thick horizontal lines represent groups of models that are not significantly different in terms of classification accuracy. From Figure 4, we conclude that PemNN is significantly more accurate than all baseline models. Among the baselines, LSTMFCN has the lowest rank, with its performance statistically similar to ResNet and FCN (as indicated by the thick horizontal line connecting these three models). \n\n\n\n\n2. *Figure 5: Different methods are hard to distinguish in the radar plot. Could the authors use a bar plot or a line plot instead?*\n\n**Author response**: \n\nThank you for your suggestion. We acknowledge that distinguishing between different methods may be challenging in the current format. To improve clarity, we will replace the radar plot with a bar plot or a line plot in our revised paper.\n\n[1] Demšar, Janez. \"Statistical comparisons of classifiers over multiple data sets.\" Journal of Machine learning research 7.Jan (2006): 1-30.\n\n[2] Ismail Fawaz, Hassan, et al. \"Deep learning for time series classification: a review.\" Data mining and knowledge discovery 33.4 (2019): 917-963.", "claims_and_evidence": "Yes, the claims are supported by clear evidence.", "methods_and_evaluation_criteria": "Yes, the evaluation methods make sense for supporting the claims.", "theoretical_claims": "The paper introduces no theoretical claims.", "experimental_designs_or_analyses": "Yes, I checked the soundness of the experimental setup.", "relation_to_broader_scientific_literature": "I am only familiar with the literature in the field of machine learning. The method uses existing building blocks to create an globally novel architecture.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "Strengths:\n* The descriptions of the experimental setup and of the methods are particularly clear.\n* The statistical significance of the results is always shown clearly.", "other_comments_or_suggestions": "* Figure 4: what do the numbers represent?\n* Figure 5: Different method are hard to distinguish in the radar plot. Could the authors use a bar plot or a line plot instead?", "questions_for_authors": "No additional questions", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zIsos9jRHp", "reviewer": "Reviewer_7QeU", "summary": "The authors propose a physics-inspired architecture to classify single molecule events from force spectroscopy data. They provide datasets, including simulations, to evaluate their method compared to previous baselines showing improved performance.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful feedback. We have addressed your questions and concerns below. If there are any remaining issues, we would be happy to discuss them further. If there are no additional concerns, we would appreciate your consideration in raising our score.\n\n1. *The main concern I have with the experimental design is the train/test split of 20/80.*\n\n**Author response**: \n\nAs suggested by you we have tested our model and baseline methods using different train/test splits on experimental datasets. The table below presents the mean accuracy (with standard deviations in parentheses) across all experimental datasets over five runs.\n\n|   Train/Test Ratio   |         5/80        |         40/60       |         60/40       |         80/20       |\n|:--------------------:|:-------------------:|:-------------------:|:-------------------:|:-------------------:|\n|         PemNN        |      79.61(5.24)    |      86.82(4.86)    |      88.50(5.09)    |      88.54(5.68)    |\n|        LSTMFCN       |     68.26(12.12)    |      85.12(7.49)    |      85.51(6.87)    |      87.66(7.66)    |\n|         ResNet       |      37.47(6.33)    |      81.01(9.13)    |      84.62(7.13)    |      84.47(9.26)    |\n|          FCN         |      35.88(7.37)    |      75.50(8.92)    |     75.48(13.15)    |     79.43(10.18)    |\n|        Triplet       |     55.58(10.17)    |     66.78(12.06)    |     69.15(12.26)    |     66.92(11.45)    |\n|     InceptionTime    |      35.32(3.97)    |     80.78(12.78)    |      81.35(9.07)    |     84.76(11.58)    |\n\nOur method shows particular advantage when the training data is limited, achieving at least 11.4% higher average accuracy compared to baseline methods. Even with increased training data, our approach maintains superior accuracy while exhibiting smaller standard deviations. We appreciate your suggestion and will incorporate this discussion into the revised manuscript. \n\n2. *The paper could benefit from slightly more detailed justification of the model architecture in the main text.* \n\n**Author response**: \n\nThank you for your suggestion. We will incorporate relevant details from appendix including your suggestions into the main text of the revised manuscript.  \n\n3. *Why are other more modern sequence modeling architectures used (i.e. Transformer) instead of an LSTM?*\n\n**Author response**: \n\nThank you for your question! We chose to use an LSTM because it is well-suited for sequential data where temporal dependencies need to be captured. Furthermore, earlier studies have shown that augmenting convolutional layers with LSTM significantly improves performance in time series classification with only a modest increase in the number of parameters [1,2,3]. However, we will be exploring more modern sequence modeling architectures in future work to assess potential performance improvements.\n\n4. *Could more detail be provided on the polymer elastic model branch?*\n\n**Author response**: \n\nWe provide a detailed description of the polymer elastic model branch here. Given i-th force curve of length $T^{(i)}$, consisting of force data $\\mathcal F^{(i)}=[F_1^{(i)},F_2^{(i)},…,F_{T^{(i)}}^{(i)}]$ and extension data $\\mathcal X^{(i)}=[X_1^{(i)},X_2^{(i)},…,X_{T^{(i)}}^{(i)}]$, the corresponding contour length ${L_c}_p^{(i)}$, for $p=1,2,…,T^{(i)}$, is computed using polymer elastic models. A subsequent filtering step selects P samples with ${L_c}_p^{(i)}\\in [0,M]$, where M is the filter threshold. If the number of qualified data points is less than P, sampling is performed with replacement. The filtered data, $[F_1^{(i)},F_2^{(i)},…,F_P^{(i)}; {L_c}_1^{(i)},{L_c}_2^{(i)},…,{L_c}_P^{(i)}]$, is processed through convolutional blocks and the LSTM layer in the physics-based branch. \n\n\n5. *Are there standard non-ml baselines that are relevant to include for this field?*\n\n**Author response**: \n\nCurrently, manual visual inspection remains the primary method for classifying force curves resulting from single proteins [4,5]. Different labs often develop their own heuristic methods to analyze single molecule data, as illustrated in [6,7]. Even though such heuristic methods can analyze data, they are approximate and require an expert to manually adjust the parameters. We provided a comparison to these non-machine learning methods on our four protein molecules (supplementary material in Section 6.5 on Page 8 and Appendix D.4 on Page 20), we showed that our model can effectively analyze AFM data by accurately capturing key statistical features while effectively filtering out confounding factors from multiple molecules.\n\n[1] Karim et al., Neural Networks 116 (2019)\n\n[2] Zhang et al., AAAI 34(04) (2020)\n\n[3] Hewamalage et al., Int. J. Forecast. 37(1) (2021)\n\n[4] Bornschlögl & Rief, Single Molecule Analysis (2011)\n\n[5] Ares et al., Nanoscale Imaging (2018)\n\n[6] Ramirez et al., J. Biol. Chem. 299(2) (2023)\n\n[7] Rajaganapathy et al., Sci. Rep. 9(1) (2019)", "claims_and_evidence": "- The proposed model outperforms baselines: this claim seems to be adequately confirmed by the experimental evaluations\n- The physics-informed module improves performance: this seems to be supported by ablations in Fig. 5 / comparisons to baselines", "methods_and_evaluation_criteria": "The authors create a simulated dataset that seems relevant for evaluating the models. I am not familiar enough with this field to comment on whether the experimental datasets considered make sense for the problem set up, but they seem reasonable.", "theoretical_claims": "n/a", "experimental_designs_or_analyses": "The main concern I have with the experimental design is the train/test split of 20/80. While I understand that in practice there may be very limited training data for the application area, it could still be interesting to evaluate the models with the larger amounts of training data available. For instance, I would be curious to see what Fig. 6 looks like if it is extended up to 80% of the training data.", "relation_to_broader_scientific_literature": "This paper seems relevant to the SMFS community to decrease the amount of manual labor needed to classify force curves.", "essential_references_not_discussed": "n/a", "other_strengths_and_weaknesses": "The paper is in general well written. The paper could benefit from slightly more detailed justification of the model architecture in the main text. Although I know that many of these points are addressed in the appendix, at least mentioning them in the main text could be useful for the reader (i.e. choice of 3 classification targets instead of 2, choice of PEM model, etc).", "other_comments_or_suggestions": "n/a", "questions_for_authors": "- Why are other more modern sequence modeling architectures used (i.e. Transformer) instead of an LSTM?\n- Could more detail be provided on the polymer elastic model branch? Are the predicted contour lengths simply passed in to the fusion block as a physics-augmented feature?\n- Are there standard non-ml baselines that are relevant to include for this field?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "BtaB8Xi9pa", "reviewer": "Reviewer_V7uf", "summary": "This paper presents a machine learning-based approach for classifying single-molecule force spectroscopy (SMFS) data from protein unfolding experiments. Specifically, the model distinguishes force measurements originating from valid single-molecule unfolding events versus artifacts. While ML-based classification of SMFS data has been explored in prior work, the novelty of this paper lies in leveraging a synthetic dataset of simulated force curves to train the classifier. The study evaluates the model’s performance on three different proteins: Titin, utrophin, and dystrophin.", "questions": "", "limitations": "", "rating": 1, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful feedback. We address your concerns below and welcome further discussion. If there are no additional issues, we would appreciate your consideration in raising our score.\n\n**A Challenging Problem:** Our lab studies novel molecules like dystrophin and utrophin to understand their mechanical properties. Initially, isolating single-molecule pulling trials was a manual, time-intensive process, requiring a full day per experimental iteration of a specific molecule. Multiple iterations are the norm in this area. Moreover, no repeated pattern is known or present to isolate data resulting from single molecule. Challenges include heterogeneity of domains, low signal to noise ratios, instrument and thermal noise, unfolding domain uncertainty, and stochastic unfolding forces. These complexities make automated classification both difficult and essential.\n\n**Novelty:** We gently but firmly disagree with the reviewer on the novelty. First, our domain expertise in SMFS was crucial in identifying the right problem for an impactful ML application. Second, while standard ML methods perform well on large datasets, SMFS has limited training data. To address this, we introduced a novel dual-branch ML architecture incorporating protein unfolding physics, a unique approach enabled by SMFS expertise.\n\n**Practical Use and Generalization:** Specific pulling requires functionalized cantilevers and tailored molecular fingerprints, making it a time-consuming, protein-specific process. While these fingerprints help classification, they introduce artifacts, as these domains do not exist in native proteins. In contrast, non-specific pulling avoids these modifications, making it more accessible but harder to classify. Our ML based approach overcomes these challenges while preserving the advantages of non-specific pulling.\n\nEven without ML, comparing specific and non-specific pulling data is complex, requiring tailored fingerprints and biochemical adjustments for each protein—a challenge beyond this article’s scope. Our lab is among the few capable of purifying dystrophin and utrophin, yet no specific pulling data currently exists for these proteins due to experimental complexity (design and execution of experiments for specific pulling need to be done separately for each protein and are quite involved). We are actively working to collect this data and plan to apply our methods upon availability.\n\nPemNN outperforms baselines by 11.4% with only ~30 experimental training samples. Even without experimental training data, it achieves average accuracies of 72.0% $\\pm$ 5.9% through pre-training simulated datasets. To test generalizability, we applied our method to two newly investigated proteins (full-length utrophin and dystrophin) using transfer learning with only ~30 experimental samples, achieving 79.4% $\\pm$ 4.8% accuracy over five runs. Our approach has streamlined analysis and reduced processing time to under an hour, significantly improving efficiency over traditional methods. Our method focuses on isolating trials from single molecule, which comes into play after the biochemistry (buffer conditions) is already decided. Thus, these factors will have minimal impact on our classification accuracy.\n\n**Comparison to non-ML methods:** Please refer to Reviewer 7QeU item 5.\n\n**Experimental vs. simulated data:** We compared unfolding forces from experimental and simulated data based on their most probable values and interquartile ranges (IQR) (see Table). Most probable values closely match, with differences from 2 pN (Titin I27O) to ~10 pN (10%) (Bact UtrN-R3, Insect UtrN-R3, DysN-R3), indicating reasonable simulation accuracy. The IQR discrepancy likely arises from using a single double-well potential for domains in simulations. Notably, models pre-trained on homogeneous simulated data effectively classify experimental data with heterogeneous domains. We will incorporate this discussion in our revised paper.\n\n|            |     Titin I27O       |     Bact UtrN-R3    |     Insect UtrN-R3    |     DysN-R3         |\n|:----------:|:--------------------:|:-------------------:|:---------------------:|:-------------------:|\n|     Exp    |     216(50)    |     82(64)    |     89(71)      |     91(66)    |\n|     Sim    |     218(36)    |     85(22)    |     97(40)      |     80(25)    |\n\nOur classification method is not error-free, so in practice, we manually inspect filtered datasets using domain expertise. However, our approach reduces dataset size to 5–10% of the original, making manual review far more efficient.\n\n**Reference:** Due to space constraints, we highlight the most relevant study. [1] applied ML to SMFS specific pulling data to identify single molecule data; specific pulling results remain relevant and limited to the protein being investigated and do not generalize to other proteins. Our emphasis is non-specific pulling, which is more generalizable across proteins.\n\n[1] Waite et al., Patterns 4.1 (2023).", "claims_and_evidence": "- The paper introduces an important and impactful task to the ML research community, particularly in the domain of SMFS data analysis.\n\n- The study is well-motivated, providing a clear explanation of how classifying force curves can help automate data filtering in protein unfolding experiments.\n\n- The experimental design is rigorous, incorporating statistical significance assessments to support conclusions.\n\n- The paper provides evidence that classifiers trained on synthetic data generalize well to experimental force curves, reducing the need for large labeled experimental datasets.", "methods_and_evaluation_criteria": "- **Novelty in Methodology:** While the application of ML to SMFS data is valuable, the ML techniques employed are relatively standard, with no major methodological innovations beyond dataset generation. The primary novelty lies in the application to non-specific pulling data rather than the model design itself.\n\n- **Evaluation Scope:** The reviewer initially raised concerns about whether the task is inherently simplified due to the presence of repeated structures in proteins. The authors clarified that only one of the three proteins (Titin) exhibits this characteristic, while dystrophin and utrophin contain heterogeneous domains. This addresses part of the concern, though further discussion on how different domain structures affect classification performance would strengthen the contribution.\n\n- **Potential Limitations in Practical Use:** While the authors argue that non-specific pulling is more prevalent and accessible, additional discussion on potential trade-offs compared to specific pulling methods would be valuable. For instance, how does classification accuracy compare between non-specific and specific pulling data, and could certain experimental conditions confound classification?", "theoretical_claims": "N/A", "experimental_designs_or_analyses": "The paper presents a well-structured experimental design, particularly in training the classifier using a Monte Carlo simulation engine to generate synthetic SMFS datasets. The approach ensures that both single-molecule and multi-molecule scenarios are included in the training data, making the classifier robust to experimental conditions. However, additional analysis on how well the synthetic data mimics real-world experimental variations (e.g., environmental noise, instrument precision) would be beneficial. The experimental validation, achieving 79.6% accuracy on real data, suggests the method is effective, but further discussion on the biological implications of misclassified events would strengthen the paper.", "relation_to_broader_scientific_literature": "This paper contributes to the ongoing efforts in automating protein folding and unfolding analysis using machine learning. Prior work has applied ML models to classify SMFS data, but this study is distinctive in its use of a dual-branch fusion model incorporating physical constraints. The approach aligns with the broader trend of integrating domain knowledge into deep learning models, a strategy seen in fields such as structural biology and molecular modeling. Additionally, the use of synthetic data for training is increasingly common in other biological data processing tasks, such as cryo-EM image classification and protein structure prediction.", "essential_references_not_discussed": "The paper should consider citing prior works on ML-based classification of SMFS data, particularly those that use conventional feature engineering or statistical methods to distinguish single-molecule events. Additionally, recent advances in physics-informed deep learning models could be relevant, as they demonstrate similar techniques of integrating domain-specific constraints into deep networks.", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "- The classification task may be relatively simple if the primary distinguishing feature is the presence of repeated patterns in force curves. The authors partially address this by noting that real-world noise, heterogeneity in protein structure, and environmental factors make classification challenging. Additional ablation studies isolating these factors would provide deeper insights.\n\n- Some figures and explanations could be clearer, particularly in illustrating how synthetic data is generated and validated against real experimental data.", "questions_for_authors": "- Can the classifier generalize to other proteins beyond the three tested? If so, what are the expected limitations?\n\n- What are the dominant features learned by the classifier? Are they interpretable in a biophysical sense?\n\n- Does the medium in which force measurements are taken (e.g., buffer conditions) influence classification accuracy? If so, how does the model handle such variations?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a dual-branch deep learning model for classifying force-extension curves in single-molecule force spectroscopy (SMFS) data. The key idea is to combine physics-based domain knowledge (via polymer elastic models) with learned representations in a fusion architecture. The model is trained on simulated and experimental datasets, and the authors present both a simulation engine and a public toolbox to support further work in the field. The model is shown to outperform several baselines, particularly in data-scarce regimes.

The paper is well-motivated and clearly written. The authors make a strong case for the practical relevance of their work, especially considering how time-consuming and expertise-intensive current SMFS data analysis pipelines are. They demonstrate state-of-the-art results, particularly under low-data conditions, which is impressive given the typical scarcity of annotated SMFS datasets. The physics-informed modeling approach is also elegant and seems to align with a trend of integrating domain knowledge into deep learning systems.

That said, several limitations were consistently raised by the reviewers. Firstly, while thoughtfully applied, the ML component relies on standard architectures such as 1D convolutions and LSTMs. It does not introduce any novel methodology that would be of clear broad interest to the ICML audience. Secondly, the performance advantage of the proposed model is strongest in very low-data settings, and diminishes as more training data is provided. This observation raises questions about general utility but is not sufficiently discussed in the paper. Moreover, the study omits comparisons to classical non-deep learning baselines, which could potentially perform well in this low-sample regime. Finally, the venue fit is a core concern: while the paper is strong from an applied and interdisciplinary perspective, it is likely to have a greater impact and receive a more informed and constructive review at a conference or journal focused biophysics or biomedical instrumentation. Most of the reviewers pointed out the lack of domain expertise that made it difficult to assess the paper.

However, under the ICML guidelines for application-driven papers, some of these concerns can be weighed differently. The ML contribution need not be a fully novel architecture, provided that the model is well-matched to the task, that the problem is important, and that the pipeline brings meaningful practical value. In that light, the paper meets the bar for originality through its careful integration of physical priors, the creation of a use-informed dataset, and its practical framing of an impactful biological problem. It also demonstrates an effective way to bridge physics-based modeling with modern ML tools. 

Therefore, considering all the discussions and relevant guidelines, I recommend a weak acceptance.
Decision: Accept (poster)