Single-molecule force spectroscopy (SMFS) techniques, such as atomic force microscopy (AFM), have emerged as powerful tools for investigating the mechanical properties and conformational dynamics of biomolecules1,2. SMFS experiments typically involve attaching a single biomolecule to a surface and applying a controlled force to manipulate its conformation. By measuring the force required to stretch or unfold the molecule, researchers can obtain valuable insights into the structure, dynamics, and mechanical stability of biomolecules at the single-molecule level. The high sensitivity and resolution of SMFS techniques have enabled the study of a wide range of biomolecular systems, including proteins, DNA, RNA, and synthetic polymers3,4. The data obtained from SMFS experiments are typically represented as force–extension curves, which depict the relationship between the applied force and the end-to-end extension of the molecule. These curves often exhibit complex features, such as sawtooth-like patterns, reflecting the unfolding of individual domains or segments of the biomolecule. The analysis of SMFS data is crucial for extracting meaningful information about the molecular processes involved. However, the high dimensionality and complex nature of the underlying molecular dynamics pose significant challenges to traditional analysis methods. Traditional methods often rely on simplifying assumptions or rely heavily on manual interpretation, which can be time-consuming and subjective. To overcome these limitations, there is a growing interest in developing computational approaches for automated and objective analysis of SMFS data. Machine learning (ML) techniques have shown great promise in this regard5-9. ML methods, particularly deep learning (DL), have excelled in pattern recognition and complex data analysis tasks, enabling the identification of hidden relationships and patterns within data. The application of DL to SMFS data has the potential to revolutionize the analysis and interpretation of these experiments. However, a key challenge in applying DL to SMFS data lies in the need for large and diverse datasets to train the models. Generating such datasets through experiments can be time-consuming and expensive. Moreover, the experimental data may not always be representative of the underlying molecular dynamics, leading to limitations in the performance of the trained models. An alternative approach is to utilize molecular simulations to generate synthetic SMFS data that captures the underlying molecular dynamics governed by a force field10-12. This strategy allows for the generation of large and diverse datasets under controlled conditions, providing a valuable resource for training DL models for SMFS data analysis.

Previous studies have explored the use of ML for SMFS data analysis. For example, a recent study used a recurrent neural network (RNN) to predict the unfolding pathway of a protein based on SMFS data13. However, the RNN approach relied on learning from experimental data, which can be limited in terms of data availability and representativeness. Another study used a convolutional neural network (CNN) to identify different unfolding events in SMFS data14. However, CNNs are typically designed for spatial data, which may not be optimal for analyzing temporal data such as SMFS traces. In this study, we propose a novel approach, termed Force-Field Neural Network (FFNN), to analyze SMFS data and extract real-time molecular conformational information. FFNN is trained on data generated from molecular simulations, which capture the underlying molecular dynamics governed by a force field. This approach leverages the advantages of both molecular simulations and DL, enabling the accurate prediction of molecular conformations from experimental SMFS data. The use of molecular simulations as a training source for FFNN offers several advantages. Firstly, it allows for the generation of large and diverse datasets under controlled conditions, ensuring the availability of sufficient data for model training. Secondly, the data generated from simulations accurately reflects the molecular dynamics governed by a force field, providing a reliable basis for training the model. Thirdly, the simulation data can be used to identify and label specific conformational states, providing valuable training information for the model. This approach has the potential to overcome the limitations of existing ML methods for SMFS data analysis, enabling a deeper understanding of molecular dynamics at the single-molecule level.

The FFNN model is trained on a dataset consisting of pairs of force-extension trajectories and corresponding molecular configurations obtained from molecular dynamics (MD) simulations. The MD simulations are performed using the CHARMM36 force field15 and the NAMD software package16. The simulations capture the unfolding and refolding events of a single titin immunoglobulin (Ig) domain, I27, under a constant force pulling protocol. The generated datasets are then used to train the FFNN model. FFNN is based on a deep neural network architecture, consisting of multiple layers of neurons that learn hierarchical representations of the input data. The input to FFNN is the force-extension trajectory, which is represented as a time series of force and extension values. The model then outputs a time series of molecular configurations, representing the predicted instantaneous conformations of the molecule. The FFNN model is trained using the backpropagation algorithm with a mean squared error (MSE) loss function. The MSE loss function measures the difference between the predicted and actual molecular configurations, providing a measure of the model's accuracy. The FFNN model is trained using a stochastic gradient descent (SGD) optimizer with a momentum parameter to accelerate the training process. The model is optimized by adjusting the weights and biases of the neurons in the network to minimize the MSE loss function. To evaluate the performance of the FFNN model, we performed a series of experiments using both simulated and experimental SMFS data. For simulated data, we tested the model's ability to predict the instantaneous conformations of I27 under different pulling speeds and forces. The results demonstrate that FFNN accurately captures the transient unfolding and refolding events of I27, as well as the associated force-extension behavior. For experimental SMFS data, we validated the model's ability to identify distinct unfolding pathways and intermediate states. The FFNN model accurately predicts the conformations of I27 from experimental SMFS data, providing insights into the underlying molecular mechanisms.

The key findings of the study are: 1. FFNN accurately predicts the instantaneous molecular conformations from experimental SMFS data, overcoming the limitations of traditional analysis methods. 2. FFNN enables the identification of distinct unfolding pathways and intermediate states, providing insights into the underlying molecular mechanisms. 3. FFNN can accurately capture the transient unfolding and refolding events of I27, as well as the associated force-extension behavior. 4. The use of molecular simulations as a training source for FFNN offers several advantages, including the generation of large and diverse datasets, accurate representation of molecular dynamics, and the ability to identify and label specific conformational states. 5. The study showcases the potential of deep learning for the analysis of SMFS data, paving the way for a deeper understanding of biomolecular dynamics at the single-molecule level.

The results of this study demonstrate the potential of deep learning for the analysis of SMFS data. The FFNN model, trained on data generated from molecular simulations, provides a powerful tool for extracting real-time molecular conformational information from SMFS experiments. FFNN overcomes the limitations of traditional analysis methods by utilizing a deep neural network architecture that can learn complex patterns and relationships in the data. The ability of FFNN to identify distinct unfolding pathways and intermediate states highlights its potential for uncovering detailed molecular mechanisms that were previously inaccessible through traditional analysis methods. The study also highlights the importance of using molecular simulations to generate training data for DL models. By capturing the underlying molecular dynamics governed by a force field, simulations provide a reliable and accurate source of data for model training. This approach ensures the robustness and generalizability of the trained models, enabling their application to a wide range of biomolecular systems. The study provides a significant advancement in the field of SMFS data analysis, opening new avenues for understanding the intricate dynamics of biomolecules. However, there are some limitations that need to be addressed in future research. Firstly, the current FFNN model is trained on a single protein, I27. Further studies are needed to evaluate the model's generalizability to other proteins and biomolecular systems. Secondly, the model is trained on data generated from MD simulations, which are based on a specific force field. The accuracy of the model may be affected by the choice of force field. Future research should investigate the impact of different force fields on the performance of FFNN. Thirdly, the current model assumes that the molecular dynamics are governed by a deterministic force field. However, biological systems are often subject to stochastic fluctuations and noise. Future work should explore incorporating stochasticity into the training data and model architecture to better reflect the complexity of biological systems.

The development of the FFNN model represents a significant advancement in the field of SMFS data analysis. By leveraging the power of deep learning and molecular simulations, FFNN provides a novel approach for extracting real-time molecular conformational information from SMFS experiments. The model's ability to identify distinct unfolding pathways and intermediate states opens up new possibilities for understanding the intricate dynamics of biomolecules at the single-molecule level. Future research should focus on expanding the applicability of FFNN to a wider range of biomolecular systems and on incorporating stochasticity into the model to better capture the complexities of biological systems.

The study has several limitations that need to be addressed in future research. Firstly, the current FFNN model is trained on a single protein, I27. Further studies are needed to evaluate the model's generalizability to other proteins and biomolecular systems. Secondly, the model is trained on data generated from MD simulations, which are based on a specific force field. The accuracy of the model may be affected by the choice of force field. Future research should investigate the impact of different force fields on the performance of FFNN. Thirdly, the current model assumes that the molecular dynamics are governed by a deterministic force field. However, biological systems are often subject to stochastic fluctuations and noise. Future work should explore incorporating stochasticity into the training data and model architecture to better reflect the complexity of biological systems.