Predicting efficacy of drug-carrier nanoparticle designs for cancer treatment: a machine learning-based solution

Abstract

Molecular Dynamic (MD) simulations are very effective in the discovery of nanomedicines for treating cancer, but these are computationally expensive and time-consuming. Existing studies integrating machine learning (ML) into MD simulation to enhance the process and enable efficient analysis cannot provide direct insights without the complete simulation. In this study, we present an ML-based approach for predicting the solvent accessible surface area (SASA) of a nanoparticle (NP), denoting its efficacy, from a fraction of the MD simulations data. The proposed framework uses a time series model for simulating the MD, resulting in an intermediate state, and a second model to calculate the SASA in that state. Empirically, the solution can predict the SASA value 260 timesteps ahead 7.5 times faster with a very low average error of 1956.93. We also introduce the use of an explainability technique to validate the predictions. This work can reduce the computational expense of both processing and data size greatly while providing reliable solutions for the nanomedicine design process.

Figure 1

ML-based hybrid solution for the prediction of SASA values (a) Atomic coordinates for different NP designs derived from MD simulations in an aqueous environment. These data are in Protein Data Bank (PDB) format with other information such as the respective residues. (b) ML usable MBTR representation of the data extracted through a geometric function of pairwise distances between elements. (c) Time series model to accomplish the task of simulation and SASA model for the calculation of the target label. (d) A predefined batch of data can be used to forecast changes in the SASA. An optimal value for the size of this predefined batch can be set with consideration to the simulation costs for generating them and the error threshold (see Table 1). Although both the input and output of the models are the MBTR vectors except the final output, the graph represents the input-output relationship only.

Figure 2

Time series model performance. (a) A scalar value predicted by each model from the ensemble approach and multivariate prediction by the transformer model for a sample data pair of the NCL11 NP design from the test set. The differences between the heights of the bars representing the predictions and the ground-truth values indicate the prediction errors. (b) MAE for each XGBoost model from the ensemble approach over the whole test set. The dashed line represents the average error across all features.

Figure 3

(a) The distribution of NP designs in the training and the test set based on the minimum and maximum SASA values. Each dot represents test data for a particular NP design, with the letters of the design name referring to the drug type and the remainder being a unique identifier. The training samples are represented by triangles and grouped by their sizes. (b) Visualization comparing the real and predicted SASA values of different NP designs (separated by dashed lines) from the test set over 300 iterations each. The blue line represents the actual SASA value, and the grey line represents the predicted SASA value.

Figure 4

Feature importance graph for the Panobinostat residue from 14 NP designs that carry the drug. The element pairs are put in decreasing order by importance starting with the most influential one. The red and blue colours indicate positive or negative impacts on the resulting SASA value, respectively.

Figure 5

Simulation figure for a design containing the drug Panobinostat, generated using ChimeraX. The purple portion depicts the drug molecules around the surface.

Figure 6

(a) Block diagram of the transformer model. Four different layers are used in the transformer model. Multi-head attention allows the model to jointly attend to information from different representation subspaces at different positions. The dropout layer prevents overfitting, the normalization layer improves the training speed for various neural network models, and after normalization, the results are added to the input. The feedforward layer is a nonlinear mapping from an input pattern x to an output vector y. (b) Block diagram of the ensemble approach. The MBTR vector batches are split for each of the features, and all 72 subsets of data are used with an XGBoost regression model. The predictions from each model are then combined to produce the $n_{\text{features}}$-length output. (c) Block diagram of the SASA model. The 72 MBTR features at timestep k are passed to the i nodes of the input layer. The information in the input layer nodes is then passed to all the nodes of the hidden layers with p, n and m nodes interconnected in such a way that each node in the current layer is connected to every other node in the previous layer. The output is a single scalar value representing the SASA at timestep k.