Quantum machine learning-based electrokinetic mining for the identification of nanoparticles and exosomes with minimal training data

Abstract

Synthetic and naturally occurring particles, such as nanoparticles (NPs) and exosomes; a type of extracellular vesicles (EVs), have garnered widespread attention across various fields, including biomaterials, oncology, and delivery systems for drugs and vaccines. Traditional methods for identifying NPs and EVs, such as transmission electron microscopy, are often prohibitively expensive and labor-intensive. As an alternative, the assessment of electrokinetic attributes such as zeta potential or electrophoretic mobility, conductance, and mean count rate, offers a more cost-effective, rapid, and reliable means of characterizing these particles. In this context, we introduce the first application of a quantum machine learning (QML)-based electrokinetic mining for the identification of green-synthesized iron- and cobalt-based NPs, as well as exosomes derived from human embryonic stem cells (hESC), human lung cancer (A549) cells, and colorectal cancer (CRC) cells, based solely on their electrokinetic attributes. Comparative analyses involving cross-validation, train-test splits, confusion matrices, and Receiver Operating Characteristic (ROC) curves revealed that classical ML techniques could accurately identify the types of NPs and EVs. Notably, QML demonstrated proficiency in differentiating between various NPs and EVs, including the distinction of EVs in the plasma of CRC patients versus those of healthy individuals. Furthermore, QML's application has been extended to the identification of NPs along with EVs in the plasma of CRC patients and experimental mice, achieving higher prediction performance even with a minimal training dataset, demonstrating that QML based electrokinetic mining could identify NPs or EVs with minimal training data, thereby facilitating novel clinical development in the realm of liquid biopsies.

Keywords: Electrokinetic analysis; Extracellular vesicle; Liquid biopsy; Machine learning; Nanoparticle; Quantum machine learning.

Graphical abstract

Fig. 1

Characterization and Electrokinetic analysis of iron- and cobalt-nanoparticles. (A, B) Representative transmission electron microscopy (TEM) image of (A) iron NPs, and (B) cobalt NPs. Scale bar: 20 nm. Both NP populations are mostly spherical in shape. (C–D) Representative graphs showing distribution of apparent ZP vs total count of (C) iron NPs, and (D) cobalt NPs for six samples of NPs. Each color represents a sample of NPs. (E–G) Bar graphs showing the mean - (E) zeta potential (ZP), (F) electrophoretic mobility (Mob), and (G) conductivity for iron (black) and cobalt (gray) NPs. Error bars display the standard error of the mean (N = 3). (H, I) Time-dependent phase of (H) iron NPs, and (I) cobalt NPs. Student's t-test was applied for comparison: iron NPs vs. cobalt NPs; Statistical significance was set at ∗P < 0.05, ∗∗P < 0.01.

Fig. 2

Visualization of the data distribution of the raw datasets using scatter plot analysis. (A–D) Pairwise comparisons of electrokinetic features, namely ZP, Mob, Cond, and MCR-for iron (blue) and cobalt (red) NPs (N = 1016). (E–H) Pairwise comparisons of electrokinetic features for A549- (blue) and hESC- (red) EVs (N = 1033).

Fig. 3

Performance evaluation of classical ML models to predict the types of NPs and EVs via confusion matrix and ROC curve. (A–H) Confusion matrices, binary classification metrics (precision, recall, F1 score), ROC, and three-dimensional scatter plots for each ML model trained for the identification of NPs. (I–P) Confusion matrices, binary classification metrics (precision, recall, F1 score), ROC, and three-dimensional scatter plots for each ML model trained for the identification of EVs. (A, E, I, M) The confusion matrix is a table that summarizes the performance of a classification model. The rows of the confusion matrix represent the true NP classes, while the columns represent the predicted NP classes by the ML models. (B, F, J, N) Precision measures the proportion of correctly predicted positive instances out of all predicted positive instances, while recall measures the proportion of correctly predicted positive instances out of all actual positive instances. The F1 score is the harmonic mean of precision and recall, and it is a measure of a model's overall performance. (C, G, K, O) The AUC-ROC is a measure of the overall performance of the model. A perfect model would have an AUC of 1, while a random model would have an AUC of 0.5. (D, H, L, P) Three-dimension scatter plots showing the distribution of predicted data via LR, and XGB on the held out 30 % test set. (Q, R) SHAP value analysis showing the contribution of major attributes for LR-based identification of (Q) NPs and (R) EVs. For the degree of uncertainty in sample was represented in (C,G,K,O) ROC plots via confidence interval (CI) with probability limit of 95 %.

Fig. 4

Performance evaluation of quantum ML model and comparative analysis of its prediction performance with classical ML models with extremely small training set for the identification of NPs. Representative (A–C) confusion matrix, (D–F) ROC curves with confidence interval, and (G–I) three-dimensional scatter plots for QML with (A, D, G) 70 % training set, (B, E, H) 50 % of initial training set, and (C, F, I) 10 % of initial training set. The test accuracies were evaluated on the held out 30 % test set. The confusion matrix shows the number of correctly and incorrectly classified NPs for each type of NP. The ROC curve shows the trade-off between the true positive rate (TPR) and the false positive rate (FPR) for different thresholds. As can be seen from the figures, the VQC model can achieve high prediction performance in identifying the types of NPs, even with a smaller training set. (J–P) Representative three-dimensional scatter plots showing the NP prediction ability via (J–N) classical ML models: LR, SVM, KNN, DT, and XGB, and (O) VQC, a QML with 0.5 % training set. (P) Bar graph showing that QML outperformed the classical ML models for the identification of NPs, even when trained with 0.5 % training set. For precision estimation, the degree of uncertainty in sample was represented in (D–F) ROC plots via confidence interval (CI) with probability limit of 95 %.

Fig. 5

QML based electrokinetic mining could detect the NPs in mouse plasma, and plasma from healthy individuals and cancer patients. (A) A schematic diagram showing the experimental plan for the collection of plasma from control- and NPs injected-mice, followed by recording of electrokinetic data, and the ML based training and prediction modules. (B–E) ROC and 3D scatter plots, and (F) the quantitative bar graph, showing the prediction performance to identify NPs in the plasma of mice using QML trained with 70 %, 50 %, 10 %, or 1 % data. (G) A schematic diagram showing the experimental plan for the collection of plasma from healthy individuals and CRC patients, and separately spiking NPs in a separate group of plasma from healthy individuals and CRC patients, followed by measurements of electrokinetic data, and the ML based training and prediction modules. (H–K) ROC and 3D scatter plots showing the QML based identification of NPs in plasma of (H) healthy and (J) cancer patients, and the corresponding bar graphs, showing the prediction performance of QML trained with 70 %, 50 %, 10 %, and 5 % data, to identify NPs in the plasma of healthy and cancer patients. (F, I, K) Bar graphs showed that QML could maintain high prediction performance, even with massive reductions in training set size. For precision estimation, the degree of uncertainty in sample was represented in ROC plots via CI (showed with confidence shape) with probability limit of 95 %.

Fig. 6

QML based electrokinetic mining with fewer observations identifies EVs from the plasma of healthy and cancer patients, and EVs mixed with NPs. (A) A schematic diagram showing the experimental plan for the collection of plasma from healthy and cancer patients, followed by the isolation of EVs and their spiking with NPs. Then, electrokinetic recording was conducted on the plasma derived EVs without or with NPs. (B–D) ROC curves and confusion matrices showing the classification of (B) healthy EVs vs cancer EVs, (C) healthy EVs vs healthy EVs spiked with NPs, and (D) cancer EVs vs cancer EVs spiked with NPs by QML trained with 70 % and 5 % data. (E) Quantitative bar graphs showing the prediction performance by QML at training set of 70 % and 5 %, inferring that QML could sustain the percentage of prediction performance, even with massive decrease in training set. For precision estimation, the degree of uncertainty in sample was represented in ROC plots via CI (showed with confidence shape) with probability limit of 95 %. In Fig. 6E, the statistical significance was determined via multiple t-tests, followed by the Holm-Sidak method, with P value = 0.05.