Advancing micro-nano supramolecular assembly mechanisms of natural organic matter by machine learning for unveiling environmental geochemical processes

Abstract

The nano-self-assembly of natural organic matter (NOM) profoundly influences the occurrence and fate of NOM and pollutants in large-scale complex environments. Machine learning (ML) offers a promising and robust tool for interpreting and predicting the processes, structures and environmental effects of NOM self-assembly. This review seeks to provide a tutorial-like compilation of data source determination, algorithm selection, model construction, interpretability analyses, applications and challenges for big-data-based ML aiming at elucidating NOM self-assembly mechanisms in environments. The results from advanced nano-submicron-scale spatial chemical analytical technologies are suggested as input data which provide the combined information of molecular interactions and structural visualization. The existing ML algorithms need to handle multi-scale and multi-modal data, necessitating the development of new algorithmic frameworks. Interpretable supervised models are crucial owing to their strong capacity of quantifying the structure–property–effect relationships and bridging the gap between simply data-driven ML and complicated NOM assembly practice. Then, the necessity and challenges are discussed and emphasized on adopting ML to understand the geochemical behaviors and bioavailability of pollutants as well as the elemental cycling processes in environments resulting from the NOM self-assembly patterns. Finally, a research framework integrating ML, experiments and theoretical simulation is proposed for comprehensively and efficiently understanding the NOM self-assembly-involved environmental issues.

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Environmental significance

Supramolecular self-assembly of NOM profoundly influences the fate of NOM and pollutants in large-scale complex environments. The difficulty in recognizing NOM self-assembly and its environmental processes keeps increasing due to the diversity of NOM molecular structures, the growing involvement of pollutants in self-assemblies and the complexity of geochemical conditions. ML is essentially advanced in environmental research through fast analyzing a large amount of input data and customizing the services of algorithms to different circumstances. With the assistance of ML, the environmental process mechanisms of emerging pollutants, bioavailability of pollutants/NOM and related global issues can be approached and unveiled. Research frameworks coupling ML, experiments and theoretical simulation are proposed to comprehensively, efficiently and innovatively understand the NOM self-assembly-involved environmental processes.

1. Introduction

Natural organic matter (NOM) is a complex supramolecular mixture widely distributed in environments, including water, sediments and living organisms.^1,2 One of the remarkable features of NOM is its ability to form self-ordered structures by virtue of high convergence and spontaneous assembling of relatively simple NOM subunits.³ Pollutants such as heavy metals and organic micropollutants may participate in or mediate the assembling processes and structures of NOM through non-covalent interactions.^4–8 Existing and functioning at and beyond the nanoscale,⁹ those self-assemblies significantly change geochemical processes and effects of supramolecular self-assemblies in environments (Fig. 1(a) and (b)). Deciphering those complex nanoscale structures has always been crucial for evaluating and predicting the fate of NOM and the eco-impact of pollutants. In environmental geochemistry, elucidating supramolecular assembly patterns and structures has long depended on experimental exploration, instrumental analyses, (i.e., spectroscopic characterization and microscopic observation) and theoretical simulation methods (typically, quantum chemical calculations such as molecular dynamics (MD) simulations) (Fig. 1(c)).^7,8,10–14 However, the complexity of NOM components and the diverse chemical conditions of environmental media result in vastly varied structural patterns and properties of supramolecular assemblies, which need substantial experiment studies and structure interpretations at the nanometer or submicron scale. Thus, it is difficult to thoroughly understand NOM supramolecular assemblies merely with the above-mentioned approaches, which could be either time-consuming or lack universality.

Fig. 1 NOM self-assembly structures and environmental behaviors obtained from experiments, instrumental analyses or simulation approaches. (a) Sandwiched supramolecular assembly between exopolymers and PFOS obtained by AFM IR-mapping and relevant photo-shield effects.¹³ (b) Aeration-triggered and PFOS-reconstructed NOM assembly and relevant bioaccessibility decline effects.¹⁴ (c) Orderly multilayer structure of NOM self-assembly obtained by coarse-grained dynamic simulation. The bead types and color: water – blue, LHA – purple, lipid – orange, peptide – red, carbohydrate – green, and lignin – yellow.¹⁰

With computational capabilities and versatile algorithms, machine learning (ML) may become an essential alternative through fast analyzing a large amount of input data (i.e., analytical results of NOM self-assembly structures attained from multi-techniques) and thus customizes the services of algorithms to the circumstances (specifically, prioritizing the environmental behaviors of assemblies).¹⁵ Integrating ML into the existing research frameworks holds the promise of substantially improving data analysis efficiency, elaborating complex chemical processes, and revealing new mechanisms of interaction between supramolecular self-assembly components. Currently, supramolecular assembly studies by ML predominantly focus on biological macromolecules such as proteins, amino acids, DNA and RNA, particularly for behavior prediction, component interaction and gene expression (Fig. 2). In the natural environment, the NOM components involved in supramolecular self-assembly cover a wide range of types, which include but are not limited to extracellular polymers^13,16 or biological macromolecules such as polysaccharides, proteins, lipids, nucleic acids^17–20 and humic substances.^21–23 These NOM components spontaneously interact with one another and aggregate under thermodynamic driving forces through non-covalent interactions such as hydrogen bonding, hydrophobic interactions, electrostatic interactions, π–π stacking and van der Waals force.^9,21,24–27 The environmental geochemistry field shares commonalities with other disciplines (i.e., materials, biology, medicine and so forth) in terms of universal self-assembly mechanisms, warranting the adoption of cross-disciplinary research approaches particularly such as ML in common. With the assistance of ML, fundamental understanding will be extended which helps close the gap between the experimental or simulation recognition of NOM supramolecular self-assemblies and their performance in real environments. Relevant studies also confirm the development tendency of supramolecular self-assembly research and applications (Fig. 3).

Fig. 2 Literature cluster analysis using ML in supramolecular assembly research based on the Web of Science Core Collection database. Bubble size reflects the number of occurrences, and bubble colors indicate different clusters classified according to co-occurrence analysis. Search details are provided in Text S1.†

Fig. 3 Development process of the exploration methodology and application fields of supramolecular self-assembly.

Given the context mentioned above, this critical review first suggested the input data sources applicable to developing predictive models especially for micro-nanoscale NOM supramolecular self-assemblies. Then, algorithm selection, model construction and model interpretability analyses were depicted and interpretable supervised ML was particularly focused on. Recent studies on supramolecular self-assembly involving ML from biology, materials, chemistry or relevant fields as well as their commonalities within environmental geochemistry were discussed. Subsequently, prominent applications and major challenges were proposed for ML-interpreting or predicting the geochemical behaviors and eco-impacts involving NOM or NOM–pollutant assemblies in environments. Finally, a combination framework of ML, theoretical simulation and experimental research was suggested for the NOM self-assembly study in the environmental fields.

2. Selection of data sources from micro-nano scale spatial chemical analyses for ML of supramolecular micro-nano self-assembly

2.1. Guide for data source selection

To interpret or predict supramolecular self-assembly processes, structures and properties by ML, the featured input data must provide multi-dimensional and multi-perspective information depicting organized nano-structures. For this purpose, ML models can accept the input data formats including (i) descriptor data calculated from physicochemical parameters which indirectly reflect the molecular properties of supramolecular assembly systems, (ii) commonly adopted inputs of spectroscopic and mass spectrometric data which directly characterize the vibration of functional groups and their molecular interactions in supramolecular assemblies, and (iii) nanometer-submicron-scale spatial spectral-imaging data which accurately depict the distribution of each component in assembled structures.

Notably, not all data types are equally informative for ML in this context, and it is crucial to integrate heterogeneous data from multiple sources and choose input data types rationally based on specific research requirements. For instance, while being valuable for providing morphological and elemental distribution information, the data from electron microscopy and energy spectroscopy imaging cannot directly depict supramolecular structures. As such, these data types can serve as supplementary data to support ML of NOM supramolecular assembly but should not be used as sole data sources. Besides, the models require substantial and sufficient training datasets which are particularly important when the ML tasks are subjected to environmental or geochemical condition changes. Adequate data should be available for each condition not only to enable the model to capture subtle changes in assemblies but also to enhance the model's generalization ability.²⁸

2.2. Molecular descriptors as widely used input data for compound assembly ML

Molecular descriptors, being essential for characterizing molecular structures, physicochemical properties and other relevant information, have been widely applied in cheminformatics, drug design and materials science as input features for ML models. To make them machine-readable during the modeling process, chemical structures need to be converted into numerical or binary vectors.²⁹ These descriptors encompass geometric descriptors based on three-dimensional conformational information,³⁰ physicochemical property descriptors directly representing molecular attributes (i.e., molecular weight, hydrogen bond donors and acceptors, polar surface area and ionization potential),^31,32 topological descriptors describing topological structures and branching of molecules (i.e., molecular connectivity index)²⁹ and quantum chemical descriptors derived from high-precision calculations (i.e., frontier orbital energies, condensed Fukui index, electrostatic potential, polarizability and electronic structure parameters obtained through Density Functional Theory (DFT)).^33,34 Functioning as digital signatures, molecular fingerprints are capable of mapping molecular structures to binary bit strings or encoding information of atomic composition, chemical bonds and spatial arrangements.^35–38

Data extracted from MD simulations can also be considered descriptors in a broader sense. While conventional molecular descriptors are mostly computed based on static structural information, MD simulations capture the dynamic behavior of molecules. By constructing computational models with assembly units and applying appropriate force fields and boundary conditions, MD simulates and reconstructs the spatiotemporal evolution trajectories of self-assembling systems. From the simulation trajectories, detailed information can be obtained such as atomic-level coordinate data, energy, temperature and pressure.^30,39,40

When molecular descriptors are utilized as input data for ML, we should be aware of two critical factors. The potential redundancy and irrelevance among descriptors possibly introduce unwanted complexity to ML models. Feature selection needs to be performed to remove unimportant features.^41–43 Furthermore, the presence of missing values among descriptors poses challenges that must be addressed through appropriate data preprocessing.⁴² For numerical descriptors, missing values can be handled either through simple statistical measures (mean or median imputation) or through similarity-based imputation where values are inferred from molecules based on their structural or property similarities. For categorical molecular descriptors (i.e., atom types and functional group types), there are three main preprocessing approaches: mode imputation where missing entries are replaced with the most frequent category, introducing a new “missing” category as a meaningful category in itself to treat the missing values,⁴⁴ and applying the similarity-based imputation approach as used for numerical descriptors. Those categorical descriptors need to be converted into numerical formats through encoding techniques such as one-hot encoding or label encoding before being fed into ML models.⁴⁵

2.3. Spectral information as a fundamental chemical data source

Comprehensive information on molecular structures and components can be obtained from various spectroscopic techniques, which lay the foundation for recognizing self-assembling molecules and their aggregation behaviors. Mass spectrometry, such as liquid chromatography-mass spectrometry (LC-MS) and gas chromatography-mass spectrometry (GC-MS), enables precise identification and quantitative analysis of molecular components in self-assembling systems in terms of molecular weight, molecular formulae and structures.^46–48 MS demonstrates robust performance in detecting single compounds, but complete signal assignment in natural complex mixtures remains challenging. Nonetheless, ML is capable of grouping isotope peaks, determining molecular formulae and, subsequently, analyzing the chemical composition of NOM.⁴⁹ Researchers have successfully elucidated the structure–activity relationships between peptide fragments and their biological activities via applying ML to the LC-MS analysis results of peptide assemblies.⁴⁶ Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) detects various organic molecules in unknown compounds and their change trends (Fig. 4(a)).^50,51 Based on the feature data of elemental ratios, double bond equivalents and aromaticity indices, it is possible to interpret and predict the NOM behaviors with respect to spontaneous combination, photochemical processes and redox reactions under specific environmental conditions.^52,53

Fig. 4 Feature data for supramolecular assemblies. (a) Van Krevelen diagrams of Carbonyl molecule distribution derived from FT-ICR-MS analysis.⁵¹ (b) Morphology and structures of PFOS-free NOM and PFOS-involved NOM assemblies shown by AFM images and IR mapping.¹⁴ (c) TERS analysis of phospholipid assemblies, showing C–H stretching intensity images and corresponding discontinuity spectra.⁵⁸ (d) RISE analysis of RPP, showing SEM images, Raman spectra of corresponding points (left) and Raman mapping (right).⁵⁹

As a non-invasive analytical method, nuclear magnetic resonance (NMR) spectroscopy characterizes the three-dimensional structure of supramolecular assemblies, internal molecular dynamic processes and intermolecular interactions.^48,54–56 Based on the NMR data, ML may establish spectral-structure relationships between the components of supramolecular self-assemblies. For instance, 1329 NMR data sets from 100 proteins along with their sequences were used as deep learning (an important branch of ML) input data for the assignment of protein backbones and side-chain chemical shifts. This chemical shift assignment provided atomic-level insights into protein assembly, subsequently enabling the reconstruction of structures for these protein assemblies.⁵⁷

Infrared (IR) and Raman spectroscopy, owing to their high or even extreme sensitivity to both intra- and intermolecular bonds, have been regarded as powerful tools to both qualitatively and quantitatively identify supramolecular assembly structures and chemical compositions.^60–62 The change in dipole moment of molecules during a given normal mode of vibration is always detected by IR spectroscopy whilst the total symmetric vibrations of large molecules having a symmetry center need to be resorted to Raman spectroscopy.⁶³ Through tracking characteristic or fingerprint peaks of organic compounds in complex biopolymers (e.g., carbohydrates, lipids, and proteins),⁶⁴ IR or Raman spectroscopy is used to analyse the biochemical changes in the structure (in particular, secondary structures) and content of bio-macromolecules such as proteins and glucose.⁶⁵ In the domain of environmental science, those spectral data may serve as input data for ML models to identify organic polymers.^66,67

Before being input into ML models, those spectral data must undergo preprocessing to ensure data quality and consistency, including polynomial fitting for baseline correction, smoothing algorithms for noise reduction, normalization to adjust spectral data to the same intensity level and first-order derivative processing to highlight characteristic peaks in the spectra.^66–69 For data implementation in the convolutional neural network (CNN) which is typically designed for image processing, two approaches are often used for converting spectral data into images by which feature extraction can be well enhanced: transforming spectra into spectrograms using short-time Fourier transforms⁷⁰ or converting spectra into scalogram images using wavelet transforms.⁷¹

The ML models that were built according to the near-IR reflectance spectroscopic results of pectin, cellulose, lignin, and phenols in cuticles and cell walls have been reported to accurately capture the content and structure variation of these assembled macromolecules.⁷² The corresponding spectral features, when being extracted by ML, can establish correlations between characteristic spectra and the chemical context.^73,74 In addition, ultraviolet-visible spectroscopy can observe the transition process of supramolecular self-assemblies from monomeric to aggregated states as well.^75,76 It should be noted that mere spectroscopic information will never depict the spatial organization and configuration of the assembled organic compounds not to mention at the nanometer or submicron scale, which, however, is key to the ML of NOM self-assembly.

2.4. Micro-nano scale spatial imaging as an indispensable data source

Morphological imaging techniques reveal the structure of supramolecular assemblies at the nanometer or submicron scale. While traditional optical microscopy techniques are unable to resolve features below 200 nm due to the light diffraction limit, some ultrahigh-resolution techniques enable the detailed characterization of supramolecular assemblies below 100 nm.^77,78 Transmission electron microscopy (TEM) has significantly contributed to studying small molecules, polymers, and biomolecules self-assembly by facilitating the discovery, visualization, and quantification of structures and dynamic processes.⁷⁹ Integrating these imaging data with ML enables in-depth analysis of, for instance, quantifying nanoparticle distribution in polymer aggregates.⁸⁰ Liquid-phase TEM videos with ML unveiled dynamic self-assembly processes of nanoparticles in solution.⁸¹ The assemblies mediated by metal ions or metal complexes through non-covalent bonds with organic ligands have been characterized by scanning tunneling microscopy (STM) which tunnels current to image conductive sample surfaces under ultra-high vacuum conditions.^26,82,83 STM generates a series of imaging data illustrating the self-assembly structures formed by molecules with identical functional groups (i.e., polycyclic aromatic hydrocarbons) adsorbing on the metal (i.e., Ag(1 1 1)) surfaces.^84,85 These data sets are suitable for ML applications aimed at predicting supramolecular assembly structures involving heavy metals. As the scanning probe technique is primarily used for analyzing the topology and surface morphology at the nanometer or submicron scale, atomic force microscopy (AFM) has been successfully adopted to predict the novel self-assembled structures of nanocomposite films via training the ML models with 595 AFM images.⁸⁶ In particular, with the data from the high-speed AFM (HS AFM) characterization of protein self-assembly processes, ML could extract the information of protein spatial positions and orientations and finally elaborate the self-assembly and dynamic behaviors on solid surfaces.^87,88 Spatial imaging data require specific preprocessing steps before being fed into CNNs, including image normalization, noise reduction and standardization of image dimensions and pixel values. However, the abovementioned spatial imaging data can only be used for ML when the self-assembly systems are composed of single or simple components due to the lack of chemical or fingerprint evidence for compound recognition. The limitations hinder the ML study of NOM self-assembly under real and complicated geochemical and environmental conditions that may be overcome by simultaneously utilizing spectroscopic and spatial imaging techniques.

2.5. Micro-nano scale spatial chemical analyses as suggested data sources of NOM self-assembly ML with environmental relevance

Considering the heterogeneity of NOM structures and the complexity of inter-molecular interactions at different environmental chemistries, the input data of ML models must reflect nanometer or submicron-scale spatial chemical features. Molecular descriptors, spectroscopic analyses or morphological imaging techniques can only provide partial information as previously discussed. The integration of chemical and micro-spatial analytical techniques can provide the most appropriate data sources of ML for multidimensional and comprehensive mechanism interpretation of NOM self-assembly. Advanced spectroscopic mapping techniques, such as IR scattering-type scanning near-field optical microscopy,⁸⁹ AFM-IR spectroscopy (Fig. 4(b)),⁹⁰ tip-enhanced Raman spectroscopy (TERS) (Fig. 4(c))⁹¹ and Raman imaging and scanning electron (RISE) microscopy (Fig. 4(d)),⁹² allow the in situ visualization of spatial distribution of chemical groups in supramolecular self-assembled systems at the nanoscale (Fig. 1(b)). The as-attained data are sufficient to develop ML models for understanding and predicting NOM supramolecular assembly processes and behaviors. The energy-dispersive X-ray spectroscopy (EDS) mapping technique coupled with electron microscopy (typically, SEM-EDS and STEM-EDS)^93,94 rapidly qualitatively and quantitatively detects the elemental compositions on the surface of samples, showing elemental migration and enrichment behaviors during the assembly processes.¹⁴ Nevertheless, the analytical results from those techniques can only be adopted as supportive data for ML input due to the lack of molecular chemical information.

In particular, to develop ML models for elucidating NOM self-assembly behaviors involving micropollutants (i.e., per- and polyfluoroalkyl substances, PFAS), the main data source is suggested to include molecular chemical micro-spatial results of AFM-IR-mapping. AFM-IR-mapping presents the nanoscale distribution of NOM and PFAS in self-assembly aggregates by mapping the characteristic IR peak of each NOM component and the fingerprint C–F bond of PFAS. In this scenario, the SEM-EDS-mapping data could be adopted to map the F element in samples to further verify the PFAS spatial distribution. When the supramolecular assembly involves inorganic pollutants (i.e., heavy metal nanoparticles), the combination of spectroscopic (mapping) analyses is needed to obtain the input data depicting chemical interactions between organics and inorganics as well as their spatial distribution. Then, the input data for ML may be collected from single-particle inductively coupled plasma mass spectrometry,⁹⁵ or high-resolution imaging of elemental and isotopic distributions using nanoscale secondary ion mass spectrometry⁹⁶ in addition to analytical methods for identifying typical NOM components. It is worth noting that the NOM self-assembly is dynamic and environmentally dependent since self-assembly processes and structures are highly influenced by environmental geochemical conditions such as temperature, pH and ionic strength. Consequently, the input data for ML models are supposed to be acquired from the analytical techniques in the targeted geochemical circumstances such that the output of ML could be of environmental relevance and significance.

3. Algorithms, models and interpretability analyses favored by ML of NOM self-assembly

3.1. Guide for algorithm selection

When selecting an appropriate ML algorithm for supramolecular self-assembly research, two key factors need to be considered. On the one hand, the choice among regression, classification, clustering and dimensionality reduction algorithms is made given the specific issues of supramolecular assembly to be solved (Table 1). On the other hand, a suitable algorithm is determined based on the input data characteristics including scale, dimensionality, quality and types (i.e., image data, molecular graphs, molecular sequences and tabular data). To be specific, traditional ML algorithms such as logistic regression (LR), random forest (RF) and support vector machine (SVM) are more sensitive to numerical data; convolutional neural networks (CNNs) are better suited for reading and processing image data; graph neural networks (GNNs) are adept at handling molecular graph data (Table 1). These neural networks are better suited for large-scale datasets.

Table 1 ML aided prediction of typical supramolecular assembly

Self-assembly component	Input	Output^a	Data points^b	ML task	Type of task	Algorithm^c
a EAC: electron accepting capacity; EDC: electron donating capacity; ETC: electron transfer capacity. b —: not mentioned. c GBT: gradient boosting tree; DT: decision tree; KRR: kernel ridge regression; PCA: principal component analysis; NMF: non-negative matrix factorization; GMM: Gaussian mixture model; PLS: partial least squares; MLR: multiple linear regression; BPNN: back propagation neural network.
Dipeptide hydrogels^100	Molecular descriptors	Whether or not a hydrogel is formed	2304	Prediction of hydrogel formation	Classification	RF, GBT, and LR
Blends of nanoparticles, polymers and small molecules^86	Assembly nature and environmental conditions	Parameters measured from AFM images describing assembly morphology	595	Prediction of new nanocomposite morphology	Regression	GBT, RF, GBR, SVM, LGER, and KRR
Proteins^87	HS AFM images	Protein location and orientation	—	Protein identification and localization	Classification	CNN (U-Net)
		Protein spatial distribution in assembly		Protein identification in the assembly	Clustering	PCA, NMF, and GMM
Proteins^57	NMR spectra and protein sequences	Signal positions, resonance assignments, structure proposals, and protein structures	100 protein sequences, 1329 NMR spectra	Prediction of protein structures	Regression and classification	ARTINA (ResNet, GNN, and GBT)
Assemblies of metals with organic ligands^85	Molecular diagrams of organics and metal substrate types	Whether or not there is a target attribute associated with the assembly	30	Prediction of molecular self-assembly structures	Classification	GNN, SVM, RF, and DT
DNA oligonucleotides and melamine cyanurate^107	Fluorescence microscopy images	Mg^2+ concentration	7000	Analysis of correlation between the supramolecular structure and Mg^2+ concentration	Classification	CNN (VGG16, VGG19, and ResNet50)
Humic substances^108	Element contents, chemical group contents, and experimental optical parameters	Redox activity of humic substances: EAC, EDC, and ETC	144	Relationship between the structure and redox activity	Regression	PLS, MLR, and BPNN
NOM^53	FT-ICR-MS results	Reactive or unreactive	—	Understanding whether the constituent molecules of NOM react after UV irradiation	Classification	LR, SVM, RF, and XGBoost

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Based on the mapping relationships to be established and the data availability, the widely-known three categories of ML algorithms – supervised, unsupervised and semi-supervised may be adopted to interpret the mechanisms and structures of NOM self-assembly. Supervised learning aims to learn the mapping relationship between input and output data. The output can either be continuous numerical values (regression algorithms) such as predicting the aggregation propensity (AP) of peptides (Fig. 5(a))⁹⁷ or discrete or categorical (classification algorithms) such as the reactivity^53,98,99 or formability^97,100 of NOM under specific environmental conditions (Fig. 5(a)). Most of the issues of NOM supramolecular self-assembly can be addressed by supervised learning, including but not limited to predicting assembly structures from the input data of elemental and component composition, the thermal stability, photoconductivity and redox capacity from the input data of assembly structures and environmental chemistry, as well as the vertical transportation rate from the input data of assembly size and density. Unsupervised learning is not associated with specific prediction tasks but focuses on identifying trends, patterns or clusters of input data alone. Dimensionality reduction algorithms were used to reduce the high-dimensional descriptors obtained from MD simulations with a large amount of spatiotemporal details to the low-dimensional data which were conducive for visualization and analysis.^101–103 Cluster analysis divides data into multiple groups which can be used to identify data association patterns. For example, clustering techniques were used to identify ordered and disordered regions in the phase transition process from MD simulation data of lipids at different temperatures. The results revealed the temperature dependence of lipid phase changes.¹⁰⁴ Unsupervised learning should contribute to data exploration and pattern recognition when the input data of ML for interpreting NOM self-assembly structures are of high dimensionality. Typically, it can be used to identify self-assembly pathways using MD simulation data or discover clustering relationships in high-dimensional IR-mapping data which directly correspond to assembly structures. Semi-supervised learning can be useful when there are abundant input data but limited corresponding output data though its applications are currently not extensive. To further improve the prediction performance, ensemble methods that combine multiple individual models have been widely adopted, such as bagging (i.e., RF), boosting (i.e., XGBoost and LightGBM) and stacking. Ensemble modeling techniques can effectively reduce overfitting and improve model generalization by aggregating predictions from multiple base models.¹⁰⁵ For example, integrating various simple weak ML algorithms such as extremely randomized trees, adaptive boosting, RF, cascade forest, LightGBM and XGBoost is used to predict whether small molecule compounds would interact with proteins.¹⁰⁶

Fig. 5 ML methods. (a) An integrated framework adopting MD simulation and experimentation results as data sources of ML for predicting and discovering tetrapeptide hydrogels.⁹⁷ (b) Using isotope-labeled FT-ICR-MS as input data for interpretable ML and paired mass distance networks to reveal photo-reactivity and photo-transformation of NOM.⁵³

3.2. Optimal model construction

Supervised learning facilitates the establishment of relationship models between variables and results. These models predict the assembly structures and quantify structure–property–effect relationships, which enhance researchers' understanding of NOM supramolecular assembly patterns. Herein, we specifically focus on discussing strategies for building supervised learning models. The model training process begins with dataset partitioning, where the training set is used for model fitting and the validation set aids in hyperparameter tuning and overfitting prevention. K-Fold cross-validation ensures the robustness of models across different data subsets and mitigates overfitting issues.^{86,98,108,109} Monte Carlo cross-validation (MCCV) offers a more flexible approach by randomly partitioning the dataset multiple times, enabling arbitrary validation iterations and potentially better handling imbalanced datasets.^110,111 However, the limitations of MCCV might be potential sample utilization imbalance, reduced result reproducibility without fixed random seeds and higher computational costs.^112,113

Apart from cross-validation, several complementary techniques are essential to prevent the overfitting of ML models. Regularization methods (in particular, L1 and L2 regularization) add penalty terms to the loss function such that the model complexity is controlled. L1 regularization promotes sparse solutions by potentially setting some weights to zero.¹¹⁴ L2 regularization prevents excessive weight magnitudes by penalizing large weights quadratically, ensuring even consideration of all features by models.¹¹⁴ Dropout randomly deactivates neurons during training, forcing the network to learn robust features.¹¹⁵ Early stopping monitors the validation performance during training and halts the process when performance begins to degrade, which effectively prevents overtraining.^114,116

The optimal average performance across validation iterations guides hyperparameter selection. With the optimal values corresponding to the best model, hyperparameters are external configurations whose slight adjustments can significantly improve or impair the model performance. However, manual hyperparameter optimization is computationally expensive and not optimal. More advanced methods employ automatic optimization algorithms to find the best hyperparameter configurations such as Bayesian optimization,^117,118 random search,^119,120 grid search^120–122 and particle swarm optimization.^123,124

Transfer learning shows great potential for leveraging the knowledge gained from the large and related datasets in enhancing the predictive performance based on comparatively small target datasets, through which the data scarcity problems could be solved. A pre-trained model refers to a deep neural network that has been trained on a large dataset for a general task typically using architectures such as GoogLeNet or ResNet.¹²⁵ The early convolutional layers of that model learn basic visual feature extractors (i.e., edges, textures, etc.).¹²⁶ Fine-tuning enables the adaptation of CNN-based models to new scenarios in two main ways: retraining the last few layers to recognize new types of patterns while keeping the early feature-detecting layers unchanged¹²⁶ and using a smaller learning rate to carefully update the models without losing their previously learned knowledge.¹²⁷

The success of transfer learning relies on finding the underlying similarities between the source and target domains. As demonstrated in Raman spectroscopy applications, the fundamental basis for transfer learning is built upon the similar hierarchical features between those Raman spectral patterns and the image patterns learned and recognized by pre-trained CNNs.⁷¹ The early layers of these models, which detected basic features such as edges and textures, could be effectively repurposed for analyzing spectral patterns and molecular interactions. This principle of leveraging similarities can be applied to molecular systems. For instance, an initial model was trained on a large non-transmembrane protein dataset and then transferred to a small transmembrane protein dataset to predict the contact points between protein chains.¹²⁸ The premise of that transfer was the structural similarities between those two types of proteins. Here is another example. A pre-trained model was obtained using a large protein dataset calculated with low-precision quantum mechanical methods and then transferred to a small fragmented protein dataset calculated with high-precision methods to accelerate quantum mechanical calculations.¹²⁹ It is the universality of quantum mechanical calculation principles that made the transfer learning possible. For fine-tuning, optimization algorithms such as stochastic gradient descent,¹³⁰ stochastic gradient descent with momentum,¹³¹ adaptive moment estimation,¹³² adadelta¹³³ and adagrad¹³⁴ are commonly employed to effectively transfer knowledge while preserving relevant features. This approach may be useful when NOM assembly data are limited. It allows the model to gain insights into the influence of non-covalent intermolecular interactions on the assembly structures via first learning from a broader range of supramolecular systems. The knowledge from the pre-trained models can then be transferred to specific NOM assembly datasets through fine-tuning.

The choice of model evaluation metrics depends on specific problem types. Generally, for regression problems, the coefficient of determination (R²) and root mean square error are commonly used. For classification problems, the F1 score, area under the curve (AUC) and accuracy are typical metrics. For supramolecular assembly structure prediction, specific evaluation metrics exist, which are root-mean-square deviation and root-mean-square fluctuation. The former measures the degree of structural change and the latter measures atomic fluctuations relative to the average structure.¹³⁵ Benchmark evaluations compare the performance of different models using unified datasets and metrics, providing references for algorithm comparison on specific tasks. For example, the XGBoost model outperformed LR, SVM and RF in AUC-based model evaluation to predict NOM reactivity under UV irradiation.⁵³

3.3. Model interpretability analyses

Predictive accuracy is not the only criterion of model evaluation, and the interpretability of the model is equally important.¹³⁶ Interpretable ML enhances the model credibility while bridging the gap between data-driven ML and NOM assembly principles. Model interpretability encompasses three key aspects: data interpretability, intrinsic interpretability and post hoc interpretability.^137,138 Data interpretability aims at understanding the degree of association between input data and prediction results, as well as the quality, distribution and representativeness of data. Taking molecular descriptor as an example, data interpretability should comprehend the physicochemical significance of each descriptor, identifying correlations between descriptors and assessing the quality and completeness of data.¹³⁷ The chemical composition, environmental parameters and assembly behaviors of NOM supramolecular self-assemblies inherently have strong correlations which, however, might not be considered to have a direct causal relationship due to hidden variables (such as metal ions in the solvent environment promoting bridging between NOM molecules)^139,140 or indirect influences (pH changes affecting the deprotonation of carboxylic and phenolic functional groups in NOM, altering the chemical properties of these functional groups and in turn influencing the NOM assembly structure).¹⁴¹ Therefore, input variables need to be selected as broadly as possible, allowing the model to demonstrate the potential impact mechanisms of NOM assembly at the data level. Common data interpretability methods consist of exploratory data analysis techniques, including traditional statistical methods and dimensionality reduction approaches such as PCA and t-SNE.^142,143

The intrinsic model interpretability refers to ML models with inherently interpretable structures and mechanisms that are easy to understand and interpret. The interpretability stems from the model design, which allows us to understand how ML works such that the trust in the models increases.¹⁴⁴ Nevertheless, a model's intrinsic interpretability often comes at the cost of accuracy,¹⁴⁵ and specifically, interpretable models such as decision trees and linear regression have transparent decision processes but limited ability to solve complex nonlinear problems.¹⁴⁶ In contrast, deep neural network models excel at capturing complex nonlinear relationships but their internal decision processes are often viewed as black boxes. As for post hoc interpretability, it is a method to complement the intrinsic interpretability of models for understanding how specific decisions are made after a black-box model is trained. Methods such as Shapley additive explanations (SHAP), locally interpretable model-agnostic explanations and partial dependence plots (PDPs) are used to understand the molecular properties, structures, environmental conditions and other features influencing the processes or properties of assembly.^53,98,147 SHAP provides local explanations and helps to understand feature interaction effects while PDPs show the global relationship between a single feature and the target variable across the entire dataset.^148–150 SHAP enables the quantification of feature importance in complex models by calculating each feature's contribution to specific predictions. Dwinandha et al.⁵³ discovered that larger, unsaturated NOM containing S and N atoms was more susceptible to photodegradation through using interpretable ML (Fig. 5(b)). SHAP can theoretically be used as a feature reduction technique via ranking the features based on their absolute SHAP values. Some studies have shown that the SHAP-based feature selection can achieve better results than traditional methods such as mutual information or ANOVA.¹⁴⁸ However, post-training approaches have two main limitations. Firstly, SHAP values are calculated based on a specific trained model whose feature interactions, that is to say, importance ranking, may change with different model architectures or training runs; secondly, the computational cost is relatively high.

However, the explanations provided by model interpretability only estimate the working mechanism of a specific ML model and may not correspond to real-world patterns.^144,151,152 The interpretations from ML need to be further validated through prior knowledge or experimental results.

4. Applications of interpretable ML in elucidating processes, architectures and properties of NOM supramolecular self-assembly in real environments

4.1. NOM supramolecular self-assembling processes

Supramolecular assembly processes are primarily driven by intrinsic properties of assembling units and external environmental conditions. For the former, the inter-component forces and energy barriers at various stages of assembly significantly influence the entire self-assembly pathway and conformation. Protein–peptide and protein–protein interactions play crucial roles in regulating supramolecular functions, which can be predicted by current ML based on protein sequences, peptide sequences or binding domain data.^153–155 Binding affinities between proteins are thus elucidated through recognizing the specific protein domains bound to other peptide segments or analyzing descriptors of protein complexes.^155,156 These algorithms have been extended to predict interactions in protein–nanoparticle complexes as well.¹⁵⁶

The thermodynamic factors in the environment such as temperature, pH, and ionic strength directly affect the non-covalent interactions between assembling units, thereby impacting the kinetic pathways. Thermal responses and sensitivities of NOM are influenced by inherent thermodynamic properties of molecules across different climatic regions and nutrient levels.¹⁵⁷ Therefore, researchers developed data-driven predictive models to forecast supramolecular assembly processes under various conditions. These models were trained using data obtained from high-throughput experiments, learning features from experimental designs (such as components, solvent conditions, temperature, and pH) to predict the phase transition and morphology of supramolecular assemblies.^158,159 Typically, temperature changes are reported to induce the phase transitions of lipids and thus regulated their self-assembly process. These transitions could alter the permeability of biological membranes, influence the sedimentation of lipid assemblies in the environment and affect the adsorption and desorption behaviors of pollutants on lipid self-assembled structures.

4.2. NOM supramolecular self-assembly architectures

A central challenge in ML of NOM self-assembly is to interpret or predict the architectures of assembled systems with diverse functionality. Conventional approaches rely on structure preselection followed by experimental validation, importantly dependent on intuition and trial-and-error methods. While these approaches have uncovered numerous groundbreaking supramolecular materials, severe limitations hinder further discovery: first, human intuition is constrained by inductive reasoning from known systems and unable to fill in the knowledge gap in the unknown areas; then, traditional intuition-based and trial-and-error methods are time-consuming and resource-intensive. Promising approaches could be computational methods.

Taking the prediction of protein assembly structures as an instance, homology modeling could be adopted based on existing sequences in the Protein Data Bank (PDB).¹⁶⁰ However, many sequences lack homologous proteins, necessitating ab initio prediction. Ab initio methods segment the sequence into fragments, search for similar known structures for each fragment, and finally assemble these fragment structures using energy functions to predict the final protein structure.^160,161 To improve precision using energy functions, researchers have begun decomposing the three-dimensional structure prediction problem into secondary structure prediction and contact map prediction. Secondary structure prediction identifies helices, sheets and other structural elements, facilitating the discovery of more suitable structural fragments. Contact maps serve as constraints for energy functions, with both approaches guiding more accurate tertiary structure predictions.^162,163 AlphaFold, developed by DeepMind, represents a series of artificial intelligence-based deep learning methods for three-dimensional protein structure prediction, which has undergone continuous iterations and updates. AlphaFold 1 predicts continuous angle distributions and distances between amino acid pairs from protein sequences, transforming these into protein-specific energy functions to infer three-dimensional structures.¹⁶⁴ AlphaFold 2 employs multiple sequence alignments and deep learning algorithms, incorporating physical and biological knowledge about protein structures. However, it can only effectively predict structures of isolated proteins, not those interacting in the real-world context.¹⁶⁵ AlphaFold 3 addresses the limitations of its predecessor, accurately predicting structures and interactions of proteins, DNA, RNA, and ligands among other biomolecules.¹⁶⁶

In recent years, ML was applied to establish relationships between the chemical structures of peptides and their self-assembly, helping to identify peptide sequences prone to form stable supramolecular structures through aggregation.¹⁰⁰ Descriptors for each compound were calculated using PaDEL for ML¹⁰⁰ to predict the formation potential of urea hydrogels³⁰ and nucleotide hydrogels⁴³ and also to determine the key structural influencing factors. This approach assisted researchers in designing and predicting peptide hydrogels with novel chemical structures. For the prediction of tetrapeptide hydrogels, researchers employed MD simulations and ML-trained regression models to predict the aggregation propensity of peptide self-assembly.⁹⁷ The selected 55 peptide sequences were used to refine the ML model through iterative processes which were applied to predict the likelihood of hydrogel formation for 8000 peptide sequences. Additionally, specific peptide hydrogels underwent biological testing (Fig. 5(b)).

5. Necessities and challenges of unveiling NOM-self-assembly-involved environmental geochemical processes by ML

5.1. Environmental geochemical processes of pollutants influenced by NOM self-assembly

5.1.1. Redox processes. NOM acts as natural photosensitizer in environmental matrixes, and the as-formed highly reactive intermediates^167,168 served as strong oxidants indirectly photodegrading various organic pollutants (e.g., amoxicillin, tetracycline, sulfamethoxazole, polybrominated diphenyl ethers, and indomethacin).^169–173 In anoxic environments such as groundwater, the quinone compounds in NOM may rapidly transfer electrons to heavy metal ions, reducing high-valence metal ions to lower valence states, which then form stable complexes with NOM and in turn inhibit electron transfer.^174,175 Previously, relevant laboratory studies mainly focused on case-by-case investigations under limited environmental conditions. Challenge in analyzing numerous case studies can be well solved by ML through dealing with vast datasets. ML has been successfully employed to reveal the potential of NOM in photochemical or redox reactivity under natural light,^176,177 UV irradiation^53,98 and anaerobic fermentation⁵² conditions with the data source of FT-ICR-MS analysis. However, a series of questions still need to be addressed regarding the photoconductivity of NOM in promoting pollutant transformation, particularly including (i) the features of NOM supramolecular self-assembly structures regulated by pollutants, (ii) the correlation between NOM self-assembly structures and pollutant transformation efficiency, (iii) the intermediates and products generated from the pollutant degradation and (iv) the impact of light and temperature on the NOM self-assembly performance.

5.1.2. Spatial transfer processes. In addition to redox processes, the NOM assembly undergoes structural and chemical composition transformation from dissolved into particulate states, resulting in photo-flocculation.^178,179 Hence, NOM is also a primary factor influencing particle sedimentation (especially nanoparticles)¹⁸⁰ with settling velocity dependent on particle size, density, and friction coefficient.¹⁸¹ Recent studies have demonstrated the excellent performance of ML in predicting the settling velocities of microparticles with various shapes.¹⁸² This success can be attributed to the conceptualization of particle morphological characteristics.¹⁸³ In future research, a comprehensive characterization framework ought to be developed in priority for the ML study of NOM and pollutant assemblies. In the framework, developing mathematical descriptors to represent the complex morphologies and compositions of these assemblies is crucial. The quantification of size, shape, and density distributions using advanced imaging techniques such as AFM and the characterization of surface properties such as charge density and hydrophobicity through spectroscopic methods are suggested to be encompassed. Then, systematic experiments are necessary to measure sedimentation rates of various NOM–pollutant assemblies under diverse environmental conditions, and the establishment of standardized protocols for data collection is significant to ensure consistency across studies. Moreover, the exploration of various ML algorithms is needed to capture the intricate relationships between assembly characteristics and sedimentation behaviors. This comprehensive approach will advance our understanding of environmental fate and behaviors of NOM–pollutant assemblies.

5.2. Bioavailability of pollutants in NOM self-assemblies in real environmental scenarios

NOM supramolecular self-assemblies may concentrate certain bioactive components and pollutants. As a result, the acquiring efficiency of energy and nutrients from assembly components by organisms can be impacted, and meanwhile, the toxic effects of pollutants may be amplified or mitigated, which even influence lethal doses.²³ As a typical example, the bioavailability of metals dependent on their solubility and oxidation state can be influenced by NOM complexation.^184,185 Predictive models based on pollutant structures revealed molecular structural features relating to the bioavailability of pollutants. Taking the micropollutants of PFAS as instances, featuring high persistence and bioaccumulation,⁶ PFAS present complicated ecotoxicological traits due to the diversity of PFAS categories. ML-based quantitative structure–activity relationship (QSAR) models were employed to predict the bioactivity of PFAS with various biological targets from the perspective of PFAS molecular structures.^186,187

Besides, the complex interactions in pollutant–water–plant root systems challenge traditional QSAR predictions. To address this issue, ML captured nonlinear relationships between molecular structures of organic pollutants and root concentration factors in complex systems.^188–190 This ML framework can be extended to assess the bioaccumulation of any emerging organic pollutant in plants. It should be emphasized that common experimental studies using high-dose exposures may not accurately reflect the ecological risks of pollutants in real environments. ML is capable of uncovering the real bioavailability and effectiveness of NOM and pollutants through training model learning with the data relevant to environmental dose levels and real environmental scenarios. Nanoparticles in natural environments can adsorb biomolecules onto their surfaces, forming a protein corona (PC). The bio-nano interactions of nanoparticle–PCs complexes then alter their bioavailability and toxicity.¹⁹¹ Predicting interactions and interaction sites will help figure out the specific protein species or structures more likely to adsorb on nanoparticle surfaces, and thus, the behaviors of these nanoparticles in organisms can be understood.¹⁵⁶

5.3. Correlation between NOM self-assembly and global environmental issues

The dynamic turnover of NOM has a major impact on element cycling (typically, cycling of carbon, nitrogen and phosphorus), which further results in a series of environmental issues such as global climate change, water eutrophication, harmful algal blooms and so forth.^192,193 With the reactive oxygen species generation from structural mineral oxygenation, the association between NOM and minerals in supramolecular self-assemblies may either help to store carbon by decelerating NOM decomposition or release a fraction of carbon to the atmosphere as CO₂ and CH₄via degrading NOM.¹⁹⁴ Disaggregation and decomposition of particulate organic matter (typically, NOM assemblies), along with exogenous input, causes steep and prolonged increases of total nitrogen, ammonium nitrogen and total phosphorus in the bottom waters of reservoirs.¹⁹⁵

To explore the process mechanisms and causative geochemical factors, long-term and large-scale sampling, observation and analyses are needed albeit only partial truths can be derived due to the insurmountable spatial and temporal restriction of those studies. Alternatively, the applications of ML, remote sensing technologies and supramolecular self-assembly analysis methods are promising in facilitating relevant research. The eXtreme Gradient Boosting ML framework has been developed using the data obtained from remote sensing technology for spatio-temporal estimation of the key nutrient – P in eutrophic lakes.¹⁹⁶ Similarly, satellite variables were used to train the RF model to predict the emission of greenhouse gas – CH₄.¹⁹⁷ It is well known that ML is capable of estimating the intermediates and products of NOM (i.e., types and quantities of greenhouse gases) during the (bio-)mineralization process using the input data of NOM structures, quantitative analyses of NOM components, microbial community and environmental parameters. Nonetheless, ML frameworks for the correlation between NOM supramolecular self-assemblies and large-scale geochemical processes have not been systematically conducted, leaving a knowledge gap in NOM-assembly-driven geochemical effects.

6. Remarks and perspectives

The molecule-, nanometer- or submicron-scale supramolecular self-assembly of NOM is capable of profoundly impacting large-scale geochemical processes. To unveil a great ocean behind a drop of water, ML-based computational modeling is among the most promising and reliable approaches in the current big data era. Accordingly, this review presented specific strategies for adopting ML in interpreting the assembling processes, structures and environmental behaviors of NOM nano-assembly, including data source recommendation, algorithm selection, model construction and interpretability for ML as well as applications of interpretable ML. Considering the importance of datasets, the data obtained from the advanced nanoscale spatial chemical analyses are suggested (i.e., AFM-IR-mapping, Raman-mapping, and SEM-Raman-mapping) which provide the combined information of molecular interactions, features and structural visualization. Thus, the existing ML algorithms may struggle to handle multi-scale and multi-modal data. With an appropriate algorithm chosen from regression, classification, clustering and dimensionality reduction, ML models can be constructed based on the mapping relationships to be established and the data availability. In particular, supervised models with interpretability are crucial for the understanding of NOM supramolecular assembly patterns owing to their strong capacity of predicting assembly structures and quantifying structure–property–effect relationships as well as bridging the gap between simply data-driven ML and complicated NOM assembly practice.

It is worth noting that the difficulty of recognizing NOM self-assembly also comes from the diversity of NOM molecular structures, the growing appearance and involvement of emerging pollutants in assemblies as well as the complicated and varied environmental geochemical conditions. The ultimate tasks of studying NOM supramolecular self-assembly in environments are to understand how different components (i.e., pollutants) regulate NOM supramolecular assembly processes and how the resulting assembly structures regulate the geochemical behaviors, bioavailability and elemental cycling processes. Given the complexity of geochemical conditions where the NOM self-assembly happens and exists, the combination of experimental investigations, molecular theoretical simulation and ML computation modeling is highly advised. The experiments conducted under the targeted environmental geochemical conditions and the accompanied advanced chemical analytical technologies are always indispensable, which provide ML with the contextualized input data and in turn validate the ML output in practical scenarios. Besides, DFT, a quantum mechanical simulation tool, denotes the NOM–pollutant interactions and electronic properties; in particular, MD reveals the structure, thermodynamics and kinetics of NOM supramolecular assemblies at the molecular level.^7,198 The theoretical simulation results uncover dynamic behaviors and mechanisms of supramolecular assembly processes specifically at the molecular and atomic levels. As another powerful assisting tool, DFT and MD simulation are suitable to examine the reliability and precision of ML models and experimental observations as well as to guide the subsequent experimental designs. Research frameworks coupling ML, experiments and theoretical simulation may provide a comprehensive, efficient and innovative view of understanding NOM nano-assembly-involved environmental issues (Fig. 6).

Fig. 6 Research proposal of coupling ML, experiments and theoretical simulation to elucidate or predict NOM supramolecular nano-assembly and relevant environmental geochemical processes (figures of MD and DFT reproduced with permission from ref. 11 and 7).

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This research was supported by the National Natural Science Foundation of China (No. 42177442) and Research and Development Plan of “Leading Goose” in Zhejiang Province (No. 2023C03128).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4em00662c

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