Prediction of Sensor Ability Based on Chemical Formula: Possible Approaches and Pitfalls

Abstract

This review presents an analysis of different algorithms for predicting the sensory ability of organic compounds towards metal ions based on their chemical formula. A database of chemosensors containing information on various classes of suitable compounds, including dipyrromethenes, BODIPY, Schiff bases, hydrazones, fluorescein, rhodamine, phenanthroline, coumarin, naphthalimide derivatives, and others (a total of 965 molecules) has been compiled. Additionally, a freely available software has been developed for predicting the sensing ability of chemical compounds, which can be accessed through a Telegram bot. This tool aims to assist researchers in their search for new chemosensors.

1. Introduction

The rapid development of industries including those that require high-purity substances and the progress in medicine related to bioimaging techniques and theranostics depend strongly on the synthesis of novel efficient sensors for cations, anions, biomolecules, microparticles, etc. The interaction between an indicator molecule and the target analyte causes a change in solution color or fluorescence, which is increasingly preferred due to the widespread use of fluorescent spectrometers and microscopes in the laboratory. Luminescence-based detection is preferred over other methods due to its higher sensitivity compared to UV–Vis spectroscopy and the need for less of the sensor compound, as well as its suitability for bioimaging. A few examples of application of fluorescent sensors of different natures for a vast diversity of objects can be found in the most recent reviews [1,2,3,4,5,6,7,8].

Of all the analytes, metal ions, particularly heavy ones, are of particular importance due to their dual role. On the one hand, they are distributed pollutants of air, water, and soil causing severe acute or chronic intoxication. On the other hand, many enzymes that are crucial for maintaining the vital functions of microorganisms, plants, fungi, and mammals depend on such ions as Fe²⁺, Fe³⁺, Cu²⁺, Zn²⁺, Ni²⁺, and others. It is important to monitor the concentration of these cations in living tissues in real time; moreover, they provide the possibility to visualize the cells using a specific fluorescent indicator if its luminescence intensity is enhanced or quenched due to interaction with metals. It is no wonder that interest in the development of fluorescent sensors draws the attention of researchers more and more (Figure 1).

One of the key advantages of fluorescent metal detection is its high sensitivity, which allows for the detection of metal ions at low concentrations. This is particularly useful in the fields of environmental monitoring, medical diagnostics, and food safety, where trace amounts of metal ions can have significant impacts. Additionally, fluorescent metal detection often allows for real-time monitoring of metal ions, which is valuable for process control and quality assurance in various industries. The use of fluorescent sensors also offers the advantage of selectivity, as the fluorescence response is specific to a particular metal ion. This allows for the differentiation between different metal ions, even in a complex sample. Another important aspect of fluorescent metal detection is its compatibility with modern imaging technologies, such as microscopy and spectroscopy. This makes it possible to visualize the distribution of metal ions in a sample, providing valuable information for various applications, including bioimaging and material science. Overall, the sensitivity, selectivity, and compatibility with imaging technologies make fluorescent metal detection an important tool for a variety of applications.

However, despite progress and innovative papers introducing new classes of chemical compounds for detecting and quantifying various metals, the development of each new sensor still often seems to result from trial and error rather than a solid theoretical foundation. Despite a thorough understanding of fluorescence mechanisms [9,10,11], knowledge of Lewis hardness and softness of functional groups, and the ability to identify ESIPT (Excited-State Intramolecular Proton-Transfer) active compounds [12], researchers still face challenges in predicting the metal ions that can be indicated by newly synthesized substances. The optimal choice of solvent for sensory response is also a significant problem. In this regard, the creation of some tools allowing the prediction of different chemical compounds’ ability to detect various metal is of interest. Development of such tools requires necessarily taking into account the accumulated literature data.

The aim of this contribution is to discuss the possible approaches to predict the metal sensing ability of chemical compounds utilizing results obtained by other researchers and analyzing potential obstacles. A prototype software for the prediction of sensing ability has been developed.

We focus on metal ions due to an additional reason. While many sensors of anions are described in the literature, authors might not be accurate enough with their claims. As we have shown previously [13,14], some compounds that change the solution color and/or fluorescence spectrum in the presence of an anion can do so because of acid-base equilibria involving an indicator and an anion, rather than a specific complex formation. In that case, the anion sensor is, in fact, a pH indicator lacking the necessary selectivity towards the anion (as all anions of the same base strength would produce the same analytical response).

2. Results and Discussion

The basic idea is simple: the user inputs the formulas of the compounds of interest in a machine-readable form. The software searches for the most similar formulas in a database and returns them to the user, along with the cations that can be detected using these compounds, the solvent used for this purpose, and a numerical value characterizing the similarity between the user’s input and the closest matches in the database. These values can be vaguely interpreted as a probability of prediction success. Therefore, the main question is which method is the most suitable for searching for the similarities. The probable options are discussed below.

All these methods handle the Simplified Molecular-Input Line-Entry system (SMILES), which is a computer-recognizable ‘chemical language’ that allows for presenting 2D chemical formulas in a compact form [15]. SMILES is widely used for the retrieval of continuous databases and the building of prediction models [16]. SMILES supports all elements in the periodic table, denoting an atom with the respective atomic symbol in square brackets (they are usually omitted). To show non-aromatic atoms, uppercase letters are used; lowercase letters refer to aromatic atoms. If atomic notation has two symbols, the latter is always lowercase. Single, double, triple, and quadruple bonds are denoted by symbols ‘-’, ‘=’, ‘#’, and ‘$’, respectively, while the symbol ‘.’ shows disconnected structures (e.g., ionized salts such as [Na⁺].[Cl⁻]). A branch from a chain is specified by placing the SMILES symbol(s) for the branch between parentheses. The string in parentheses is placed directly after the symbol for the atom to which it is connected. If it is connected by a double or triple bond, the bond symbol immediately follows the left parenthesis. To identify the ring structure, the opening and closing ring atoms are numbered. Being a string representation of a chemical formula as a molecular graph and obeying relatively simple rules, SMILES became very popular among researchers for the purposes of computer chemistry. However, SMILES is not the only way of converting structural chemical information into text variables. The International Chemical Identifier (InChI) also allows for encoding information about chemical structure in a textual form suitable for use in databases. The International Chemical Identifier Key (InChIKey) is a condensed, 27-character-long form of InChI that contains no information about molecular structure and only makes sense when linked to the ‘parent’ InChI. However, it is convenient to use for searching the duplicated entries. Nevertheless, SMILES is arguably the most distributed and commonly used language.

2.1. Levenshtein Distance and Levenshtein Ratio

Since the SMILES entries in both the database and user input are just the symbolic sequences read by a computer as string variables, it is tempting to find the similarities between them using metrics such as Levenshtein distance (LD) and Levenshtein ratio (LR) [17]. LD (also known as edit distance) is the minimum number of single-character edits (insertions, deletions, or substitutions) required to transform one word into the other. For any two strings a and b of corresponding length of len(a) and len(b), LR is linked to LD by the following equation:

$$LR=\frac{len(a)+len(b)-LD}{len(a)+len(b)}$$

(1)

It should be kept in mind while calculating the LD value that the cost of insertion and deletion is 1, while the replacement operation is considered to contribute 2 to LD (as it can be seen as a pair of connected edits: deletion of a symbol and insertion of a new one).

When comparing the user input with all entries from the database, a series of LR values can be obtained. The lines from the database with the highest LR values are returned to the user as a result, providing information about cations detected with the help of compounds that are most similar to those input.

This method is advantageous as it is relatively simple, has minimal user arbitrariness (as it has no tunable variables that may influence the outcome), requires no preliminary processing of the SMILES, and consumes minimal computing time.

2.2. Tokenization and Vectorization

The tokenization process involves converting a sequence of symbols into a set of tokens, which are shorter symbolic sequences with assigned meanings. SMILES strings do not contain spaces such as in natural languages, so they must be segmented using specific rules. However, choosing the token size can be problematic since different split character lengths can produce slightly different results, as demonstrated by J. Shao et al. [18]. Additionally, if the splitting interval is too short, the set of unique tokens may be limited, while if it is too long, the SMILES may not produce enough tokens. However, single-character tokenization has been successfully used to predict chemical reaction outcomes [19,20].

Accounting of special symbols such as ‘(’, ‘[’, etc., is another problem as completeness of their deletion or substitution (as performed by authors in [18]) is also at the researcher’s discretion. Finally, it is noteworthy that two-character notated chemical elements (such as Si or Cl) should also be replaced with unique single-character signs to avoid splitting.

Another way to perform vectorization is by using n-grams for symbol sequences in SMILES of molecules. This method was used in our algorithm, where the n-gram size was equal to five. We believe that this is a more valid form of representing SMILES because several variations of character sequences can be taken into account, and there is no need to separate characters from each other with a space or any other character.

Vectorization (or word embedding) follows tokenization. Each SMILES entry in the database and user input is represented as a vector of length equal to the number of identified tokens. If the i^th token occurs in a given SMILES K times, the i^th value of the corresponding vector is equal to K.

Another way to perform vectorization is through a term frequency—inversed document frequency (TF-IDF) procedure, which considers the importance of each token across the total list of SMILES in a simple manner. The more frequent a word, the less weight it has. TF-IDF stands for a product of two parts: term frequency (TF), which estimates the value of a token within the frame of a single entry, defined as the relative frequency of token t within the given SMILES entry d:

$$TF=\frac{f_{t,d}}{{\displaystyle {\sum }_{t^{\prime }\in d}{f}_{t^{\prime },d}}}$$

(2)

where f_t,d is the number of times a token t appears in a given SMILES entry d.

The inversed document frequency (IDF) measuring the quantity of information provided by a token is calculated as follows:

$$IDF=\log \frac{N}{\left|\{d\in D:t\in d\}\right|}$$

(3)

where N is the total number of SMILES in corpus consisting of the database and user input, and |{d ∈ D: t ∈ d}| is the number of documents where the token t t appears (considering TF ≠ 0).

Finally, the TF-IDF metric is the product of the TF and IDF terms. It can be calculated for each token, and the TD-IDF value for the i^th token is placed in the i^th position of each SMILES vector.

There are different ways to define both TF and IDF, which affect the resulting TF-IDF value. It should be kept in mind, for example, while working with different libraries or programming languages, as they may apply different expressions for computing TF-IDF metrics.

Nonetheless, as a result of tokenization and vectorization, the SMILES from database and user input are transformed into a set of vectors consisting of TF-IDF values $\left\{a_i|a_iϵ\left[0,1\right], i=1,2,\dots ,N+1\right\}$, where $N$ is the database size. Vectors representing user input can be compared with each vector of the database using cosine similarity. This measure of similarity between two numeric sequences can be calculated as follows:

$$\cos \theta =\frac{A\cdot B}{‖A‖‖B‖}=\frac{{\displaystyle \sum _{i=1}^M{A}_i{B}_i}}{\sqrt{{\displaystyle \sum _{i=1}^M{A}_i^2}}\sqrt{{\displaystyle \sum _{i=1}^M{B}_i^2}}}$$

(4)

where A·B is the scalar product of two vectors, A and B, ||A|| ||B|| is the product of their magnitudes, and A_i and B_i are the i^th value of vectors.

2.3. Fingerprint Similarity Methods

In the methods described above, tools for natural language processing are used. However, there are many other ways to process SMILES of molecules, such as representing them as fingerprints. We used a standard fingerprinting algorithm (rdkit.org, accessed on 29 March 2023) that is similar to that used in the Daylight fingerprinter: it identifies and hashes topological paths (e.g., along bonds) in the molecule and then uses them to set bits of user-specified lengths (2048 bits) in a fingerprint. After that, one can use different similarity metrics, including Tanimoto similarity (T), Euclidean distance, and others.

Tanimoto similarity takes into consideration the intersection c of fingerprints a and b and their united power following the expression:

$$T=\frac{N_c}{N_a+N_b-N_c}$$

(5)

where N_a and N_b are the quantities of elements in the sets a and b, and N_c is the quantity of elements in the intersection of a and b sets.

The Euclidean distance (ED) between vectors is yet another applicable measure of similarity between two sets. It is calculated following the expression:

$$ED=\sqrt{N_a+N_b-2N_c}$$

(6)

where N_a, N_b, and N_c have the same notation as in the case of the Tanimoto similarity coefficient (Equation (5)). It should be noted that the formulas mentioned above are valid for binary (dichotomous) variables.

Several other measures can be also applied to define the degree of similarity between the two string variables, a and b, including, e.g., the Sørensen–Dice coefficient s (Equation (7)), the overlap coefficient oc (Equation (8)), etc.:

$$s=\frac{2n_t}{n_a+n_b}$$

(7)

where n_t is the number of character bigrams (sequences of two adjacent elements) bound in both strings a and b, n_a is the number of bigrams in string a, and n_b is the number of bigrams in string b.

$$oc(a,b)=\frac{\left|a\cap b\right|}{\min (\left|a\right|,\left|b\right|)}$$

(8)

The overlap coefficient is defined as the size of the intersection divided by the smaller size of the two sets, a and b. If a is a subset of set b or vice versa, the overlap coefficient is equal to 1.

2.4. Pitfalls of the Methods of Finding Similarities between SMILES

First, we would like to distinguish between two types of unfavorable outcomes: (1) failure to reproduce the results of a search for similarities; and (2) failure to predict the sensor ability of the user’s compound (software returns incorrect cations).

The main obstacle to reproducibility is an abundance of tunable parameters. The outcome of tokenization depends on the token size and the processing of special symbols. The type of procedure used (simple, TF-IDF, or machine-learning-based) affects the outcome of vectorization. If the TF-IDF protocol is used, the choice of equations used to calculate term frequency and inverse document frequency matters. If any neural network is implemented, the training parameters are also crucial.

Changing any of these variables, including the expressions used to define TF and IDF, the character split length, or the dictionary of special symbols processed, could potentially alter the predicted cation sensing ability. The approach based on finding Levenshtein ratios seems optimal because it does not require additional procedures for data processing (such as tokenization or vectorization) and does not depend on tunable variables.

In addition, it should be noted that training a neural network model, even after fivefold cross-validation, still carries the risk that predictions may only work well for the united training and validation datasets.

This brings us to the fact that the overall success of predictions, regardless of the approach used, depends primarily on the content quality of the database used. The main sources of erroneous prediction outcomes caused by database-related reasons can be divided into three subgroups:

• Incomplete database: if the database contains no entries about sensors for specific cations or a specific class of chemical compounds considered promising for fluorescent sensing of metal ions, no method can return reliable predictions with high similarity metrics;
• Erroneous entries in the database due to mistakes made by individuals filling the database (e.g., typos in SMILES or misplacement/swapping of cations from different lines);
• Erroneous entries in the database due to mistakes/fraud committed by researchers whose papers served as a source. For example, there may be false claims about the indicator ability of certain compounds towards specific cations or typos in chemical formulas of sensor compounds, etc.

The first two types of errors can be avoided by broadening the dataset and paying special attention while filling up the database. Unfortunately, recognizing the third type is much harder (although not impossible).

2.5. Program for Prediction of the Sensing Ability of Organic Compounds towards Cations

Considering all of the above, we have developed software for predicting the fluorescent sensing ability of organic compounds towards metal ions. It utilizes the methods described above, including an approach based on the calculation of the Tanimoto coefficient, Levenshtein ratio, Euclidean distance, as well as vectorization by means of a TF-IDF matrix and cosine similarity method. The user needs to convert the structures of interest into SMILES form and select one of the methods for searching for similar structures in the database. The output results contain the 10 closest matches for each user input compound and cation—for which these compounds are sensors—the similarity parameter (either Tanimoto coefficient, Levenshtein ratio, Euclidean distance, or cosine similarity value, which characterizes the closeness between the user input structure and the most similar entries from the database), and a number of entries from the database. The latter allows for finding more specific information such as the solvent used and reference to the source of information provided as a digital object identifier (DOI). If some of the user structures are identical to those in the database, any method returns the identical entries from the database with all information mentioned above. In this case, the Tanimoto coefficient, Levenshtein ratio, or cosine similarity value is equal to 1, while the Euclidean distance has a 0 value.

In addition, for the convenience of users, we have created a Telegram bot that helps to collect results with one click [21] (Figure 2).

To start using the Telegram bot, the user should follow the link or scan the QR code (Figure 2). Once the bot is launched, the user needs to enter the SMILES of the molecule of interest and select one of the four methods to search for similar structures (or choose all methods at once). The Telegram bot provides the user with a figure and a *.csv file as outputs. The figure displays structures and cations arranged in order of decreasing similarity to the requested molecule. The *.csv file is more informative and includes SMILES, cation, solvent, article DOI, InChI, InChIKey, and the value of the selected similarity parameter. All structures are sorted by decreasing similarity coefficient. The Supplementary Materials video file shows the bot functioning.

3. Materials and Methods

3.1. Database

The following reviews [22,23,24,25,26,27,28,29,30,31,32] and papers [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266] served as a source of information about fluorescent sensors for metal ions. Ignoring the duplicate entries, data on a total of 965 compounds were collected, including dipyrromethenes, BODIPY, Schiff bases, hydrazones, as well as fluorescein, rhodamine, phenanthroline, coumarin, naphthalimide derivatives, and some others. They were saved in an MS Excel file with a .xlsx extension and organized in the following table with columns for SMILES, InChI, InChIKey, cation, medium, and source. The dataset is freely available at [267].

This dataset contains various classes of sensors for different metal ions (Figure 3).

At the initial stage of investigating the dataset, our goal was to assess the correlation between various molecular descriptors and ion characteristics. For sensor characterization, we utilized a standard set of 42 parameters (Chem.rdMolDescriptors.Properties.GetAvailableProperties), including molecular weight (amw), number of rotatable bonds for a molecule (NumRotatableBonds), number of H-bond donors for a molecule (NumHBD), number of heteroatoms (NumHeteroatoms), and more. To describe ions, we selected Pauling electronegativity, ionization potential, and ionic radius as descriptors. However, upon conducting a Pearson correlation analysis, we found that there was not a strong dependence between the physical—chemical characteristics of sensors and cations (Figure 4).

Since the chemical binding of ions is determined by the electron density distribution of sensors and, among other factors, the polarizing ability of ions, we decided to calculate the dipole moment, diagonal elements of the polarizability tensor, and energy gap for sensor molecules using a semi-empirical level. The polarizing ability of ions was evaluated as the ratio of charge and Van der Waals radius. For this purpose, we used the more accurate GFN2-XTB method in combination with the iMTD-GC algorithm as described in XTB [268]. However, upon analyzing the correlation matrix, we found no dependence between the calculated values (Figure 5).

It became necessary to develop a new approach, based on different descriptors, to evaluate the relationship between sensors and ions. The new approach uses linear algebra methods.

3.2. Software

The software was developed using Python programming language (version 3.8) and several libraries, including Levenshtein [269], RDKit [270], scikit-learn [271], and aiogram [272]. The program consists of several subroutines, including file upload, preprocessing, four subroutines for finding the closest matches between database entries and user input, postprocessing, and output. The output presents the results of the search in graphical form as a table with columns for entry number, predicted cation, and corresponding similarity parameters. The first 10 most similar compounds from the database are presented as 2D chemical structures in SMILES format. The code is freely available at [268] and can be used with any IDE of the user’s choice.

4. Conclusions

A database containing information on 965 chemical compounds that can be used as fluorescent chemosensors for various metal ions was created based on the literature data. A freeware for predicting the sensing ability of chemical compounds for metal ions was developed and is available as a Telegram bot (https://t.me/mol_sim_bot (accessed on 5 April 2023)). We did not observe a clear correlation between different molecular descriptors and ionic properties. Therefore, instead of derivation of an equation linking potential chemosensors and analytes, we suggested another approach to finding similarities between user input and database queries. Four algorithms were discussed and successfully applied: finding the Levenshtein ratio, Tanimoto coefficients between molecular fingerprints, Euclidean distances, and tokenization/vectorization routines.

We hope that the database and software developed will be useful for researchers working in the field of developing new fluorescent chemosensors for metal ions. The database will be supported and expanded in the future.