The systematic workflow diagram (Fig. 2) comprehensively illustrates the operational pipeline of our detection system, encompassing critical modules including electrode modification, electrochemical measurement, feature engineering, and data analysis.

Chemicals and materials

The SEB antigen antibodies were supplied by the State Key Laboratory of Pathogen and Biosecurity. \(\beta\)-Mercaptoethylamine was procured from Shanghai Macklin Biochemical Co., Ltd. Ultrapure water was obtained from China National Pharmaceutical Group Chemical Reagent Co., Ltd. 2.5% Glutaraldehyde was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. Potassium ferricyanide \(({\hbox {K}}_{3}[{\hbox {Fe}}{\hbox {(CN)}}_{6}])\) was acquired from Xilong Scientific Co., Ltd. Phosphate-buffered saline (PBS) used in this study was sourced from Sigma-Aldrich. A 5 mM solution of \({\hbox {K}}_{3}[{\hbox {Fe}}{\hbox {(CN)}}_6]\) served as the electrolyte in the experiments, owing to its favorable redox properties that are easily measurable.²⁵. All other chemicals utilized were of analytical grade and did not require further purification. Antibodies and antigens were prepared in PBS buffer, while all other solutions were formulated using ultrapure water.

Instruments

Electrochemical experiments were conducted using a CHI660e Electrochemical Workstation (Shanghai Chenhua Co., Ltd., Shanghai, China). Screen-printed electrode (SPE) were obtained from Ercon Inc. (Wareham, MA, USA). As depicted in Fig. 3A, the electrodes measure 34 mm in length, 12 mm in width, and 0.3 mm in thickness; the working electrode has a diameter of 4 mm. The substrates for both the working and auxiliary electrodes are composed of gold, while the reference electrode is made of silver. All experiments were carried out in a 5 mL beaker.

Electrode modification

The quantitative detection of SEB was conducted utilizing electrochemical immunoassay techniques. The modification and measurement process of the SPE is illustrated in Fig. 3. This procedure consists of four key stages: electrode pretreatment and modification, antibody immobilization, antigen capture, and subsequent electrochemical measurement and analysis. A series of chemical modification steps were implemented to functionalize the surface of the working electrode, thereby enhancing its biocompatibility, stability, and sensitivity.

Chemical modification and functionalization

Pretreatment of the electrodes significantly enhances their voltammetric characteristics and activity²⁶. The pretreatment steps for the SPE are as follows: Initially, 20 μL of a 10 mM cystamine solution was applied precisely to the surface of the working electrode, ensuring uniform coverage across the entire area. This cystamine solution introduced \(-\hbox {NH}_{2}\) groups, which serve as functional groups for subsequent chemical reactions. The working electrode was then incubated at room temperature, allowing cystamine to react with the electrode surface and form covalent amino groups. After 2 h of incubation, the electrode was washed with phosphate-buffered saline (PBS) and then allowed to air-dry naturally. Subsequently, 20 \(\upmu\)L of a 2.5% glutaraldehyde solution was applied precisely to the cystamine-modified surface of the electrode, again ensuring uniform coverage. Glutaraldehyde acts as an electrophilic reagent that reacts with the amino groups introduced by cystamine (nucleophilic reagents), resulting in stable imine bonds²⁷, as illustrated in Fig. 3B. Following a 15-minute incubation period, the electrode surface was washed with PBS and allowed to air-dry naturally to remove any unreacted glutaraldehyde and other contaminants, thereby minimizing their impact on subsequent measurements.

Immobilization of antibodies on the electrode and specific binding of antigens

The introduction of functional groups and the formation of chemical bonds during the pre-treatment process not only enhance the chemical reactivity and specificity of the electrode surface but also provide active sites for subsequent antibody immobilization, thereby improving the performance of the biosensor²⁸.

On the chemically modified SPE working electrode surface, 20 μL of a 100 μg/mL SEB antibody solution was applied and incubated at room temperature for 2 h. Following incubation, the electrode surface was washed with PBS buffer to remove any unbound antibodies. Subsequently, 20 μL of 0.5M ethanolamine was applied to the working electrode area and incubated at 37 °C for 15 min to react with any unreacted glutaraldehyde. This step deactivates residual electrophilic reagents and prevents non-specific cross-linking reactions with subsequently added biomolecules (such as antibodies)²⁹. The electrode was then washed again with PBS buffer and allowed to air-dry at room temperature. At this stage, the immunoelectrode was successfully obtained.

A series of antigen solutions with varying concentrations were prepared, with 20 μL of each solution applied to the surface of the working electrode and incubated at 37 °C for 15 min. Following incubation, the electrode was washed with PBS buffer to remove any unbound antigens from the antibody-coated surface and then thoroughly dried (as illustrated in Fig. 3C). Subsequently, the Cys-NH2/GA/SEB Ab(SEB)/SEB (where Cys-NH2 refers to cystamine; GA denotes glutaraldehyde; SEB Ab(SEB) represents staphylococcal enterotoxin B antibody; and SEB stands for staphylococcal enterotoxin B) electrode was immersed in a 5 mM K3[Fe(CN)6] solution for electrochemical measurement (as depicted in Fig. 3D).

To ensure adequate recognition of antigens by antibodies immobilized on the electrode surface, it is essential that the quantity of antibody molecules significantly exceeds that of antigen molecules. In this study, the concentration of anti-SEB solution utilized ranged from 10 to 100,000 times greater than that of the SEB solution. Furthermore, all chemical reagents employed in this experiment do not interfere with SEB activity, thereby preventing degradation or other alterations to SEB.

Electrochemical measurement parameter settings

When the immunoelectrode adequately captures antigen molecules from the sample, it generates a specific electrochemical response. Quantitative analysis of this phenomenon through electrochemical measurements allows the detection of minute amounts of antigen content within the sample.

The SEB antigen-antibody complex generally exhibits minimal electrical activity and redox properties. It influences the oxidation-reduction reaction of \(\hbox {K}_{3}[\hbox {Fe}\hbox {(CN)}_6]\) during the reaction process, manifesting as varying degrees of inhibition depending on the SEB concentration³⁰. CV experiments are typically conducted in a \(\hbox {K}_{3}[\hbox {Fe}\hbox {(CN)}_6]\) electrolyte solution with a potential range of − 0.3 to 0.5 V, a scan rate of 100 mV/s, and a sampling interval of 1 mV. The sensitivity is set at 1e−4 A/V.

Antibody characteristics and challenges

Antibodies, also known as immunoglobulins, are highly specific proteins synthesized by the immune system. They are characterized by their intricate structure and distinct functions. As depicted in Fig. 4A, antibodies consist of two heavy chains and two light chains, which together form an antigen-binding site. This binding site is situated between the variable regions of both the light and heavy chains and is stabilized by multiple disulfide bonds, as illustrated in Fig. 4B. Each heavy chain and light chain comprises a variable region and a constant region; it is the variable region that determines the antibody’s specificity³¹ through its ability to recognize and bind to particular antigen molecules. The binding process relies not only on structural complementarity between the antibody and the antigen but also on the formation of a stable antigen-antibody complex. This complex modifies the biochemical properties of both the antigen and antibody, thereby triggering various biological effects such as activation of immune cells or suppression of antigen function³².

However, the intricate structure and specificity of antibodies present considerable challenges to traditional immunoassay methods. Conventional techniques typically depend on the signal intensity generated by antibody-antigen interactions for measurement; however, this signal is often influenced by the complexity of antigen structures and experimental conditions. The high specificity and sensitivity of antibody binding sites imply that even minor structural alterations or environmental fluctuations can significantly affect detection outcomes, leading to data instability and poor reproducibility. For instance, factors such as impurities in the sample, temperature variations, or pH changes may disrupt the signal from antibody-antigen interactions, resulting in inconsistencies in detection signals that compromise both accuracy and reliability of results.

Artificial intelligence methods present substantial advantages in addressing these challenges. Machine learning algorithms adeptly process and analyze complex data patterns, enabling the identification and correction of noise and interference within signals. By training on extensive experimental datasets, AI can effectively model the intricate characteristics of antibody-antigen interactions, thereby enhancing detection accuracy. Moreover, AI technology facilitates the integration of data from diverse experimental conditions, mitigating variability in antibody-antigen interactions and yielding more consistent and stable results. This capability for data integration allows AI to compensate effectively for differing experimental environments and conditions, thus improving result consistency and reproducibility. Furthermore, AI algorithms possess the ability to optimize and adjust the detection process in real-time, which enhances automation levels while reducing errors associated with manual operations. Consequently, this leads to faster and more accurate immunoassays.

Dataset

The dataset utilized in this study is derived from electrochemical experiments. Following the completion of all modification steps, the electrode was immersed in a potassium ferricyanide solution, and cyclic voltammetry curves were recorded using an electrochemical workstation to obtain experimental data. The experimental setup is illustrated in Fig. 1. SEB was categorized into six concentration gradients based on the common detection range: 0, 1 ng/mL, 10 ng/mL, 100 ng/mL, 1 μg/mL, and 10 μg/mL (as depicted in Fig. 5A). In accordance with immunoassay principles, a uniform antibody concentration of 100 μg/ml was employed throughout the study to ensure adequate capture of the target substance. Different concentrations of SEB antigen were added dropwise to the modified electrodes; after a incubation period of fifteen minutes, they were rinsed with PBS buffer and dried. Subsequently, the electrodes were submerged in a 5 mM K3[Fe(CN)6] solution where six cyclic voltammetry curves were recorded. Figure 5B presents the cyclic voltammetry curves obtained from antigen-antibody complexes formed by exposure to varying concentrations (0 ng/mL, 10 ng/mL, and 1 μg/mL) of SEB antigen combined with a constant antibody concentration of 100 μg/mL.

The experiment employed chemical reagents as shown in Fig. 4 for electrode modification. We conducted multiple cyclic voltammetry tests over a span of six months utilizing a concentration of 100 ng/mL SEB antigen. The cyclic voltammetry curve displayed in Fig. 5C demonstrates the stability achieved through electrode modification. To evaluate reproducibility within our experimental framework, five consecutive cyclic voltammetry scans were performed using a concentration of 10 ng/mL SEB antigen; resulting curves exhibited remarkable similarity-thereby confirming repeatability (Fig. 5D). The entire experimental procedure was completed within seventy-five seconds.

According to research observations, significant changes in the redox peaks of the cyclic voltammetry curve were noted with increasing concentrations of SEB antigen. At a zero antigen concentration, the cyclic voltammetry curve displayed distinct redox peaks, indicating a prominent redox reaction involving potassium ferricyanide at the electrode surface. However, as the concentration of SEB antigen increased, these redox peaks gradually diminished and ultimately disappeared. This phenomenon may be attributed to the formation of antigen-antibody complexes. With rising antigen concentrations, the binding between antigens and antibodies leads to several effects:

1. 1.

   Competitive Blocking Effect: Antigens competitively occupy active sites on the electrode surface, thereby reducing contact between potassium ferricyanide molecules and the electrode and diminishing the intensity of the redox reaction.

2. 2.

   Electrochemical Shielding Effect: The formation of antigen-antibody complexes impedes electron transfer by creating a shielding layer that weakens the current signal associated with the redox reaction.

As further increases in antigen concentration occur, an escalation in antibody-antigen complex formation takes place, occupying nearly all active sites on the electrode surface, which hinders effective interaction between potassium ferricyanide molecules and electrodes. Consequently, this results in either a reduction or complete disappearance of observable redox peaks.

Data preprocessing

In traditional electrochemical measurements, specific points on the CV curve are typically utilized to indicate the concentration of reactants, rather than relying on the curve as a whole. In this study, we selected a series of representative points from the CV curve as input features for electrochemical reactions to train our machine learning model. As illustrated in Fig. 6A, eleven features were extracted from the CV curves obtained from the aforementioned experiments (Mathematical definitions are detailed in Table 1.): maximum current (maxI), maximum voltage (maxV), minimum current (minI), minimum voltage (minV), beginning current (beginI), ending current (endI), the area of the curve (area), oxidation integral difference (OID), max-min current slope (k), zero current voltage (zeroIV), and shortest top-bottom curve distance (distance).

Subsequently, we employed a model training approach based on the Random Forest algorithm to rank feature importance as depicted in Fig. 6B. In our subsequent analysis, three features with low importance (maxV, zeroIV, beginI) were excluded. The remaining eight features were then selected as inputs for training the machine learning model. By screening and distinguishing more significant features within cyclic voltammetry curves across different concentrations and establishing a regression model accordingly; we aimed to focus on signals pertinent to our target while minimizing interference from nonspecific or irrelevant signals.

Ultimately, the dataset generated by these electrodes comprises 42 samples and 8 features that are used to predict SEB concentration. A total of 36 samples were designated as the training set while 6 samples served as the test set.

Notwithstanding the notable advancements made by metaheuristic algorithms in structural optimization in recent years^33,34. Exemplified by the greylag goose algorithm that effectively addresses complex structural optimization problems through simulating the coordinated flight patterns of geese flocks³⁵, their transference to feature selection tasks in electrochemical detection presents substantial challenges. Innovative approaches such as the 2-archive multi-objective cuckoo search algorithm^36,37,38, which enhances multi-objective optimization efficiency through a novel dual-archive mechanism, and the multi-objective brown bear optimization algorithm that solves constrained optimization problems by emulating brown bear foraging behaviors³⁹, demonstrate formidable global search capabilities in engineering optimization contexts. However, their application to electrochemical feature selection exposes inherent limitations.

Regarding computational complexity, metaheuristic algorithms typically necessitate extensive iterative global search procedures, with certain implementations requiring hundreds of complete objective function evaluations per iteration^40,41,42. This engenders substantial computational overhead, potentially creating severe efficiency constraints in resource-limited applications. In marked contrast, random forest algorithms generate feature rankings through a single training cycle, enabling computationally economical and expeditious feature screening. Concerning result stability, metaheuristic outcomes exhibit pronounced sensitivity to initial parameter configurations and random seed values, frequently yielding divergent results across executions-a manifestation of their inherent instability. The random forest approach, conversely, delivers superior stability by aggregating results from multiple decision trees, thereby producing consistent and reliable feature selection outcomes. Most critically, in terms of interpretability, metaheuristic feature selection processes rely on intricate optimization mechanisms to determine optimal feature subsets, resulting in opaque decision pathways. The random forest methodology, by contrast, constructs an electrochemically meaningful feature space incorporating temporal characteristics of CV curves (e.g., redox peak potentials/currents), with feature importance metrics enabling quantifiable tracing of individual feature contributions.

When compared to conventional multi-objective metaheuristic methods prevalent in structural optimization, the proposed methodology demonstrates three principal advantages:

1. (1)

   Systematic incorporation of electrochemical theory into feature selection to preclude mathematically optimal yet electrochemically inconsistent solutions;

2. (2)

   Establishment of an interpretable evaluation framework for feature contributions enabling hierarchical traceability of critical signal sources;

3. (3)

   Implementation of a lightweight computational workflow that maintains accuracy while significantly reducing processing time, thereby better accommodating on-site rapid detection requirements.

This establishes a novel feature selection paradigm for electrochemical analysis that harmonizes operational efficiency, interpretability, and domain-specific adaptability.

Principal Component Analysis (PCA) was utilized to conduct dimensionality reduction on eight features within the electrochemical data, thereby enhancing our understanding of the intrinsic structure of the data and facilitating visualization analysis. PCA, a widely recognized technique for dimensionality reduction, effectively transforms high-dimensional data into a lower-dimensional space while preserving the most significant feature information.

The eight-feature dataset was projected onto a two-dimensional plane through PCA dimensionality reduction, resulting in an intuitive visualization of the data, as illustrated in Fig. 6C. The clustering observed within the data clearly delineates distinct formations in feature space, indicating a specific classification structure corresponding to different concentrations of SEB features. Furthermore, no outliers or anomalies were detected, underscoring the strong consistency and reliability of the dataset. This consistency not only validates the efficacy of both feature extraction and preprocessing methods in accurately representing SEB characteristics at varying concentrations during electrochemical reactions but also highlights the stability and repeatability inherent in the electrochemical measurement process. This provides a robust foundation for subsequent regression analyses.

Machine learning model analysis

In the field of machine learning, regression models serve as a fundamental yet powerful tool for modeling and predicting continuous output variables. The primary objective is to generate predictions by understanding the relationship between input features and the corresponding output. Typically, it is posited that the output variable can be represented through either a linear or nonlinear combination of one or more input features. For example, in simple linear regression, the output variable \(y\) is expressed as a linear function of the input variable, accompanied by an error term, as illustrated in Eq. (1):

Here, we aim to estimate the parameters \(\beta _0\) and \(\beta _1\), which facilitates predictions and interpretations of the dependent variable \(y\). The primary objective of linear regression is to adjust the training data so that the predicted values closely align with the actual observed values. Simple linear regression employs a single independent variable in its predictive framework, whereas multivariate or multiple linear regression incorporates several independent or predictor variables into the forecasting process.

In this study, we utilized a multivariate linear regression model to analyze and predict SEB concentration. This method is widely recognized in both statistics and machine learning for exploring the linear relationships between multiple independent variables and a continuous dependent variable. Its fundamental form can be expressed by Eq. (2):

In this equation, \(y\) represents the dependent variable (output variable) being predicted, while \(x_1, x_2, \ldots , x_p\) denote the independent variables (input features). The parameters of the model, \(\beta _0, \beta _1, \beta _2, \ldots , \beta _p\), represent the slopes, associated with each independent variable. Additionally, \(\epsilon\) is the error term that accounts for random errors not explained by the model. The multivariate linear regression model estimates these parameters using training data to accurately predict new observations. In practical applications, various statistical methods-such as Ordinary Least Squares (OLS)-can be employed to fit the model and determine optimal parameter estimates.

Linear regression is particularly well-suited for handling small to medium-sized datasets due to its rapid modeling speed, strong interpretability, and high computational efficiency. Figure 6D illustrates the complete workflow for predicting SEB concentration using a linear regression algorithm. This process begins with experimental data preprocessing followed by feature extraction and selection; it ultimately culminates in both training and testing phases of the model.

Initially, electrochemical CV experiments are conducted on SEB electrode sheets with established concentration gradients to obtain raw data. This data undergoes preprocessing steps, including standardization and cleaning, to ensure consistency and quality. Subsequently, a series of key features are extracted from the preprocessed CV curves, capturing the essential characteristics of the electrochemical reactions. Feature selection is then performed to identify those features that significantly influence SEB concentration prediction, thereby enhancing the model’s accuracy and robustness. During the model training phase, the dataset is divided into training and test sets. The training set is utilized to develop the regression model and conduct hyperparameter tuning. Regression coefficients are estimated from this training data, allowing the model to effectively capture the relationship between input features and SEB concentration. This process typically involves optimizing a loss function; regression coefficients are determined when this loss function reaches its minimum value, ultimately resulting in a linear regression equation. Once trained, the model can be employed to predict SEB concentrations within the test set. The test set serves as a means of validating both the generalization capability and predictive performance of the model. A range of evaluation metrics (e.g., \(R^2\), MAPE) are used to assess performance; predicted results are compared against actual values to visually demonstrate both effectiveness and predictive accuracy. Finally, the derived regression model is applied for predicting SEB concentrations in unknown samples.