Characterizing DPPM inhibition of butyrylcholinesterase: integrated enzymatic kinetics and Raman spectroscopy with chemometric analysis

Abstract

Butyrylcholinesterase (BChE) may serve as a scavenger enzyme protecting against various toxic compounds, but we still don't fully understand how it interacts with fentanyl analogues. We investigated how Despropionyl meta-methyl fentanyl (DPPM) inhibits equine BChE by combining traditional enzyme kinetics with Raman spectroscopy and machine learning approaches. We measured enzyme activity across different substrate and inhibitor concentrations, then fit the data to four different inhibition models using nonlinear regression. Statistical comparison using Akaike Information Criterion clearly showed that mixed inhibition best explained our results (AIC = 269.62), with DPPM binding more strongly to the free enzyme (K_ic = 528.7 μM) than to the enzyme–substrate complex (K_iu = 1471.0 μM). Raman spectroscopy revealed structural changes when the enzyme was inhibited, and we used principal component analysis to separate the enzyme's spectral signature from background interference. Three machine learning algorithms – artificial neural networks, random forest, and support vector machines – could distinguish between active and inhibited enzyme with 92% accuracy using leave-one-out cross-validation. The spectral features that worked best for classification included changes at 1028 cm⁻¹ (phenylalanine), 1539 and 1557 cm⁻¹ (protein backbone), and lower frequencies (454–875 cm⁻¹) associated with larger-scale protein movements. These results provide direct molecular evidence for the mixed inhibition mechanism we found through kinetics. Our work shows how combining different analytical techniques can reveal details about enzyme inhibition. The findings also have practical implications for understanding toxicity of fentanyl and its different analogues and could help develop better detection methods for these dangerous compounds.

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Introduction

Butyrylcholinesterase (BChE) is one of two primary cholinesterases that naturally occur in the body; however, it is often overlooked in favor of a closely related enzyme, acetylcholinesterase (AChE, EC 3.1.1.7).^1–5 Although BChE and AChE are very similar, sharing approximately 50–60% of their amino acid sequence, AChE has been studied more extensively, and much of the data on BChE is extrapolated from these studies.^1,6,7 This is mainly because AChE has a well-established biological function, as it targets and hydrolyzes the neurotransmitter acetylcholine, allowing neurons to return to a resting state.^1,3,5,6 BChE, on the other hand, does not have a known primary biological function, but many have been previously proposed. One of these possible functions is acting as a scavenger molecule by targeting compounds that would attack or inhibit AChE, a function that is supported by the observation that BChE can hydrolyze harmful substances such as cocaine.^2,4,5,7,8 Other proposed functions include serving as an activator enzyme, contributing to the development of the nervous system during the fetal stages of life, the ability to be used as a biomarker for physiological conditions such as Alzheimer's or obesity, and the numerous genetic mutations of BChE possibly serving different purposes, although these variants have shown to have no significant effect on those that carry them.^2,4–8 BChE has also been shown to interact with multiple compounds, including butyrylcholine, acetylcholine, succinylcholine, and toxic substances, demonstrating broader substrate specificity compared to AChE and many other enzymes.^1,2,4,5,8 These unique properties and the lack of specific information have made BChE a recent research focus, especially in the fields of enzyme kinetics and inhibition.

In humans, the structure of BChE is typically reported as a globular tetramer, composed of four individual monomers of approximately 574 amino acids bound by hydrophobic interactions and disulfide bonds, although Leung et al. has also proposed a staggered dimer of dimers structure.^1,2,4,9 Up to 15% of the structure consists of aromatic amino acids such as phenylalanine, tyrosine, and tryptophan.¹ Each monomer within the structure houses a 20-angstrom deep gorge where interaction with substrates occurs.² The BChE gorge is slightly larger than the gorge present in AChE, which leads some researchers to believe that the size of the gorge is what allows BChE to interact with multiple substrates as opposed to AChE.⁷ The aromatic rings and the relatively large gorge are also what allow BChE to be studied via spectroscopic methods, as any structural changes that occur during a reaction will likely be seen in these areas.

Fentanyl has become a primary focus for medical, legal, political, and research fields in recent years due to the danger it poses. Fentanyl is a synthetic opioid with morphine-like pharmacological effects, providing therapeutic analgesia and relaxation while producing side effects such as slowed breathing, hypoxia, bradycardia, and hypotension.¹⁰ Fentanyl was originally created in the 1960s to serve as an analgesic in the medical industry, however, it is now illicitly manufactured and illegally sold on the drug market.^10–13 Fentanyl is a highly dangerous and potent substance, as only a small amount can be lethal if not immediately counteracted with an opioid antagonist medication. Fentanyl is often mixed with other drugs to enhance effects and make them cheaper to produce. Oftentimes, the drug mixture contains a lethal amount of fentanyl, unknown to the drug user, resulting in an overdose. In recent decades, overdose deaths from synthetic opioids, specifically fentanyl, have skyrocketed, as highlighted by the National Institute on Drug Abuse.^10–13 Moreover, opioids in general are so prevalent in society that traces of opioids and opioid metabolites can be found within the natural environment across the world.¹⁰ Fentanyl is not only an issue for drug manufacturers, dealers, and users, but also people working in the medical field, police, forensic science, and the general population.

Fentanyl analogues are another issue to consider. The basic structure of fentanyl is composed of a piperidine ring surrounded by three functional groups: a phenethyl group, a propionyl group, and a benzene ring.¹⁴ By adding, removing, or modifying any of these groups, a fentanyl analogue is created.¹⁴ These analogues often have different properties than core fentanyl, such as longer duration of effects, enhanced side effects, higher potency, and different metabolic pathways.^14–16 Many fentanyl analogues have been created, making it difficult for researchers to keep up with the constantly expanding number of fentanyl compounds.^14–16 The analogue of interest in this study is Despropionyl meta-methyl fentanyl¹⁷ (DPPM) (Fig. 1). This analogue differs from the core fentanyl structure by the removal of the propionyl group and the addition of a methyl group on the benzene ring.

Fig. 1 Structure of despropionyl meta-methyl fentanyl.¹⁷

Fentanyl is a known inhibitor of BChE, as shown by Rania et al., though the exact mechanism of inhibition is still unknown.¹⁸ Although coming in contact with fentanyl may not always cause an overdose, inhibition of BChE via fentanyl can be dangerous, as it may leave AChE open to attack by other compounds, leading to an excess of acetylcholine in the neuronal synapse, causing issues such as muscle paralysis, seizures, and possibly death.² Enzyme inhibition occurs when a molecule interacts with an enzyme that slows or stops natural function completely, and it may occur through one of four main pathways. In competitive inhibition, the inhibiting molecule attaches to the active site of the enzyme, preventing the substrate from binding to the enzyme and therefore preventing the reaction from taking place.¹⁹ In noncompetitive inhibition, the inhibiting molecule will bind at a location other than the active site of the enzyme, inducing a structural change that may prevent the substrate from attaching properly, causing the reaction to slow or stop completely.¹⁹ In uncompetitive inhibition, the inhibiting molecule will attach to the enzyme–substrate complex, preventing the products of the reaction from being released.¹⁹ Lastly, in mixed inhibition, the inhibitor may bind to either the free enzyme or the enzyme–substrate complex and may bind at either site.¹⁹ Additionally, enzyme inhibition may be reversible or irreversible.^3,19

This research aimed to identify the mode of inhibition of BChE from DPPM exposure by employing a combination of enzymatic assays, spectroscopic methods, and computational modeling. To generate kinetic data, enzymatic activity was measured across a range of substrate and inhibitor concentrations using Ellman's assay, a commonly used colorimetric method in which the intensity of the color change directly corresponds to the activity of the enzyme.²⁰ To quantify the color change, a UV-Vis spectrophotometer was utilized to measure the absorbance of light at wavelength of 405 nm by samples throughout the reaction. A sample resulting in a higher absorbance than another sample indicates that the color change was more intense, and therefore the enzyme was more active in that sample. Data was collected during two separate experimental days under the same experimental conditions and combined to have sufficient results for analysis. These data points were fitted to competitive, noncompetitive, uncompetitive, and mixed inhibition models using nonlinear regression in R. The model selection was based on statistical criteria to identify the best-fitting inhibition type. Additionally, Raman spectroscopy (RS) and machine learning (ML) were applied to confirm structural changes, further explore inhibition models, and confirm the inhibition mechanism. RS is a method that shines a laser on a sample and detects the scattering of the light, particularly the inelastic Raman scattering. Raman provides insight into the structure and bonds found within a sample. Since inhibition of an enzyme causes structural changes, RS can detect the differences between native and inhibited enzymes. RS is also well suited for enzyme samples, as it can analyze solids, liquids, and substances in solutions. ML techniques were utilized to analyze data from the RS. Principal Component Analysis (PCA) isolates enzyme-specific changes by identifying and subtracting contributions from unwanted components in mixture solutions. Artificial neural network, random forest, and support vector machine analysis of selected spectral features compare active and inhibited enzyme states to detect and interpret inhibition effects.

To reveal the inhibition mechanism of DPPM on BChE, this study integrates the three previously discussed techniques: enzymatic assays, RS, and ML. Enzymatic assays provide kinetic data to determine the inhibition type, while RS identifies specific peaks and functional groups that change when the inhibitor binds. ML helps analyze the data by distinguishing between active and inhibited enzyme states based on their spectroscopic signatures, allowing us to identify which molecular vibrations are most affected by inhibition. As a proof-of-concept, this multidisciplinary approach explores whether combining these techniques can effectively characterize enzyme inhibition. By studying DPPM's inhibition mechanism, we aim to establish a new framework for investigating enzyme inhibition, with potential applications in understanding and comparing different fentanyl analogues.

Materials and methods

The following components for the enzymatic assay were purchased from Millipore Sigma (Burlington, MA): butyrylcholinesterase (BChE, EC 3.1.1.8) sourced and lyophilized from equine serum, 5,5′-dithiobis (2-nitrobenzoic acid) (DTNB, Ellman's reagent), butyrylthiocholine iodide (BtCh), and Tris(hydroxymethyl) aminomethane hydrochloride (Tris-HCl). All Ellman's reaction components were buffered with Tris-HCl, pH 7.5, prepared with 18.2 MΩ cm filtered water from the Barnstead Nano-Pure purification system from Thermo Fisher Scientific (Waltham, MA). Despropionyl meta-methyl fentanyl (DPPM) was purchased from Cayman Chemical (Ann Arbor, MI). The enzymatic assays were performed in clear, flat-bottom 96-well plates purchased from Avantor (Randor, PA) and were analyzed at 405 nm for 10 min at 37 °C with the BioTek Epoch2 microplate UV-Vis spectrophotometer from Agilent Technologies (Santa Clara, CA). A simplified scheme of Ellman's assay used in this experiment is shown in Fig. 2. Additionally, 3 wells of DTNB blank, composed of only DTNB and buffer, were analyzed to compare to experimental wells and remove the contribution, if any, from DTNB.

Fig. 2 Ellman's assay reaction scheme.

Raman spectra of the samples were collected using a DXR3 Raman Microscope from Thermo Fisher Scientific (Waltham, MA) utilizing a 785 nm laser and OMNIC software. Machine learning techniques were performed using the MathWorks MATLAB R2020b version 9.9.0.1570001 (Natick, MA, USA) supported by the Eigenvectors Research Inc. PLS Toolbox 9.0 (Manson, WA, USA), and R version 4.4.2 ²¹ with packages including “tidyverse”,²² “caret”,²³ “nnet”,²⁴ “randomForest”,²⁵ “e1071”,²⁶ “ggplot2”,²⁷ “gridExtra”,²⁸ “corrplot”,²⁹ “reshape2”,³⁰ “RColorBrewer”,³¹ “pheatmap”,³² “minpack.lm”³³ and “renz”.³⁴ These software tools enabled computational modeling and creating graphics of kinetic data and chemometric modeling of our Raman spectral data.

Enzyme samples were prepared by dissolving BChE powder in buffer. Inhibited samples were prepared by adding fentanyl residue dissolved in buffer to the enzyme solution. Samples were left to incubate overnight in the fridge before performing an enzymatic assay or Raman spectroscopy. The concentration of DPPM fentanyl in the enzyme solution was determined to be approximately 566 μM. This concentration was selected based on preliminary experiments to achieve partial inhibition suitable for kinetic characterization while maintaining measurable enzyme activity across the substrate concentration range tested. To obtain an average reaction velocity (µM min⁻¹), we used the standard approach: measuring the initial slope (ΔOD/Δtime) from the OD versus time graph, converting this to molar units, and using this velocity for further kinetic analysis. Representative absorbance-time curves are shown in SI Fig. S1. These values were compiled into a data frame, with columns representing substrate concentration and velocities for each condition (control and DPMM inhibitor).

For RS, glass microscope slides were covered with aluminum foil with the non-shiny surface facing outwards to minimize interference due to fluorescence.³⁵ Three drops of approximately 10 µL of sample were placed on the slide for analysis. These drops were measured immediately. A 10× magnification lens was used to select the area of analysis within the drop. The measurement parameters were as follows: 785 nm laser, 25 µm pinhole aperture, 400 line per mm grating, 5 spectra per drop, 20 exposures per spectra, 25 seconds per exposure. All spectra were collected and imported into MATLAB to be analyzed.

Analysis of enzymatic assay data was performed in R using the “renz” package for initial parameter estimation, biochemically constrained nonlinear modeling was used to determine inhibition mechanisms using nonlinear least squares (NLS) regression.³⁴ The “renz” is a free package used in R to assist with the analysis of enzymatic data.³⁴ The “renz” package provided initial estimates of K_m and V_max values for uninhibited and inhibited conditions separately using the dir.MM function.³⁴ This gave us preliminary K_m and V_max estimates for each condition, which we then used as a reference for the more sophisticated NLS modeling. A unified modeling approach was applied to analyze all kinetic data simultaneously, incorporating biochemical constraints to ensure physiologically meaningful parameter estimates rather than purely mathematical optimization.^34,36,37 We used nonlinear regression rather than Lineweaver–Burk plots because the double-reciprocal transformation can magnify experimental errors and make it harder to reliably compare different inhibition models. All computational scripts and detailed code implementations are provided in the SI.

The modeling strategy utilized established Michaelis–Menten kinetic equations for the four classical inhibition mechanisms (eqn. (1)–(4)):^36,37

Competitive inhibition

Noncompetitive inhibition

Uncompetitive inhibition

and mixed inhibition

where v is reaction velocity, S is substrate concentration, I is inhibitor concentration, K_i is the inhibition constant, and K_ic and K_iu are competitive and uncompetitive inhibition constants, respectively. These well-established kinetic formulations were fitted to the combined dataset using bounded nonlinear least squares regression (nlsLM function from the “minpack.lm” package in R).³³ Biochemical constraints were implemented based on established enzyme kinetic principles: competitive inhibition models were constrained to maintain V_max within ±10% of baseline while allowing K_m to increase; noncompetitive models required V_max to decrease while constraining K_m to ±10% of baseline; uncompetitive models enforced proportional decreases in both parameters; and mixed inhibition models allowed V_max decreases with flexible K_m variation. These constraints prevent mathematically optimal but biochemically implausible parameter combinations. Parameter uncertainty was quantified using 95% confidence intervals calculated via the t-distribution with appropriate degrees of freedom, indicated deviations beyond expected experimental variability. Model selection employed the Akaike Information Criterion (AIC) with support levels classified as strong (ΔAIC < 2), moderate (2–4), weak (4–10), or negligible (>10), where the ΔAIC represents the difference from the best model.

Biochemical validation was performed by comparing fitted parameter changes against expected inhibition patterns. Competitive inhibition was validated by V_max stability (≤12% change) and K_m increases (≥1%); noncompetitive inhibition required V_max decreases (≤−10%) with K_m stability (≤12% change); uncompetitive inhibition necessitated proportional decreases in both parameters (≤−10%); and mixed inhibition required significant V_max reduction (≤−5%) regardless of K_m behavior. Biochemical validation criteria were implemented as mechanistic constraints during bounded optimization (using nlsLM) with lower and upper parameter bounds set based on expected inhibition patterns, ensuring parameter estimates reflected real biochemical mechanisms.

For the Raman spectra, PLS_Toolbox was used to baseline correct (automatic Whittaker filter) and normalize the spectra, remove the effect of unwanted components from the spectra, and perform ML analysis on the spectra. Raman spectra were acquired from mixture solutions to isolate and compare the spectral signatures of BChE in its active and inhibited forms. Solutions included BChE in Tris buffer, BChE with DPPM in Tris buffer, DPPM in Tris buffer, and only Tris buffer solution. Principal Component Analysis (PCA) was performed to decompose mixture spectra into principal components (PCs) with loadings mapping Tris buffer and DPPM to specific PCs based on their spectral signature. Loadings of principal components (PCs) corresponding to Tris and DPPM were analyzed, and these contributions were subtracted via linear combination from each mixture spectrum to isolate BChE-specific spectra.³⁸ The resulting active and inhibited BChE spectra underwent ML analysis to determine which spectroscopic features best distinguish between the two enzyme states. We first employed random forest feature selection to identify the 50 most discriminative wavenumbers from the full spectral dataset. Random forest calculates variable importance by measuring how much each wavenumber contributes to classification accuracy across multiple decision trees, filtering out redundant or non-informative spectral regions.³⁹

Using the selected features, we compared three machine learning algorithms to find the optimal classification approach. Artificial Neural Networks (ANN) required initial parameter optimization using 5-fold cross-validation to determine the optimal number of hidden neurons (testing ranges from 3 to 15) and decay parameters (0.01 to 0.5) that prevented overfitting. Random forest was constructed with 500 trees (n_tree = 500), with mtry set to the square root of the number of features and default values for nodesize and maxnodes parameters.²⁵ Support Vector Machine (SVM) used radial basis functions with cost = 1 and gamma = 1/number of features, values commonly applied in spectroscopic classification studies.⁴⁰

All models were then evaluated using leave-one-out cross-validation (LOOCV), where each sample serves as a test case while remaining samples train the model. For the neural networks, we used the previously optimized parameters during LOOCV to avoid data leakage between parameter tuning and performance evaluation phases, while random forest and SVM proceeded directly to LOOCV evaluation. This approach provides performance estimates, particularly valuable for smaller datasets.⁴¹ The prediction scores represent the probability of class membership: neural networks output direct probability estimates through sigmoid activation functions, random forest calculates probabilities by averaging votes across all trees, and SVM generates probabilistic outputs by transforming decision values through Platt scaling.⁴² Prediction scores represent the model's probabilistic outputs before classification thresholds are applied, while accuracy, sensitivity, specificity, precision, and F₁-score evaluate model performance based on the final classified labels after applying classification thresholds.

The feature selection process revealed which specific wavenumbers underwent the most significant changes after inhibitor binding, which helped us to understand how the molecular fingerprint was affected by the inhibition. By ranking wavenumbers according to their discriminative power, we could identify functional groups and molecular vibrations most affected by DPPM binding. This approach determined the precise molecular signatures changes associated with enzyme inhibition, providing both quantitative classification performance and biochemical insights into the inhibition mechanism.

Results

We first examined the basic relationship between substrate concentration and enzyme activity (Fig. 3). As expected, both the control and DPMM-treated samples showed the characteristic hyperbolic curves typical of Michaelis–Menten kinetics. However, the DPMM treatment affected the enzyme's performance substantially. The inhibited samples consistently showed lower reaction velocities across every substrate concentration we tested. This wasn't just a subtle effect – the reduction in activity was substantial and persistent throughout the entire concentration range, which told us right away that we are observing significant enzyme inhibition. We further investigated the inhibitory effects of DPMM on BChE through a systematic kinetic analysis that combined preliminary screening with detailed mechanistic modeling. Our approach began with the “renz” package in R, specifically using the dir.MM function to obtain initial parameter estimates from control and inhibited enzyme samples.³⁴ For the uninhibited BChE, we found a V_max of 3310.5 μM min⁻¹ and a K_m of 387.5 μM. However, when we analyzed the DPMM-treated samples using the same method, both parameters changed dramatically: the V_max dropped to 2112.2 μM min⁻¹ while the K_m increased to 430.6 μM. The dir.MM function essentially fits individual Michaelis–Menten curves to each dataset separately – it doesn't make any assumptions about inhibition mechanisms. Both kinetic parameters changed in response to DPMM treatment. This pattern ruled out some possibilities straight away. If DPMM were acting as a pure competitive inhibitor, we would expect to see the Michaelis constant increase while maximum velocity stayed the same. Conversely, pure noncompetitive inhibition typically leaves the Michaelis constant unchanged while reducing maximum velocity. Since we observed changes in both parameters, we suspected either uncompetitive or mixed inhibition was occurring.

Fig. 3 Relationship between substrate concentration and BChE reaction velocity. Data points represent individual measurements for untreated enzyme (blue) and DPMM-treated samples (red). Fitted curves show the typical Michaelis–Menten hyperbolic relationship. The consistent reduction in velocity across all substrate concentrations demonstrates potent inhibitory activity of DPMM. Shaded areas represent 95% confidence intervals calculated using the t-distribution.

To get a more detailed answer about the mechanism, we moved beyond the simple curve-fitting approach and implemented a more sophisticated analysis. We started by establishing baseline parameters using standard nonlinear regression on the control data only, which gave us a maximum velocity of 3313.8 μM min⁻¹ (with a standard error of 192.9) and a Michaelis constant of 388.4 μM (standard error of 54.3). Both parameters were highly significant statistically, and importantly, these values matched with what we had obtained from the “renz” package analysis.

The next step involved testing four different inhibition mechanisms using their established mathematical equations. But rather than letting the fitting algorithm find any mathematically optimal solution, we imposed biochemically reasonable constraints on the parameters. Our constraint strategy was based on what we know about how different inhibitors should behave. For competitive inhibition, we allowed the Michaelis constant to increase substantially but kept the maximum velocity relatively unchanged. This reflects the fact that competitive inhibitors compete with substrate for the same binding site, making it appear that the enzyme has lower affinity for substrate, but they don't change the enzyme's inherent catalytic capacity. For noncompetitive inhibition, we did the opposite – we required the maximum velocity to decrease significantly while keeping the Michaelis constant relatively stable. Uncompetitive inhibition needed both parameters to decrease proportionally, while mixed inhibition was allowed more flexibility since it combines aspects of the other mechanisms.

When we compared all four models using the Akaike Information Criterion (Fig. 4 and Table 1), mixed inhibition occurred as the best model with an AIC value of 269.6. The competitive model came in second but with weaker support (AIC = 275.3, ΔAIC = 5.7), while both noncompetitive and uncompetitive models performed poorly with AIC values around 296 (ΔAIC = 26.4 and 26.4 respectively). The mixed inhibition model fit our data with a V_max of 2982.4 μM min⁻¹ and a K_m of 303.6 μM (Table 2). Also, it gave us two inhibition constants: K_ic = 528.7 μM for binding to the free enzyme and K_iu = 1471.0 μM for binding to the enzyme–substrate complex. These constants indicate that DPMM fentanyl binds more tightly to the free enzyme than to the enzyme–substrate complex – nearly three times more. This suggests that DPMM primarily acts by competing with substrate for the active site, but it can also bind to the enzyme–substrate complex to some extent. This dual binding capability explains why we see characteristics of both competitive and uncompetitive inhibition in our data. The mixed inhibition model represents the best-supported mechanism among all tested alternatives (Fig. 4). The visual comparison of AIC values clearly demonstrates the superior performance of the mixed inhibition model, with the differences in AIC scores providing statistical evidence for mechanism selection.

Fig. 4 Statistical comparison of inhibition models using Akaike Information Criterion (AIC). Colors indicate statistical support levels: strong (green), weak (orange), and none (red). Mixed inhibition shows the lowest AIC (269.62) with strong support, while other models demonstrate poorer fits. Lower AIC values indicate better model performance.

Table 1 Statistical comparison of inhibition models

Model	Parameters	AIC	ΔAIC	RSE
Competitive	3	275.3	5.7	113.3
Noncompetitive	3	296	26.4	181.1
Uncompetitive	3	296	26.4	181.4
Mixed	4	269.6	0	97.7

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Table 2 Kinetic parameters for DPMM inhibition models

Model	V max estimate (±SE)	K m estimate (±SE)
Competitive	3305.3 ± 193.9	392.3 ± 55.3
Noncompetitive	2816.7 ± 251.7	349.6 ± 76.5
Uncompetitive	2816.7 ± 253.3	330.1 ± 73.3
Mixed	2982.4 ± 140.9	303.6 ± 38.1

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Fig. 5 illustrates the fitted curves for all four inhibition models overlaid with experimental data points, clearly showing how the mixed inhibition model provides superior description of the data across the entire substrate concentration range. The visual comparison reveals that while all models capture the general trend, the mixed inhibition model shows the best agreement with experimental observations, particularly at higher substrate concentrations where the distinction between mechanisms becomes most apparent. We also performed validation checks on our models. The mixed inhibition model passed our biochemical criteria with a 10% decrease in maximum velocity and a 22% decrease in the Michaelis constant from baseline. Interestingly, the competitive inhibition model failed our validation test. Even though it achieved mathematical convergence, it only showed a 1% increase in the Michaelis constant. For genuine competitive inhibition at the DPMM concentration we used (566 μM), we would expect to see much larger increases – typically 15% or more. The small change we observed suggests that competitive inhibition alone cannot explain DPMM's effects.

Fig. 5 Michaelis–Menten kinetics curves for DPMM inhibition models. Experimental data points for control (blue) and DPMM-inhibited (red) conditions with fitted curves for each inhibition model. AIC values are shown for each model. Mixed inhibition (AIC = 269.6) provides the best fit for experimental.

From the inherent kinetic parameters and the mixed inhibition model at the experimental DPMM concentration (566 μM), we calculated the apparent kinetic parameters, which we then compared to direct fitting results from the ‘renz’ package to validate our mechanistic interpretation.³⁴ We used the mixed inhibition model to calculate what the enzyme kinetics should look like under inhibition conditions.⁴³ These calculations gave a V_max of 2153.6 μM min⁻¹ and a K_m of 454.0 μM. When we compared these values to what we actually measured using the simple dir.MM approach (2112.2 μM min⁻¹ and 430.6 μM), the agreement was obvious – within about 2% for V_max and 6% for K_m. This close correspondence gave us confidence that our mechanistic model accurately describes how DPMM inhibits BChE. Our statistical analysis included proper confidence intervals calculated using the t-distribution, which showed that all parameter estimates were highly significant. The mixed inhibition model also had the lowest residual error (97.69 μM min⁻¹) compared to the other models, further supporting our mechanistic conclusion.

The original Raman spectra of the sample are shown in Fig. 6, zoomed in to view only the fingerprint region from 450–1800 cm⁻¹ where some differences were observed. This figure consists of the average spectra for four different samples labelled with what is present in each: “BChE DPPM Tris” is the inhibited enzyme sample, “BChE Tris” is the uninhibited enzyme sample, “DPPM Tris” is the fentanyl analogue solution with no enzyme, and “Tris” is only the buffer solution. To isolate the spectral features that are specific to BChE structural changes upon inhibition, we employed principal component analysis (PCA). The PCA technique helped us figure out which parts of the spectra came from the buffer and which parts came from DPPM. Since we had collected separate spectra of just the buffer and just DPPM, we could use those as references. The contributions of these non-target chemicals were then subtracted from the mixture spectra by linear combination to obtain reconstructed spectra representing active and inhibited BChE. The reconstructed spectra for the two forms of enzyme are shown in Fig. 7. Here, the peaks are very similar, but some differences can be seen at some of the major peaks without the need for statistical analysis. Table 3 shows these peaks and the structure or group to which they were assigned.

Fig. 6 Original Raman spectra of samples.

Fig. 7 Reconstructed Raman spectra.

Table 3 Raman peak assignments

Peak	Functional group or structure^1,44–46
607	C–Cl bond
620, 1003, 1029	Phenylalanine
653	C–Cl bond/aliphatic chain
760, 1543, 1554	Tryptophan, amide II
890, 979, 1185	Aliphatic chain
912	Aliphatic chain/carboxylic acid dimer
1048, 1057	Aliphatic chain/aromatic ring
1250	Amide III/phenylalanine/tyrosine
1296	Amide III
1404	CO2 stretching
1635	Tryptophan/phenylalanine

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The ML analysis of reconstructed Raman spectral data successfully distinguished between active and inhibited BChE states with high accuracy across all three algorithms tested. Initial feature selection using random forest identified 50 wavenumbers from the complete spectral dataset that showed the greatest discriminative power between enzyme states, active and inhibited.

Leave-one-out cross-validation revealed that both neural networks and support vector machine achieved the highest classification accuracy of 92%, while random forest achieved 84% accuracy. The neural network model demonstrated perfect specificity (100%) with 85% sensitivity, correctly classifying all active BChE samples while misclassifying two inhibited samples as active. SVM performance was more balanced, showing 92% sensitivity and 92% specificity with high precision (92%) and F₁-score (92%). Random forest exhibited the highest sensitivity (92%) but lower specificity (75%), resulting in more false positive classifications (Table 4).

Table 4 Statistical comparison of machine learning models

Method	Accuracy	Sensit.	Specif.	Precision	F 1
Neural network	0.92	0.85	1	1	0.92
Random forest	0.84	0.92	0.75	0.8	0.86
SVM	0.92	0.92	0.92	0.92	0.92

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The comparison of model performance (Fig. 8A) demonstrates that while all three approaches achieved good discrimination, SVM provided the most balanced performance across all metrics, making it the optimal choice for this classification task. The superior performance of neural networks and SVM over random forest suggests that the spectral features contain complex, non-linear relationships that are better captured by these algorithms.

Fig. 8 Machine learning analysis of BChE inhibition using Raman spectroscopy. (A) Leave-one-out cross-validation accuracy showing neural networks and SVM achieved 92% accuracy, outperforming random forest (84%). (B) Prediction scores for each sample grouped by actual enzyme state. For inhibited samples (left), correct predictions fall below the 0.5 threshold, while for active samples (right), correct predictions fall above the 0.5 threshold. (C) Top 50 discriminative wavenumbers ranked by importance.

Analysis of prediction scores provides additional insights into models’ behavior and classification certainty (Fig. 8B). In this plot, each point represents the probability score assigned by each algorithm to individual samples, with values below 0.5 (dashed line) indicating prediction of the inhibited state and values above 0.5 indicating prediction of the active state. The distance from the 0.5 threshold reflects the model's confidence in its prediction – points closer to 0 or 1 represent high-confidence predictions, while points near 0.5 indicate closer to uncertain classifications. Samples are grouped by their actual class, where active BChE is labeled as BChE_Tris and inhibited BChE is labeled as BChE_DPPM_Tris, allowing visualization of correct classifications (points on the appropriate side of the threshold) versus misclassifications (points on the wrong side). This figure demonstrates that most prediction errors occur for samples with probability scores close to the decision boundary, indicating these represent borderline cases that are inherently more difficult to classify.

The most discriminative spectral features (Fig. 8C) revealed important insights into the molecular changes accompanying DPPM inhibition. The highest-ranking feature at 1028 cm⁻¹ corresponds to phenylalanine ring breathing vibrations, suggesting significant changes in aromatic residue environments upon inhibitor binding.¹ Additional important features at 1539 and 1557 cm⁻¹ fall within the Amide II region (1500–1580 cm⁻¹), indicating alterations in protein backbone conformation and hydrogen bonding patterns.^47,48 The feature at 1557 cm⁻¹ may also contain contributions from tryptophan vibrations, as these can overlap in this spectral region.¹ The prevalence of aromatic amino acid features among the top discriminators points to substantial changes in the protein's aromatic residues following inhibition. Features at 998 cm⁻¹ assigned to phenylalanine further supports aromatic residue involvement in the inhibition mechanism.⁴⁴ The substantial representation of low-frequency vibrational modes (454–875 cm⁻¹) suggests that DPPM binding affects collective protein motions, that is consistent with allosteric conformational changes that could propagate beyond the binding site.⁴⁹ These spectroscopic changes align well with the mixed inhibition kinetics observed in enzymatic assays, where both competitive and non-competitive components indicate multiple binding interactions and allosteric effects.

The ML approach successfully identified spectral signatures that differentiate enzyme states, with the combination of amide band alterations and aromatic residue changes providing the strongest discriminative power. This spectroscopic fingerprint offers molecular-level insights into the structural basis of DPPM inhibition that complement the kinetic characterization obtained through traditional enzymatic assays.

Discussion

Our study reveals that DPPM inhibits BChE through a mixed inhibition mechanism, with the DPPM showing preferential binding to the free enzyme form over the enzyme–substrate complex. Statistical analysis strongly supports this conclusion, with the mixed inhibition model achieving the lowest AIC value (269.62) and demonstrating better fit than alternative mechanisms.⁵⁰ This finding has important implications for understanding how fentanyl analogues interact with cholinesterases at the molecular level. The inhibition constants reveal that DPPM binds nearly three times more tightly to the free enzyme (K_ic = 528.7 μM) than to the enzyme–substrate complex (K_iu = 1471.0 μM). This pattern suggests that while DPPM can access both binding states, its primary mode of action involves competing with substrate for the active site, with secondary binding occurring when substrate is already bound.⁵¹ The mixed inhibition pattern we observed differs from the purely competitive inhibition that might be expected for a molecule targeting the active site, indicating that DPPM's binding induces conformational changes that affect both substrate binding and catalytic efficiency.

The Raman spectroscopy results provide molecular-level evidence supporting the mixed inhibition mechanism.⁵² The machine learning analysis identified spectral changes in both amide backbone regions and aromatic amino acid environments, consistent with the dual binding modes suggested by our kinetic data.⁵³ The detection of changes at 1028 cm⁻¹ (phenylalanine ring breathing) and 998 cm⁻¹ (aromatic C–C stretching) indicates that DPPM binding affects the local environment of aromatic residues, likely within or near the active site.¹ Simultaneously, the presence of discriminative features in the Amide II region (1539 and 1557 cm⁻¹) suggests backbone conformational changes that could propagate beyond the immediate binding site.⁴⁷

These structural changes align well with mixed inhibition kinetics, where binding to the free enzyme produces local effects around the active site (competitive component), binding to the enzyme–substrate complex reduces product formation (uncompetitive component), and allosteric conformational changes affect overall catalytic efficiency (non-competitive component).⁵⁴ The low-frequency vibrational modes we detected (454–875 cm⁻¹) support this interpretation, as these typically reflect collective protein motions that could facilitate allosteric communication between binding sites.⁴⁹

While all three algorithms demonstrated robust classification performance, random forest was employed for feature importance analysis due to its ability to provide explicit, biologically interpretable rankings of discriminative wavelengths. The high accuracy achieved by both neural networks and support vector machines (92%) in distinguishing between active and inhibited enzyme states demonstrates that DPPM binding produces consistent, detectable structural signatures. The superior performance of these non-linear algorithms over random forest suggests that the relationship between spectral features and enzyme states involves complex interactions that linear methods cannot fully capture. This finding supports the idea that enzyme inhibition involves coordinated changes across multiple structural elements rather than simple local changes.

Our results have broader implications for understanding fentanyl toxicity. The inhibition of BChE would compromise the enzyme's proposed protective role as a scavenger molecule, potentially leaving acetylcholinesterase more vulnerable to inhibition by other compounds.⁴ The integration of enzymatic kinetics with spectroscopic analysis proved particularly valuable for mechanistic studies. While kinetic data alone indicated mixed inhibition, the spectroscopic evidence provided molecular details about which structural elements change during inhibition. This combined approach offers a more complete picture of enzyme-inhibitor interactions. From a therapeutic standpoint, mechanistic insights into BChE inhibition may inform the rational design of safer opioid analgesics with reduced off-target enzyme interactions. Understanding which structural features drive enzyme inhibition allows medicinal chemists to optimize compounds for selectivity, potentially reducing adverse effects while maintaining analgesic efficacy. Additionally, characterizing the reversibility and dynamics of enzyme inhibition may reveal novel targets for overdose reversal strategies beyond traditional naloxone treatment.

However, several limitations should be considered when interpreting these results. We examined only one fentanyl analogue, and the structural diversity among these compounds means our findings may not apply broadly to other analogues.¹⁴ The use of equine rather than human BChE, while biochemically justified, introduces potential species-specific differences.⁵⁵ The spectroscopic analysis also faced technical challenges, particularly from sample drying during measurement, which introduced variance unrelated to inhibition. Despite achieving good discrimination accuracy, addressing these technical issues could further improve the method's precision and reliability for mechanistic studies.

Future work should expand this approach to other fentanyl analogues to determine whether mixed inhibition represents a common mechanism or if structural variations lead to different inhibition patterns. Comparative studies with known cholinesterase inhibitors could help validate the spectroscopic signatures we identified and establish whether these structural changes are specific to mixed inhibition or occur with other mechanisms as well. Additionally, investigating sequential and simultaneous exposure to fentanyl analogs and other BChE inhibitors, such as organophosphate compounds, would provide valuable mechanistic insights into potential binding site competition, synergistic effects, or altered inhibition mechanisms.

The methodology we developed here demonstrates the potential for combining traditional enzyme kinetics with modern analytical techniques to gain deeper insight into inhibition mechanisms. This integrated approach could prove valuable for studying other enzyme-inhibitor systems, particularly those involving complex or previously unknown mechanisms. As fentanyl analogues continue to emerge, having robust methods for characterizing their biochemical effects becomes increasingly important for understanding their toxicological profiles and developing appropriate countermeasures.

Conclusion

This study characterized DPPM fentanyl inhibition of BChE through the combination of enzymatic kinetics and Raman spectroscopy. Statistical analysis definitively identified mixed inhibition as the mechanism, with DPPM binding preferentially to free enzyme (K_ic = 528.7 μM) over enzyme–substrate complex (K_iu = 1471.0 μM). Raman spectroscopy provided molecular evidence supporting these kinetics, revealing changes in aromatic residues (1028 cm⁻¹) and protein backbone (1539, 1557 cm⁻¹) upon inhibition. Machine learning algorithms achieved 92% accuracy in distinguishing between enzyme states, thereby confirming that these structural alterations represent consistent inhibition signatures.

Our combinatorial approach demonstrates how integrating kinetic and spectroscopic techniques reveals mechanistic details that individual techniques cannot provide. The methodology established here offers a framework for investigating other fentanyl analogues and enzyme-inhibitor systems where mechanisms are complex or unknown. As synthetic opioids continue emerging, such detailed mechanistic understanding becomes essential for toxicological assessment and countermeasure development.

Author contributions

A. B., A. N., and A. O. contributed to data collection, analysis, and manuscript preparation. J. H. supervised experimental work, enzyme kinetics analysis, and contributed to manuscript review. L. H. supervised the Raman experimental work, computational and machine learning analyses. All authors have read and approved the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: (1) complete R code implementing the renz package analysis using dir.MM for initial parameter estimation, and (2) constrained four-model inhibition analysis with nlsLM, including biochemical validation routines and all kinetic datasets used in this study. See DOI: https://doi.org/10.1039/d5an01018g.

Raw and processed Raman spectroscopic datasets are available from the corresponding author upon request.

Acknowledgements

We thank Texas Tech University for technical support. This work did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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