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. 2025 Aug 19;39(1):67. doi: 10.1007/s10822-025-00648-7

Computational QSAR study of novel 2-aminothiazol-4(5H)-one derivatives as 11β‐HSD1 inhibitors

Katarzyna Mądra-Gackowska 1, Szymon Baumgart 2, Mateusz Jędrzejewski 3,4, Renata Studzińska 2, Łukasz Szeleszczuk 3, Marcin Gackowski 5,✉
PMCID: PMC12364743  PMID: 40828332

Abstract

This research aims to develop a predictive model to support the design of new 11β-hydroxysteroid dehydrogenase type 1 (11β-HSD1) inhibitors based on the pseudothiohydantoin scaffold, offering potential for novel treatments of metabolic disorders. The Quantitative Structure–Activity Relationship (QSAR) analysis was performed on 56 2-aminothiazol-4(5h)-one derivatives, for which the 11β-HSD1 inhibitory activity was previously reported. Gaussian software was employed for geometry optimization, while Dragon software was used to calculate the molecular descriptors. The study used an Artificial Neural Network (ANN) algorithm for regression analysis between the top ten preselected descriptors and the activity of the studied analogs. A predictive model was developed using a network architecture 10-11-1 with a Broyden–Fletcher–Goldfarb–Shanno learning algorithm. The model’s reliability was supported through cross-validation and y-randomization strategies. The model exhibited high accuracy with a determination coefficient (R2) of 0.9482, and its validity was confirmed through internal validation with a cross-validated R2 (Q2) of 0.9944. Three classes of 3D descriptors (GETAWAY, 3D-MoRSE, and RDF descriptors) and four groups of topological indices (GALVEZ, 2D autocorrelations, 2D matrix-based descriptors, and Burden eigenvalues) were used to generate the QSAR model. The developed model was applied to predict the 11β-HSD1 inhibitory activity of four designed series of 2-aminothiazol-4(5h)-one derivatives, suggesting that compounds with cyclohexyl and 2-(tetrahydro-2H-pyran-2-yl)methyl residues substituted at the amino group, and various substituents at C-5 of the thiazole ring, could be potential candidates for upcoming chemical synthesis and biological assessment.

Keywords: 2-aminothiazol-4(5h)-one derivatives, Pseudothiohydantoin derivatives, Quantitative structure–activity relationship (QSAR), 11β-hydroxysteroid dehydrogenase type 1 (11β-HSD1) inhibitors, Metabolic diseases, Artificial neural networks (ANNs)

Introduction

11β-Hydroxysteroid dehydrogenase type 1 (11β-HSD1) is a key enzyme involved in the metabolism of glucocorticosteroids, hormones essential in the regulation of energy metabolism, modulation of immune and inflammatory processes, and the stress response [1]. The 11β-HSD1 enzyme is an NADPH-dependent oxidoreductase that catalyzes the conversion of biologically inactive cortisone into cortisol [2]. Together with 11β-hydroxysteroid dehydrogenase type 2, it regulates the body’s cortisol metabolism. 11β-Hydroxysteroid dehydrogenase type 1 is expressed in many tissues, with high expression in the liver, adipose tissue, central nervous system (CNS), skeletal muscle, pancreatic islets, immune system cells, and gonads [3, 4]. Particular attention should be paid to the activity of 11β-HSD1 in the liver due to the process of gluconeogenesis and in adipose tissue due mainly to adipogenesis and lipolysis [5, 6]. Abnormal 11β-HSD1 activity in these two tissues is associated with the occurrence of metabolic syndrome (MetS) [5]. Metabolic syndrome is a disease entity characterized by a combination of several disorders, including central obesity, hypertension, type 2 diabetes, dyslipidemia, and insulin resistance [7]. In transgenic mice with overexpression of 11β-HSD1 in adipose tissue, typical features of metabolic syndrome were observed, including obesity, insulin resistance, hypertension, and dyslipidemia [4]. Overactivity of 11β-HSD1 particularly affects visceral fat, as evidenced by studies conducted in animal models and among obese humans [8, 9]. Increased 11β-HSD1 activity leads to an increase in cortisol levels, which directly affects the activity of lipoprotein lipase, an enzyme responsible for the hydrolysis of circulating triacylglycerol (TAG) into free fatty acids and glycerol [10]. Increased availability of free fatty acids leads to their uptake and storage, especially in the visceral region. In addition, chronic excess cortisol also affects the process of adipocyte differentiation, leading to an increase in the number of mature adipocytes and their significant hypertrophy [10]. This is evidenced by, among others, transgenic mouse models with excessive expression of 11β-HSD1 in adipose tissue, in which visceral obesity (with enlarged adipocytes), insulin resistance, hyperlipidemia, and hypertension were observed [9]. Similarly, liver-specific overexpression enhances gluconeogenesis and contributes to insulin resistance [11]. Higher expression of 11β-HSD1 in the liver was also found in patients with diagnosed hypertension linked to cortisol-induced angiotensinogen upregulation [12]. Genetically modified mice with excessive hepatic expression of 11β-HSD1 developed hypertension and a mild form of insulin resistance [13].

Due to the critical role of 11β-HSD1 dehydrogenase in the pathogenesis of metabolic syndrome, inhibition of 11β-HSD1 is currently a promising target in treating metabolic diseases. Scientific reports confirm that administration of 11β-HSD1 inhibitors in people with type 2 diabetes leads to a reduction in blood sugar levels, and thus to a decrease in insulin resistance and body weight [14]. In the first two decades of the twenty-first century, a significant development of selective 11β-HSD1 inhibitors was observed. Several compounds had the opportunity to be tested in the early phases of clinical trials, including BVT-3498, AMG-221, or PF-915275. Still, the results were unsatisfactory, resulting in the studies’ discontinuation [15–17]. For this reason, further research and optimization are needed to develop a group of potent and selective 11β-HSD1 inhibitors, as the presented group of drugs still has potential and may provide a new method of treating metabolic diseases.

Previous studies on the search for selective 11β-hydroxysteroid dehydrogenase type 1 inhibitors were based on a group of compounds containing a 2-aminothiazol-4(5H)-one (pseudothiohydantoin) group in their structure. In the course of recent studies, six series of 2-aminothiazol-4(5H)-one derivatives (each containing 9 or 10 compounds) were synthesized containing an allyl group at the amino group [18], a methyl group [19], an isopropyl group [20], and a tert-butyl group [21], adamantly [22] and cyclopentyl [23] differing in substituents at C-5 of the thiazole ring (Fig. 1). All obtained series were tested for inhibition of 11β-hydroxysteroid dehydrogenase type 1. The present study was conducted based on 56 pseudothiohydantoin derivatives to develop a mathematical model capable of guiding the design of structurally favorable 2-aminothiazol-4(5H)-one analogues. Considering the limited success of previous inhibitors in clinical trials, there is a critical need for computational models that can accelerate the design and screening of more effective candidates. The present QSAR approach addresses this challenge by predicting 11β-HSD1 inhibitory activity with high accuracy.

Fig. 1.

Fig. 1

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Structures of synthesized 2-aminothiazol-4(5H)-one derivatives—11β-HSD1 inhibitors

Results and discussion

QSAR analysis was used to study the structure–activity relationship of fifty-six 2-aminothiazol-4(5H)-one derivatives as 11β‐HSD1 inhibitors. 3D representations of each structure were created with Gauss View 6 and optimized with the DFT method b3lyp/6–311 + + g(d,p) available in the Gaussian 16 software. Examples of three-dimensional structures of molecules with defined geometry are presented in Fig. 2.

Fig. 2.

Fig. 2

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Geometrically optimized structures of selected 2-aminothiazol-4(5H)-one analogs: a 1c; b 2e; c 3g; d 4h; e 5i; f 6j

During the molecular modeling study, over 5000 molecular descriptors were calculated for geometrically optimized structures by Dragon Software. To improve the predictive performance of QSAR models, the 10 best descriptors were selected from a large pool of candidates. Selected descriptors belonged to the following descriptor blocks: Galvez topological charge indices, 2D autocorrelations, 2D matrix-based descriptors, GETAWAY descriptors, Burden eigenvalues, 3D-MoRSE descriptors, and RDF descriptors (Table 1 and Table 3). These descriptors were subsequently employed as independent variables to build multiple different models using artificial neural networks as a post-processing algorithm and, in turn, to forecast the 11β‐HSD1 inhibitory activity of studied and 39 newly designed compounds.

Table 1.

Values of molecular descriptors selected for model building for the investigated 2-aminothiazol-4(5H)-one derivatives

Compound Sample Descriptors
Mor05u MATS1s R3v + R2s GGI2 RDF030u SpMin8_Bh(m) SpPosA_B(m) VE2_B(p) VE1_D/Dt
1a Train − 1.968 − 0.084 0.062 5.636 0.667 3.243 0.000 1.512 0.264 2.704
1b Train − 2.439 − 0.092 0.052 5.474 1.111 6.356 0.000 1.482 0.246 2.807
1c Train − 2.81 − 0.067 0.047 5.266 1.111 8.778 0.403 1.463 0.23 2.961
1d Train − 3.487 − 0.051 0.045 5.281 1.111 10.062 0.466 1.446 0.214 3.16
1e Train − 3.295 − 0.078 0.033 4.844 1.333 9.841 0.434 1.456 0.219 3.125
1f Test − 3.051 − 0.108 0.043 4.903 1.778 8.762 0.223 1.464 0.23 2.866
1g Test − 2.587 − 0.083 0.052 5.992 1.333 5.301 0.488 1.455 0.215 3.044
1h Validation − 2.478 − 0.09 0.052 6.129 1.778 7.611 0.482 1.765 0.204 3.38
1i Train − 3.736 − 0.014 0.026 4.498 1.778 17.303 0.721 1.413 0.202 3.088
1j Train − 3.425 − 0.033 0.037 4.65 1.556 13.332 0.427 1.464 0.226 2.858
2b Validation − 2.108 − 0.064 0.053 5.296 1.111 4.283 0.000 1.495 0.285 2.697
2c Train − 2.32 − 0.04 0.051 5.447 1.111 6.827 0.000 1.475 0.262 2.822
2d Train − 2.924 − 0.025 0.047 5.454 1.111 8.279 0.000 1.453 0.241 2.866
2e Train − 2.958 − 0.054 0.036 5.057 1.333 7.982 0.000 1.464 0.248 2.926
2f Test − 2.54 − 0.084 0.044 4.801 1.778 6.275 0.000 1.481 0.266 2.841
2g Test − 2.422 − 0.058 0.055 5.919 1.333 3.828 0.381 1.462 0.242 2.951
2h Train − 2.297 − 0.064 0.055 6.059 1.778 5.841 0.381 1.813 0.229 3.336
2i Train − 3.153 0.01 0.028 4.955 1.778 16.037 0.624 1.413 0.226 2.925
2j Train − 3.261 − 0.005 0.039 4.978 1.556 12.073 0.000 1.476 0.26 2.738
3b Train − 3.072 − 0.075 0.037 5.469 1.111 7.167 0.000 1.47 0.25 2.848
3c Train − 3.483 − 0.059 0.043 4.797 1.111 11.555 0.370 1.448 0.234 3.001
3d Train − 3.34 − 0.049 0.037 4.829 1.111 11.908 0.583 1.435 0.218 3.175
3e Validation − 4.134 − 0.074 0.029 4.51 1.333 12.56 0.468 1.443 0.223 3.148
3f Validation − 3.776 − 0.096 0.037 4.56 1.778 11.551 0.215 1.451 0.234 2.921
3g Train − 3.716 − 0.068 0.041 5.499 1.333 8.078 0.630 1.445 0.217 2.987
3h Validation − 2.785 − 0.073 0.04 5.23 1.778 9.349 0.611 1.756 0.206 3.337
3i Train − 4.776 − 0.02 0.023 4.247 1.778 20.1 0.785 1.404 0.204 3.017
3j Test − 4.139 − 0.032 0.032 4.348 1.556 16.081 0.466 1.451 0.229 2.892
4b Validation − 3.485 − 0.098 0.032 4.38 1.333 7.685 0.000 1.457 0.248 2.98
4c Train − 3.646 − 0.083 0.035 4.516 1.333 10.047 0.498 1.438 0.233 3.106
4d Validation − 4.195 − 0.073 0.029 4.581 1.333 11.435 0.727 1.426 0.218 3.294
4e Train − 4.442 − 0.096 0.025 4.352 1.556 11.148 0.617 1.434 0.221 3.269
4f Train − 3.823 − 0.118 0.029 4.157 2.000 10.146 0.248 1.44 0.232 3.025
4g Train − 3.921 − 0.089 0.029 4.842 1.556 6.750 0.906 1.437 0.212 3.006
4h Train − 3.758 − 0.095 0.032 4.965 2.000 8.877 0.786 1.731 0.2 3.338
4i Train − 5.29 − 0.044 0.021 4.061 2.000 18.613 0.809 1.398 0.202 3.073
4j Train − 4.654 − 0.057 0.025 4.015 1.778 14.667 0.694 1.442 0.224 3.031
5a Train − 4.833 0.036 0.023 5.268 1.111 14.08 0.899 1.415 0.228 3.542
5b Test − 5.499 0.018 0.027 4.744 1.556 17.706 1.051 1.403 0.216 3.749
5c Train − 5.778 0.022 0.026 4.497 1.556 20.236 1.079 1.394 0.206 3.885
5d Train − 6.719 0.023 0.018 4.962 1.556 20.889 1.079 1.387 0.197 3.991
5e Train − 6.36 0.005 0.019 4.373 1.778 21.212 1.18 1.393 0.198 3.988
5f Test − 6.08 − 0.004 0.023 4.409 2.222 20.041 1.079 1.394 0.201 3.888
5g Validation − 5.89 0.032 0.024 4.98 1.778 16.544 1.181 1.4 0.174 4.28
5h Train − 5.675 0.03 0.029 5.084 2.222 18.804 1.181 1.622 0.16 4.294
5i Train − 6.559 0.035 0.019 4.624 2.222 28.349 1.232 1.37 0.181 4.237
5j Train − 6.707 0.034 0.021 4.637 2.000 24.203 1.079 1.398 0.19 4.05
6b Train − 3.424 − 0.003 0.033 5.248 1.111 13.119 0.551 1.447 0.214 3.185
6c Train − 3.59 0.004 0.04 4.674 1.111 15.545 0.72 1.431 0.202 3.267
6d Train − 4.384 0.008 0.034 4.706 1.111 16.909 0.782 1.42 0.19 3.322
6e Train − 4.147 − 0.013 0.029 4.493 1.333 16.624 0.772 1.427 0.195 3.334
6f Train − 3.857 − 0.027 0.034 4.475 1.778 15.573 0.695 1.432 0.202 3.288
6g Test − 3.675 0.004 0.036 5.321 1.333 12.253 0.883 1.431 0.193 3.648
6h Train − 3.557 0.001 0.033 5.763 1.778 15.331 0.822 1.71 0.184 3.641
6i Train − 4.853 0.027 0.022 4.203 1.778 24.047 0.868 1.394 0.181 3.63
6j Train − 4.608 0.023 0.029 4.27 1.556 20.197 0.773 1.434 0.2 3.463
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Table 3.

Sensitivity analysis results for the MLP 10-11-1 network

Name Definition [26] Category [26] Dimensionality Error
MLP 10-11-1		 Rank
GGI2 Topological charge index of order 2 topological Galvez topological charge indices (GALVEZ) 2D 16.81 1
MATS1s Moran autocorrelation of lag 1 weighted by I-state 2D autocorrelations 2D 14.70 2
SpPosA_B(m) Normalized spectral positive sum from the Burden matrix, weighted by mass 2D matrix-based descriptors 2D 13.18 3
R3v +  R maximal autocorrelation of lag 3/weighted by van der Waals volume GETAWAY descriptors 3D 10.43 4
R2s R autocorrelation of lag 2/weighted by I-state GETAWAY descriptors 3D 10.12 5
VE1_D/Dt The coefficient sum of the last eigenvector from the distance/detour matrix 2D matrix-based descriptors 2D 9.40 6
SpMin8_Bh(m) Smallest eigenvalue n. 8 of the Burden matrix, weighted by mass Burden eigenvalues 2D 8.70 7
Mor05u Signal 05/unweighted 3D-MoRSE descriptors 3D 7.98 8
RDF030u Radial Distribution Function-030/unweighted RDF descriptors 3D 7.93 9
VE2_B(p) The average coefficient of the last eigenvector from the Burden matrix, weighted by polarizability 2D matrix-based descriptors 2D 7.86 10
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The Automated Network Search (ANS) algorithm was used to train approximately five hundred neural networks with varying characteristics. After evaluating the training, test, and validation performances, including correlation coefficient and sum of squares error, a multilayer perceptron (MLP) 10-11-1 network with the ID 344 was chosen as the best model for representing the connections between specific descriptors and 11β‐HSD1-inhibitory activity, addressing the regression problem under study. Many different algorithms and activation functions were used during network creation. The predictive network used a Broyden–Fletcher–Goldfarb–Shanno (BFGS) learning algorithm and exponential functions for both the hidden and output layers. The network consists of ten artificial neurons in the input layer, eleven artificial neurons in the hidden layer, and one neuron in the output layer. The ’10-11-1 model’ refers to the architecture of the best-performing artificial neural network employed in this study, consisting of 10 input neurons, 11 neurons in the hidden layer, and a single output neuron representing predicted activity.

The predictive QSAR MLP 10-11-1 model is characterized by a high correlation between the experimental logarithm of the percentage of 11β‐HSD1 inhibition (log I11β‐HSD1) value and the value predicted by the network. The correlation coefficients are 0.99 for training, 0.95 for the test set, and 0.93 for validation. The sum of squares error between observed and predicted values was 0.002 for the training, 0.03 for the test, and 0.06 for the validation sample. Validation procedure was performed as described by Roy et al. [24] and confirmed that the MLP 10-11-1 model may be implemented to predict the 11β‐HSD1 inhibitory activity of novel compounds based on a pseudothiohydantoin scaffold. The most commonly used quality metrics in assessing the reliability and precision of predictions of QSAR models [25] are presented in Table 2.

Table 2.

Selected validation parameters of the predictive MPL10-11-1 model

Parameter [24] Value Threshold [24] Meaning [24]
Inline graphic 0.9482 ~ 1 (1 means perfect correlation)

Measures the variation of observed

data with the predicted ones
Inline graphic 0.9944 >  =  0.5 Cross‐validated R2 (Q2) checked for internal validation
Inline graphic 1.5649

Evaluates the model using

the predicted residual sum of squares
Inline graphic 0.0843 Index of errors in the context of predictive modeling studies
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A graphical representation comparing predicted values of log I11β‐HSD1 with experimentally determined values confirms that the network predicts the data relatively well (Fig. 3). A positive relationship with a strong strength is observed on this scatter plot.

Fig. 3.

Fig. 3

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A scatter plot of experimental versus predicted log I11β‐HSD1 values. Correlation coefficient values: training set R = 0.99; test set R = 0.95; and validation set R = 0.93

To assure high accuracy of predictions and prevent overfitting, ten key descriptors were first selected to use in building the ANN model and used as input variables (Table 3). Moreover, the model was validated on a separate test and validation set. The high Q2 value (0.9944) confirms the generalizability of the model. Four of these ten descriptors were 3D geometrical descriptors, while the remaining six were representatives of 2D topological descriptors. This designates that two- and three-dimensional molecular structures play a crucial role in the biological activity of the investigated compounds. The regression analysis using artificial neural network algorithms and subsequent sensitivity analysis showed the significance of specific descriptors for the 11β‐HSD1 inhibitory activity of the investigated 2-aminothiazol-4(5H)-one derivatives. This analysis identified the molecular features that have the most significant impact on the activity of the compounds being studied. The ranking of descriptors used in the 10-11-1 MLP model, listing them in order of importance along with their dimensionality, block, and definition, is presented in Table 3. Figure 4 illustrates the relative importance of each molecular descriptor in the MLP 10-11-1 model, based on error reduction contribution in a sensitivity analysis. Each variable entering the model had an error quotient exceeding 1, indicating that all preselected descriptors were significant for the MLP 10-11-1 network. It would be excluded if a variable had no effect or worsened the network’s performance.

Fig. 4.

Fig. 4

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Sensitivity analysis: feature importance of the top 10 descriptors

A series of previous studies on the search for selective 11β-hydroxysteroid dehydrogenase type 1 inhibitors indicate that the presence of large hydrophobic groups (adamantyl and cyclopentyl) in the 5-position of the thiazole ring positively affects the 11β-HSD1 inhibitory activity of compounds containing a pseudothiohydantoin scaffold [18–23]. In particular, the adamantyl group is known for positively modulating the therapeutic index of numerous experimental compounds, thereby enhancing the drug-like characteristics of a lead compound without increasing its toxicity. After carefully considering the above observations and the QSAR model built in the present study, 39 new potential inhibitors for 11β-hydroxysteroid dehydrogenase type 1 have been designed. The introduction of bulky hydrophobic groups, such as cyclohexyl and tetrahydropyran-methyl moieties, was rationalized by the significant contribution of 3D descriptors like RDF030u and GETAWAY indices (Table 3), which suggest favorable steric and shape complementarity with the enzyme’s binding site. These inhibitors are based on a pseudothiohydantoin scaffold containing cyclohexyl, 2-(tetrahydrofuran-2-yl)methyl, 2-(tetrahydro-2H-pyran-2-yl)methyl, cyclopropyl residues substituted at the amino group and differing in substituents at C-5 of the thiazole ring listed in Table 4.

Table 4.

Designed 2-aminothiazol-4(5H)-one derivatives with 11β-HSD1 inhibitory activity predicted by the MLP 10-11-1 model

graphic file with name 10822_2025_648_Figa_HTML.gif
Compound R R1 R2 Predicted log I11β‐HSD1
7b graphic file with name 10822_2025_648_Figb_HTML.gif H CH3 1.3214
7c H C2H5 1.3654
7d H n-C3H7 1.9376
7e H CH(CH3)2 1.9213
7f CH3 CH3 1.9128
7 g H C6H5 1.8244
7 h H p-BrC6H4 1.3436
7i C5H10cycl 2.0133
7j C3H6cycl 1.9882
8a graphic file with name 10822_2025_648_Figc_HTML.gif H H 0.0000
8b H CH3 0.9940
8c H C2H5 1.0459
8d H n-C3H7 1.2294
8e H CH(CH3)2 1.8577
8f CH3 CH3 1.9598
8 g H C6H5 1.1073
8 h H p-BrC6H4 1.8062
8i C5H10cycl 1.9745
8j C3H6cycl 1.2989
9a graphic file with name 10822_2025_648_Figd_HTML.gif H H 0.0000
9b H CH3 1.2529
9c H C2H5 1.2989
9d H n-C3H7 1.4561
9e H CH(CH3)2 1.4561
9f CH3 CH3 2.0031
9 g H C6H5 1.3518
9 h H p-BrC6H4 1.9668
9i C5H10cycl 2.0226
9j C3H6cycl 1.9816
10a graphic file with name 10822_2025_648_Fige_HTML.gif H H 0.0000
10b H CH3 0.9889
10c H C2H5 1.0366
10d H n-C3H7 1.1541
10e H CH(CH3)2 1.1541
10f CH3 CH3 0.9889
10 g H C6H5 0.7169
10 h H p-BrC6H4 0.6904
10i C5H10cycl 1.8769
10j C3H6cycl 1.7425
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The obtained predictions show that 2-aminothiazol-4(5H)-one derivatives bearing cyclohexyl and 2-(tetrahydro-2H-pyran-2-yl)methyl moiety substituted at the amino group may produce the most promising 11β-hydroxysteroid dehydrogenase type 1 inhibitors. Among all designed analogs, the most active compounds are 7d, 7e, 7f, 7i, 7j, 8f, 8i, 9f, 9h, 9i, and 9j, which at the concentration of 10 μM may presumably inhibit the activity of isoform 1 by more than 80.00%.

The pseudothiohydantoin scaffold is essential and effective in medicinal chemical research and drug design. Numerous compounds with a 2-aminothiazol-4(5H)-one core have been synthesized with different substituents. Additionally, various therapeutic properties, including 11β-hydroxysteroid dehydrogenase type 1 inhibitory activity, have been described in scientific literature as mentioned above.

The present investigation has created a validated QSAR model using artificial neural networks. This model helps to solve regression problems between molecular structure and 11β‐HSD1 inhibitory activity of 2-aminothiazol-4(5H)-one derivatives. It has facilitated the design of new compounds and was used to predict the inhibitory activity towards 11β‐HSD1 of newly designed compounds (Table 4). The MLP 10-11-1 model includes ten of the most informative descriptors selected from a large dataset (Table 3 and Table 6) to prevent overtraining and identify the most critical molecular properties that affect the 11β‐HSD1 inhibitory activity of the pseudothiohydantoin-based compounds being studied. Based on the preselection process, descriptors related to atomic properties such as intrinsic state, atomic mass, polarizability, and four unweighted ones significantly impacted the inhibitory activity towards 11β-hydroxysteroid dehydrogenase type 1. These indices contain 2D and 3D information from the molecular structure, suggesting that the model has a reasonable level of predictability because the modeling activity is influenced by more than just a single molecular dimension.

Table 6.

Molecular descriptors used to train ANN models

Symbol Variable rank Importance
Mor05u 100 1.000000
MATS1s 98 0.975098
R3v + 85 0.850106
R2s 83 0.832084
GGI2 79 0.787630
RDF030u 74 0.740510
SpMin8_Bh(m) 71 0.712326
SpPosA_B(m) 70 0.697505
VE2_B(p) 69 0.691941
VE1_D/Dt 67 0.673839
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Descriptors belonging to seven different classes (GALVEZ, 2D autocorrelations, 2D matrix-based descriptors, GETAWAY descriptors, Burden eigenvalues, 3D-MoRSE descriptors, and RDF descriptors) contributed to the modeling of 11β‐HSD1 inhibitory activity of the studied analogs. The first 3 descriptors, according to the sensitivity analysis conducted (Table 3), contribute most to the QSAR model and describe the two-dimensional structure of the molecules analyzed. The top-ranked descriptor GGI2 relates to electronic charge distribution, a key factor in enzyme binding, while MATS1s incorporates electronic and structural properties. These findings align with previous reports emphasizing the role of electrostatics and molecular topology in 11β-HSD1 inhibition [27–29].

GGI2 is the topological charge index of order 2 and is ranked first in the sensitivity analysis. It is part of the Galvez topological charge indices derived from the first ten eigenvalues of the corrected adjacency matrix of compounds [30, 31]. The GGIn descriptors are linked to the topological charge index of order n, where ‘n’ indicates the order of eigenvalue. The GGI2 descriptor assesses molecule charge transfer calculated from the adjacency topological matrix.

The MATS1s descriptor in the model mentioned above falls under the 2D autocorrelations category of Dragon descriptors [27]. It is based on the autocorrelation of the topological structure of Moran. Calculating this descriptor involves summing different autocorrelation functions for various fragment lengths, resulting in different autocorrelation vectors for the lengths of the structural fragments [28]. When calculating this descriptor, an intrinsic state is also used as a weighting component based on a physicochemical property. Therefore, MATS1s addresses the topology of the structure or its parts concerning the intrinsic state of the molecules being studied.

The third participating descriptor SpPosA_B(m) is derived from the Burden matrix, which is derived from the adjacency matrix, and weighted by atomic mass [32]. The adjacency matrix, also known as the vertex adjacency matrix, is a crucial tool for calculating molecular descriptors [33]. This is one of the essential graph theoretical matrices representing the entire set of connections between adjacent pairs of atoms. The adjacency matrix provides branching information, which may also be relevant for modeling pharmacological activity.

The fourth and fifth indices in the ranking list regarding relevance to the developed model belong to the GETAWAY (Geometry, Topology, and Atom-Weights AssemblY) descriptors. The R3v + and R2s descriptors reference 3D molecular geometry, atom-relatedness, and chemical information. These descriptors are computed using spatial autocorrelation formulas, connectivity indices, and traditional matrix operations [34]. Their computation involves analyzing the individual atoms within the molecule to measure their atomic van der Waals volume and intrinsic state, respectively. Past findings have indicated that GETAWAY descriptors can capture both local and distributed information regarding the molecular structure, making them a valuable asset in developing reliable models [35]. It has been observed that utilizing GETAWAY along with descriptors containing information on the entire molecular structure appears to create more accurate models when the property being modeled depends specifically on the 3D aspects of the molecule, such as in the case of biological activities. However, while all the molecular descriptor sets effectively model the octanol–water partition coefficient, GETAWAY and topological descriptors produce the most reliable regressions, as in the present study [36].

Descriptors VE1_D/Dt and VE2_B(p), being the sixth and last ranked, respectively, belong to the class of 2D matrix-based descriptors, as does the already mentioned descriptor SpPosA_B(m). VE1-D/Dt denotes the aggregate of coefficients in the last eigenvector obtained from the distance/detour matrix, derived from the distance and detour matrices. It is calculated as the length from the shortest to the longest path between vertices from the branching or cyclicity vertices and reflects substructure information about the cation sections [29]. The VE2_B(p) comprises the sum of the coefficients of the last eigenvector, weighted by polarizability. The value of VE2_B(p) increases with the number of graph vertices [37].

The seventh significant molecular descriptor SpMin8_Bh(m) is categorized under Burden eigenvalues. This index is computed using molecular graphs containing hydrogen atoms through the Burden matrix [38]. Generally, each matrix in the Dragon calculation has the first eight largest positive eigenvalues denoted as SpMaxk_Bh(w) and the first eight smallest negative eigenvalues denoted as SpMink_Bh(w). In this context, k represents the eigenvalue rank and w indicates the atomic property, such as atom polarizability (p), intrinsic state (s), and atomic mass (m) as seen in the case of SpMin8_Bh(m). This particular molecular descriptor accounts for molecular mass and can be utilized to address the challenge of identifying molecular structural similarity or diversity of studied compounds.

Mor05u is another significant index that is a part of MoRSE descriptors, which stand for Molecular Representation of Structures based on Electron diffraction. It represents the unweighted signal 05. 3D-MoRSE descriptors offer insights into compounds based on their 3D structure through a molecular transform derived from an equation employed in electron diffraction studies. By considering multiple atomic properties, these descriptors can effectively encode highly adaptable representations of a compound and mirror the three-dimensional arrangement of atoms within a molecule [29].

Lastly, RDF030u (Radial Distribution Function 3.0/unweighted) is a descriptor within the Radial Distribution Function (RDF) category. These indices gauge the likelihood of an atom existing within a spherical volume with a radius of R. They are determined using radial basis functions centered on various interatomic distances from 0.5 to 15.5 Å. RDF descriptors’ calculations consider the atoms’ quantity, properties, and the distances between them. The RDF030u descriptor is influenced by the molecular structure within a 3.0 Å atomic radius, relative to the mass center. Thus, it details the likelihood of atoms being distributed within a spherical area with the abovementioned radius. This may be a crucial consideration when analyzing the chemical properties of a compound [39, 40].

A limitation of this study is the lack of experimental validation of the predicted inhibitory activities. In addition, the dataset used is relatively small and limited to a congeneric series, which may restrict model generalizability to broader chemical spaces. The absence of external validation or prospective predictions limits our ability to assess how the model performs on unseen chemotypes. Moreover, reliance on in silico descriptors without integrating pharmacokinetic profiling reduces the translational potential of the proposed candidates. These limitations highlight the importance of future experimental work and validation using structurally diverse analogs. Future work will involve synthesis and biological evaluation of the most promising series of predicted compounds, i.e., pseudothiohydantoin compounds with cyclohexyl and 2-(tetrahydro-2H-pyran-2-yl)methyl residues substituted at the amino group.

Conclusions

The current research, QSAR analysis was conducted using the ANN algorithm to develop a mathematical model for predicting the 11β-hydroxysteroid dehydrogenase type 1 inhibitory activity of fifty-six 2-aminothiazol-4(5H)-one derivatives. These derivatives have been synthesized, and their activity has been evaluated in vitro recently. The predictive MLP 10-11-1 model was chosen from a pool of 500 trained networks based on its predictive accuracy. The QSAR model incorporates ten molecular descriptors reflecting the compounds under study’s 2D (topological) and 3D (spatial) properties. The results showed that molecular conformation and shape, electrostatic properties, intrinsic state, molecular mass, and polarizability primarily influenced the activity of the compounds studied. Furthermore, the obtained structural information helped in the design of new compounds. The validation process confirmed the satisfactory predictive performance, allowing the implementation of the elaborated model to predict the 11β‐HSD1 inhibitory activity of four series of newly designed analogs. The results obtained from the predictions indicate that pseudothiohydantoin compounds with cyclohexyl and 2-(tetrahydro-2H-pyran-2-yl)methyl residues substituted at the amino group, and various substituents at C-5 of the thiazole ring, could be potential candidates for upcoming chemical synthesis and biological assessment. This may also contribute additional information regarding the desired biological activity for future in silico studies. Findings from this study could aid in estimating 11β‐HSD1 inhibitory activity and developing drugs for metabolic diseases based on the pseudothiohydantoin scaffold. Nevertheless, the findings presented here are based on a relatively small and congeneric dataset and require future experimental validation and application to more diverse chemical scaffolds to fully assess the generalizability of the model.

Materials and methods

Energy optimization of 2-aminothiazol-4(5H)-one derivatives

The dataset of 2-aminothiazol-4(5H)-one derivatives used in this study was obtained from previously published experimental studies on the synthesis and in vitro evaluation of 11β-HSD1 inhibitors [18–23]. All quantum–mechanical calculations for the 56 studied 2-aminothiazol-4(5H)-one derivatives (Table 5) were performed using Gaussian 16 (Gaussian Inc., Wallingford, CT, USA) [41]. Compound models were initially prepared with GaussView 6 (Gaussian Inc., Wallingford, CT, USA) [42] and then optimized using the B3LYP functional with the 6–311 + + G(d,p) basis set [43–47]. The nature of the stationary points was confirmed by frequency calculations at the same level of theory, ensuring that the optimized structures exhibited no imaginary frequencies.

Table 5.

Chemical structures of the studied 2-aminothiazol-4(5H)-one derivatives possessing 11β-HSD1 inhibitory activity

graphic file with name 10822_2025_648_Figf_HTML.gif
Compound R R1 R2 % of 11β-HSD1 inhibition 10 µM [18–23] log I11β‐HSD1
1a CH2=CH-CH2- H H 0 0
1b H CH3 0 0
1c H C2H5 0 0
1d H n-C3H7 0 0
1e H CH(CH3)2 0 0
1f CH3 CH3 0 0
1 g H C6H5 0 0
1 h H p-BrC6H4 13.46 1.16
1i C5H10cycl 71.27 1.86
1j C3H6cycl 38.03 1.59
2b CH3- H CH3 0 0.00
2c H C2H5 0 0.00
2d H n-C3H7 0 0.00
2e H CH(CH3)2 21.13 1.34
2f CH3 CH3 22.25 1.37
2 g H C6H5 0 0.00
2 h H p-BrC6H4 17.00 1.26
2i C5H10cycl 48.00 1.69
2j C3H6cycl 23.00 1.38
3b graphic file with name 10822_2025_648_Figg_HTML.gif H CH3 0 0.00
3c H C2H5 0 0.00
3d H n-C3H7 0 0.00
3e H CH(CH3)2 18.86 1.30
3f CH3 CH3 18.06 1.28
3 g H C6H5 0 0.00
3 h H p-BrC6H4 27.58 1.46
3i C5H10cycl 54.53 1.74
3j C3H6cycl 20.94 1.34
4b graphic file with name 10822_2025_648_Figh_HTML.gif H CH3 16.29 1.24
4c H C2H5 20.11 1.32
4d H n-C3H7 29.17 1.48
4e H CH(CH3)2 44.27 1.66
4f CH3 CH3 29.70 1.49
4 g H C6H5 26.85 1.44
4 h H p-BrC6H4 10.31 1.05
4i C5H10cycl 82.54 1.92
4j C3H6cycl 23.61 1.39
5a graphic file with name 10822_2025_648_Figi_HTML.gif H H 22.27 1.37
5b H CH3 62.15 1.80
5c H C2H5 69.22 1.85
5d H n-C3H7 72.37 1.87
5e H CH(CH3)2 76.40 1.89
5f CH3 CH3 65.99 1.83
5 g H C6H5 46.32 1.68
5 h H p-BrC6H4 15.30 1.21
5i C5H10cycl 82.82 1.92
5j C3H6cycl 74.13 1.88
6b graphic file with name 10822_2025_648_Figj_HTML.gif H CH3 10.94 1.08
6c H C2H5 21.33 1.35
6d H n-C3H7 56.58 1.76
6e H CH(CH3)2 82.93 1.92
6f CH3 CH3 53.17 1.73
6 g H C6H5 64.29 1.81
6 h H p-BrC6H4 86.96 1.94
6i C5H10cycl 90.49 1.96
6j C3H6cycl 71.25 1.86
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Molecular descriptors

Five thousand two hundred seventy molecular descriptors were acquired from DFT calculations and Dragon 7.0 (Talete, Milano, Italy) software to provide mathematical representations of a molecule’s chemical information for QSAR modelling [48, 49]. These descriptors, which are categorized into 30 logical blocks, encompass 0D constitutional, 1D structural, 2D topological, and 3D geometrical descriptors. Following objective feature selection, the acquired descriptors were reduced to 921 molecular parameters by eliminating variables with zero or missing values, constant and near-constant values, parameters with a standard deviation lower than 0.0001, and highly correlated parameters (|r|> 0.95).

Regression analysis

The statistical analysis was conducted using Statistica 14.1.0.4 software (TIBCO Software Inc., Palo Alto, CA, USA). The logarithm of the percentage of 11β‐HSD1 inhibition was calculated before conducting QSAR modeling, and the distribution of dependent variables was analyzed to identify potential outliers, but none were found in the data. In the next step, the Statistica Random Forest algorithms were used to narrow down descriptors to the 10 most important ones suitable for modelling (Fig. 5 and Table 6). This was done to simplify the regression model, prevent overfitting, and enhance its predictive performance [50]. All molecular descriptors were scaled using min–max normalization to the range [0,1] before ANN modeling.

Fig. 5.

Fig. 5

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Descriptor importance plot

In the subsequent phase, post-processing algorithms known as STATISTICA Automated Neural Networks (SANN) were utilized to determine connections between molecular descriptors representing the properties of molecules and their 11β-HSD1-inhibitory activity. The developed model addresses the regression issue, meaning the network’s output is qualitative and indicated as the logarithm of the percentage of 11β‐HSD1 inhibition.

The Statistica ANS module automatically splits the studied derivatives into training, a test, and a validation sample in a 70:15:15 ratio for learning, cross-evaluation of network quality, and the management of the impact of the learning algorithm. In the network training process, the molecular descriptors are put into the designated input units, following which the hidden and output layer units are sequentially executed. The activation value of each unit is calculated by adding together the outputs of the units in the previous layer, weighted according to their importance. Then it is used by the activation function to generate the output of the neuron. The neuron/s of the output layer are allocated to the desired response (11β-HSD1-inhibitory activity in the case of the present study) following the completion of the entire network’s execution [50, 51]. The ANS module of the software used enabled scaling input and target variables. It allowed for the development of different networks with varying activation and error functions and complexity. Users may define hyperparameters such as network size and training algorithm control parameters. Dropout regularization and early stopping were employed to reduce overfitting, and a hold-out test set was maintained. The SANN framework is compatible with key types of neural networks, including multilayer perceptrons, radial basis function networks, and Kohonen self-organizing feature maps. Following the training of the networks, the most effective networks were exhibited, allowing for selecting the top-performing network without the need for a time-consuming trial-and-error approach [51]. The network architecture was optimized using STATISTICA’s Automated Network Search, which tested various topologies. The optimal network (10-11-1) was selected based on performance metrics on training, test, and validation datasets. Hyperparameters such as learning algorithm (BGFS), activation function (exponential), and training cycles were automatically optimized. The ANN model utilized a single hidden layer with 11 neurons, optimized using dropout (0.2) and early stopping. The significance of the variables for the QSAR model was assessed through a sensitivity analysis. Eventually, the model was utilized to forecast the 11β-HSD1-inhibitory activity of newly developed 39 2-aminothiazol-4(5H)-one analogs, coded as 7b-10j.

Author contributions

Conceptualization, K.M.-G., M.G. and R.S.; methodology, M.G, and M.J.; software, M.J. and M.G.; validation, M.G. and Ł.S.; formal analysis, K.M.-G, M.G. and M.J.; investigation, K.M.-G, S.B., R.S., M.J. and M.G.; resources, M.G. and M.J.; data curation, K.M.-G, M.J. and M.G.; writing—original draft preparation, K.M.-G, S.B., M.J., M.G. and R.S.; writing—review and editing, K.M.-G, M.G., S.B., M.J., and Ł.S..; visualization, K.M.-G and S.B.; supervision, M.G., Ł.S. and R.S.; project administration, K.M.-G and M.G. All authors reviewed the manuscript.

Funding

This research received no external funding.

Data availability

The dataset supporting the findings of this study, including compound identifiers, geometry-optimized molecular structures (in MOL format), and all Dragon-calculated molecular descriptors prior to feature selection and scaling, as well as the experimentally determined 11β-HSD1 inhibitory activity for synthesized compounds, is openly available in Zenodo under the Creative Commons Attribution 4.0 International License (CC BY 4.0). The data can be accessed at: [10.5281/zenodo.16537212].

Declarations

Conflict of interest

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Citations

  1. Zhang R, Kan JB, Lu S, Tong P, Yang J, Xi L, Liang X, Su D, Li D, Liu Y (2019) S100A16-induced adipogenesis is associated with up-regulation of 11 β-hydroxysteroid dehydrogenase type 1 (11β-HSD1). Biosci Rep. 10.1042/BSR20182042 [DOI] [PMC free article] [PubMed]

Data Availability Statement

The dataset supporting the findings of this study, including compound identifiers, geometry-optimized molecular structures (in MOL format), and all Dragon-calculated molecular descriptors prior to feature selection and scaling, as well as the experimentally determined 11β-HSD1 inhibitory activity for synthesized compounds, is openly available in Zenodo under the Creative Commons Attribution 4.0 International License (CC BY 4.0). The data can be accessed at: [10.5281/zenodo.16537212].

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