The new approach, known as Fragment-Based Drug Design (FBDD), or FBDD, appeared in the late 1990s in pharmaceutical research [16] [17] [18] . This approach involves the screening of organic molecules of very low molecular mass, the fragment molecules. The latter are distinguished from molecules traditionally present in the chemical libraries of pharmaceutical companies and academic laboratories by their low molecular complexity and their moderate size. Fragment molecules can in fact be considered as fractions of molecules commonly called “lead-like” and “drug-like”, used for high-throughput screening campaigns.

Figure 1 below is the molecular structure of 1,3,4-thiadiazole (TH) which was used for modeling.

The equation and the statistical parameters of the model established by Dou et al. [15] are presented below:

pIC 50 = − 11.36472 + 0.18089 ∗ α ( S-C-N ) − 5.70651 ∗ l ( C=N ) + 0.02973 ∗ μ ( D ) − 0.40993 * Δ S f 0 (1)

This equation will be used to predict the antidiabetic activity of new 1,3,4-thiadiazole derivatives.

The effects of substituents on the antidiabetic activity of the molecules were studied in order to detect the substituents which influence the pIC₅₀. The approach adopted is as follows:

• Classification of 1,3,4-thiadiazole derivatives in decreasing order of pIC₅₀;

• Identification of substituents of molecules with the highest pIC₅₀ values.

Thus, by ranking all the 1,3,4-thiadiazole derivatives in decreasing order of the potential for inhibiting antidiabetic activity (pIC₅₀), the first five (5) were selected. Those compounds with the best values of antidiabetic activity will serve as the basic structure for the design. Table 1 includes the 2D structures of these molecules and the pIC₅₀ values.

The calculation of the thermodynamic quantities of the molecules was carried out from optimization and calculation of the frequencies at the level of theory DFT/B3LYP/6-31+G (d, p) [19] [20] [21] . The quantities such as the variation of entropy, the variation of enthalpy and the variation of the free enthalpy of formation of the new derivatives of antimalarial activity were determined by means of the following formulas proposed by Otchersky et al. [22] .

Δ H f 0 ( M , 0 K ) = ∑ a t o m s x Δ H f 0 ( X , 0 K ) − ∑ ​ D 0 (2)

Δ H f 0 ( M , 298 K ) = Δ H f 0 ( M , 0 K ) + ( H M 0 ( 298 K ) − H M 0 ( 0 K ) ) − ∑ a t o m s x ( H X 0 ( 298 K ) − H X 0 ( 0 K ) ) (3)

Avec:

∑ ​ D 0 = ∑ ​ x ε 0 − ε 0 ( M ) − ε Z P E (4)

∑ ​ D 0 : Atomization energy;

ε 0 ( M ) : Total energy of the molecule;

ε Z P E : Energy of the zero point of the molecule;

H X 0 ( 298 K ) − H X 0 ( 0 K ) : Enthalpy corrections of atomic elements. These values are included in Janaf’s table [23] ;

H M 0 ( 298 K ) − H M 0 ( 0 K ) = H c o r r − ε Z P E ( M ) : Molecule enthalpy correction;

H c o r r : Thermal correction enthalpy.

Δ S f 0 ( M , 298 K ) = S M − ∑ a t o m s x Δ S ( 298 K ) (5)

x : Number of Atoms of X in the Molecule

Δ G f 0 ( M , 298 K ) = Δ H f 0 ( M , 298 K ) − T Δ S f 0 ( M , 298 K ) (6)

Lipinski defined a set of rules for estimating the oral bioavailability of a compound from its two-dimensional (2D) structure. These rules concerning physico-chemical activities were defined after the analysis of 2245 drugs on the market or in the final phase of development [24] .

➢ The molecular molar mass which must be less than 500 g/mol;

➢ The number of hydrogen bond acceptor atoms which must be less than or equal to 10;

➢ The number of hydrogen bond donor atoms which must be less than or equal to 5;

➢ The M LogP coefficient which must be less than or equal to 5.

Compounds whose physico-chemical activities do not satisfy at least 2 of the rules are highly likely to present absorption problems. These criteria correlate the physico-chemical activities with oral administration and a molecule for which two of the criteria are outside these limits is less likely to be absorbed orally [24] . New compounds with better pIC₅₀ values than existing ones can be developed with the aim of improving research on antidiabetic drugs.

Figure 2 below represents the domain of applicability, the area in which the model can predict.

The values of the levers of the molecules are lower than the value of the threshold lever h*(h* = 0.882). Also, all molecules are inside the domain of applicability of the model.

Note that the alphabetical letters in the diagram are the molecule codes used to establish the mathematical model.

o AIH (Human Intestinal Absorption) refers to the ability of the human intestine to absorb the drug. The greater the human intestinal absorption percentage, the better the human intestine absorbs the drug (0% - 20%) poor absorption; 20% - 70% medium absorption, 70% - 100% strong absorption.

o Caco-2 (nm/s) and MDCK (nm/s) predicts the intestinal permeability of a compound on Caco-2 cells (<4 poor permeability, between 4 - 70 average permeability, >70 high permeability) and MDCK.

o BBB (Blood Brain Barrier), this descriptor indicates the penetration of a compound to cross the blood-brain barrier which controls the passage of most compounds from the blood to the Central Nervous System (CNS).

o PBB (Plasma Protein Binding) predicts the degree of drug binding to proteins in the blood (<90 low binding, >90 high binding).

o Cytochromes P450 are key enzymes involved in the metabolism of different endogenous or exogenous molecules. They exist in several iso-forms (CYP1A2, CYP2C19, CYP2C9, CYP2D6, CYP3A4) but the most important are the last two. The prediction of the interaction of our best inhibitors with these iso-forms was also. essential since the inhibition of these iso-enzymes is certainly one of the main causes of drug interactions resulting in toxic or adverse effects [25] .

o hERG (human Ether-to-go-go-Related Gene) hERG (human Ether-à-go-go-Related Gene) is a gene encoding a voltage-gated potassium channel that moves potassium out of the cell. The blockage of this channel leads to fibrillations in cardiology which can lead to cardiac arrest.

o AMES-Test (Salmonella typhimurium reverse Mutation Assay) AMES-Test (Salmonella typhimurium reverse Mutation Assay) is a simple method to test the mutagenicity of a compound. It uses several strains of the bacterium Salmonella typhimurium carrying mutations in genes involved in the synthesis of histidine, so that they require histidine for their growth. This test consists in evaluating the ability of a compound to cause a mutation allowing a return to growth on a medium without histidine.

These different parameters were determined from the PreADMET online server [26] (https://preadmet.bmdrc.kr/).

The modification made to the molecular structures of the compounds in Table 1 according to the form and nature of the substituents enabled us to propose new molecules. The different structures obtained codified (TH) are presented in Table 2.

The calculation of the frequencies of these different molecules at the level of the B3LYP 6-31+G (d, p) theory after geometric optimization, provides information

on the value of the bond angle (α(S-C-N)), the length of the bond L(C=N), the standard entropy of formation ( Δ S f 0 298K), and the dipole moment µ(D). Obtaining these values allowed us to predict the antidiabetic activity (pIC₅₀) of these different molecules from the QSAR model obtained. Table 3 presents the different values of the descriptors and the predicted pIC₅₀ of these compounds.

The study of Table 3 indicates fourteen (14) new molecules obtained. With pIC₅₀ values between 2.532 and 2.751, the new molecules present pIC₅₀ higher than the pIC₅₀ of the base compound ranging from 2.320 to 2.526. This

highlights that all new thiadiazole derivatives may be more active than the compounds in the experimental database.

Figure 3 below gives us an idea of the appearance of the different levers of the 14 new compounds.

However, the lever of the TH8 molecule (h_ii = 0.944) is greater than the threshold lever of the model (h* = 0.882). The prediction of the antidiabetic activity of this compound from the model is therefore doubtful.

The standard thermodynamic quantities of formation, such as the enthalpy of formation Δ H f 0 (kcal/mol), the entropy of formation Δ S f 0 (kcal/mol) and the free enthalpy of formation Δ G f 0 (kcal/mol) have were determined from the formula of Otchersky et al. in order to demonstrate the possibility of formation of new, more active 1,3,4-thiadiazole derivatives. It should be known that a variation of the enthalpy translates the thermicity of a chemical reaction, when that of the entropy provides information on the level of disorder in the system. On the other hand, a change in free enthalpy reflects the spontaneity with which the reaction occurs. The values of these calculated quantities are given in Table 4.

The results show that all the values of the standard thermodynamic quantities of molecule formation are negative. The negative values of the enthalpy and the free enthalpy translate respectively an exothermic reaction and a spontaneous reaction under the conditions of the study. With regard to entropy, a negative value reflects a decrease in disorder. Thus, the formation of all compounds occurs spontaneously with a release of heat and a decrease in disorder. At this

level, we note that the quantities determined at the B3LYP/6-31+G (d, p) theory level confirm the formation of all these new compounds at the temperature of 298.15 K and 1 atm.

The determination of the Lipinski parameters, the values of which are recorded in Table 5, enabled us to verify the oral bioavailability of the molecules.

The quantities characterizing the determined Lipinski rule are the molar mass (M), the number of hydrogen donors (HBD), the number of hydrogen acceptors (HBA) and the lipophilicity (MlogP) were determined.

Analysis of the data in the table shows that the values of the molar mass of the compounds are less than 500 g/mol except for compound TH1 (510.50 g/mol) Also, the values of the number of hydrogen bond donor atoms (HBD) are all less than 5. As for the numbers of hydrogen bond acceptor atoms (HBA), they are all less than 10. At the level of (M Logp), all the values of our studied series are less than or equal to 4.15 (≤4.15). This parameter gives good intestinal absorption due to a good balance between solubility and permeability by passive diffusion according to this characteristic. Therefore, these compounds can be orally administrable drugs.

The prediction of the absorption, distribution, metabolism, excretion and toxicity of the new molecules was carried out from the online server PreADMET. We determined parameters such as, Human Intestinal Absorption (HIA), in vitro cell permeability caco-2, in vitro cell permeability MDCK (Mandin Darby Canine Kidney), plasma protein binding (PPB), penetration blood-brain barrier (BBB), inhibition of cytochrome P450 enzyme (CYP2D6, CYP2C9, CYP2C19, CYP2A4), inhibition of hERG (human Ether-à-go-go-Related Gene), carcinogenicity and mutagenicity. These different parameters are listed in Table 6.

HIA (%) is the percentage of human intestinal absorption (from 0% - 20% poor absorption; from 20% - 70% medium absorption, from 70% - 100% strong absorption). Caco-2 (nm/s) and MDCK (nm/s) predict the intestinal permeability of a compound on Caco-2 (<4 poor permeability, between 4 - 70 medium permeability, >70 high permeability) and MDCK cells. PPB (Plasma Protein Binding%) predicts the degree of drug binding to proteins in the blood (<90 low binding, >90 high binding). BBB (Blood–Brain Barrier %) predicts the penetration of the blood-brain barrier (<0.1 low absorption in the Central Nervous System (CNS), 0.1 - 2 medium absorption in the CNS and >2 high absorption in the CNS). Cytochromes of P450 (CYP2D6, CYP2C19, CYP2C9 and CYP2A4) are important in the oxidative metabolism of compounds. hERG (human Ether-à-go-go-Related Gene) is an ion (potassium) channel moving potassium out of its cell. AMES-Test (Salmonella typhimurium reverse Mutation Assay) predicts the mutagenic potential of a molecule.

Examination of the table shows us that at the level of absorption for values of human intestinal absorption (HIA) greater than 70%, suggests that these compounds are efficiently absorbed in the human intestine. Regarding the permeability on the Caco-2 cell, the values of the compounds (TH1, TH2, TH9, TH10, TH11) are less than 4 nm/s, therefore poor permeability and the other compounds have values between 4 and 27.4619 nm/s. These latter compounds have an average permeability as regards the permeability on the MDCK cell, the values are between 0.048 and 57.2175 nm/s, this shows that the new compounds are permeable on the Caco-2 and MDCK cells. Concerning the binding of plasma proteins (PPB), the values are greater than 90% for the compounds TH10 (93.969%), TH8 (97.752%), TH1 (100.000) and TH13 (92.374) hence a strong binding on plasma proteins. It is clear that the other compounds have poor BBB permeability, i.e. low absorption at the blood-brain barrier (CNS), except compound TH7, which has average BBB permeability.

Concerning the metabolism of xenobiotics, not all the compounds are inhibitors of the CYP2C19 and CYP2C9 enzymes except compound TH1 which inhibits the CYP2C9 enzyme. Not all the compounds are inhibitors and substrates of the CYP2D6 enzyme and only compound TH12 is an inhibitor and substrate of the CYP3A4 enzymes. We can say that all molecules can easily be metabolized by CYP2D6 and CYP3A4 enzymes.

For the toxicity test, the compounds present a low and medium risk for Herg inhibition except for the TH1 molecule which presents an ambiguity for Herg inhibition. Compounds TH3, TH4, TH5, TH8, TH13, TH14 are non-carcinogenic in mice and rats, and mutagenic according to the AMES test. As a result, the proposed new molecules can therefore be like drugs because they have good properties of absorption, distribution, metabolism and toxicity.