## 3 Results and Discussion
The minima and maxima  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**No 1**} & **Sequence** & **ID 2** & **IC\({}_{50}\)** & **Log IC\({}_{50}\)** & **Predicted** \\ \hline  
of the functions have a long history in terms of their practical applications in life to solve the problems of the so-called \"optimizations\" [39]. According to the plot, the minimum of the function was reached by peptides IPI and LPL (number 6 and 8, respectively). It can be concluded that the minimal structural requirements for a tripeptide to act as a DPP IV inhibitor is for it to be composed of hydrophobic amino acids (Leu, Ile) and the ones with rings (Pro). According to [PERSON] et al. [40], the presence of hydrophobic residues may enhance the interactions between the ligand (peptide) and the enzyme (DPP IV). Moreover, the S1 subsite of DPP IV was composed of hydrophobic pockets, which are important in enzyme inhibition by peptides [40]. [PERSON] et al. [6] reported that DPP IV possessed two pockets, namely, S1, consisting of Tyr631, Val656, Trp659, Tyr662, Tyr666, and Val711; and S2, which was charged due to the presence of Arg125, Glu205, Glu206, Phe357, Ser209, and Arg358. According to other scientific data, three pockets can be distinguished in DPP IV: S1 (Tyr547, Ser630, Tyr631, Val656, Trp659, Tyr662, Asn710, Val711, His740), S2 (Glu205, Glu206, and Tyr662), and S3 (Ser 209, Arg358, Phe357) [6]. The tripeptides from the studied dataset that reached the maximum on the plot were WRD, WRI, WRL, and WRN (numbers 15, 20, 22, and 24 in the plot, respectively). The impact of Trp and/or aliphatic amino acids, like, e.g., Ala or Ile, has already been discussed (see above). In the case of hydrophilic residues, like Arg (R) and/or Asn (N), their role in DPP IV inhibition remains unknown [21], but, as it could be seen above, Arg is a residue forming the charged pocket of DPP IV [6]. The molecular weight of the tripeptides that reached the minimum of the function (see Figure 6b) was ca. 345 Da, whereas the MW of the tripeptides reaching the maximum of the function ranged from ca. 473 to 476 Da. According to [PERSON] et al. [6], the molecular weight of the peptides is one of the factors affecting, e.g., the bioavailability of peptides, mode of action, and/or bioactivity. [PERSON] et al. [6] analyzed the molecular weight of 222 peptides  
Figure 6: Relationships between molecular weight and predicted tripeptide DPP IV-inhibitory activity (model based on MW). (**a,b**) equation and plot, being non-linear functions of the DPP IV-inhibiting activity and adequate plot, respectively. with different chain lengths for their IC\({}_{50}\) values (uM). It was found that peptide DPP IV inhibitors with MW lesser than 500 Da had IC\({}_{50}\) lower than 1000 uM (logIC\({}_{50}\) = 3). These findings are in line with the results obtained in the present study, indicating that predicted logarithmic values of IC\({}_{50}\) of tripeptides located in the minimum and maximum of the plot (Figure 6b) ranged from 1.45 (IPI; minimum of the function) to 2.82 (WRI; maximum of the function). Among the results presented in Figure 6, four peptides with the lowest molecular weight (MW) had the following predicted log IC\({}_{50}\) values: 1.45 (IPI and LPL), 1.47 (VPL), and 2.41 (LQP). There are no significant differences in predicted log IC\({}_{50}\) (MW) between peptides with a molecular weight lower or higher than 500 Da. The molecular weight of 500 Da is the upper limit for compounds recommended as orally delivered drugs according to the Rule of Five [41]. This rule may also be applied to the bioactive components of food. Recommendation takes into account the fact that molecules with too high a molecular weight and containing too many groups able to form hydrogen bonds have lower bioavailability than the smaller ones. On the other hand, peptides too long to fulfill the Rule of Five are considered to be compounds with relatively high bioavailability [42, 43].