**1. Introduction**

Cancer is a complicated illness that is featured by uncontrolled cell proliferation and the development of tumors that may remarkably extend to the entire organ or other organs systemically [1]. It represents one of the most global deadly diseases, particularly in western countries. It was estimated that in 2020, ~ 9.9 million people have died due to cancer [2]. Its current treatment strategies include γ-radiation, chemotherapy, suicide gene therapy, or immunotherapy, which are fundamentally mediated by promoting apoptosis [3]. Chemotherapy is the most efficacious method for metastatic tumors treatment. However, the cancer cell's multidrug resistance, high cost, and untoward effects of these drugs represent the main holdbacks to the success of chemotherapeutic treatment [4]. Therefore, searching for sources of safe and effective treatment has become a crucial research area.

Casein kinase 2 (CK2) is one of the first discovered Ser/Thr kinases [5–7] that is involved in many cell processes from gene expression and protein synthesis to cell growth, proliferation, and differentiation [8]. The well-studied tetrameric form of this kinase is

**Citation:** Ibrahim, S.R.M.; Bagalagel, A.A.; Diri, R.M.; Noor, A.O.; Bakhsh, H.T.; Muhammad, Y.A.; Mohamed, G.A.; Omar, A.M. Exploring the Activity of Fungal Phenalenone Derivatives as Potential CK2 Inhibitors Using Computational Methods. *J. Fungi* **2022**, *8*, 443. https://doi.org/10.3390/jof8050443

Academic Editors: Tao Feng and Frank Surup

Received: 18 March 2022 Accepted: 21 April 2022 Published: 24 April 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

composed of two catalytic alpha proteins, CK2α and/or CK2α', that differ only in their C-termini [9–11], and two regulatory CK2β proteins that are responsible for substrate specificity [11–13]. It has minimal substrate specificity; therefore, it is able to phosphorylate a large number of proteins involved in multiple signal transduction pathways [14]. This enzyme is ubiquitously expressed [7] and constitutively active in cells; hence, its activity is not relied on extracellular stimuli [5,15,16]. Many reports have found that the overexpression of CK2 in many cancer types leads to inhibiting apoptosis and promoting cancer cell survival [5,8]. It is clear that its downregulation revered cancer progression and enhanced apoptosis [17], suggesting that CK2 can be considered a valuable target for anticancer agents [8,18].

Natural metabolites and their derivatives have long been established as a wealthy source for the discovery of novel anticancer drugs [19]. It was reported that ~5% of the anticancer drugs approved by the FDA are unmodified natural metabolites, and ~50% of the approved drugs are either chemically-modified natural metabolites or synthesized relied on natural metabolites structures [20].

It is noteworthy that different metabolites belonging to various classes, such as flavonoids, coumarins, anthraquinones, pyrazolotriazines, polyhalogenated benzimidazoles, and benzotriazoles, have been known as CK2 inhibitors [21]. Additionally, CIGB-300 and CX-4945 are CK2 inhibitors that are already in human trials as anticancer drugs. CX-4945 (Silmitasertib) has been designated by the FDA for treating cholangiocarcinoma, and many clinical investigations are ongoing with it versus different types of cancers [22]. Furthermore, CIGB-300 is under investigation for cervical cancers [23].

Fungi are eukaryotic micro-organisms that inhabit nearly all kinds of environments in nature, where they play a fundamental role in maintaining eco-balance [24–28]. Fungi have drawn immense research attention since their cultivation, isolation, characterization, and purification demonstrated the existence of a vast number of metabolites with unique and diversified chemical classes and bioactivities [29–34]. Many reports revealed the characterization of diverse classes of fungal metabolites with CK2 inhibitory potential [35–37].

Phenalenones are a unique class of secondary metabolites, having a fused three-ring system [38]. They are produced by higher plants and fungi [39]. They are known as phytoalexins, which are biosynthesized by the plant in response to an external threat, such as mechanical injury or pathogenic infections [40]. Fungal phenalenones have immense structural diversity, such as hetero- and homo-dimerization and high degrees of nitrogenation and oxygenation, as well as being complexed with metals, incorporating with additional carbon frameworks, or isoprene unit by the formation of either a linear ether (e.g., **8** and **12**) or a trimethyl-hydrofuran (e.g., **3**–**7**, **9**–**11**, **13**, and **14**) moiety. It has been reported to possess various bioactivities, including antimicrobial, anti-plasmodial, anticancer, antidiabetic, antioxidant, and cytotoxic effects [40]. These metabolites exhibit cytotoxic capacities towards various cancer cell lines; however, there are limited or lacking studies that explore the mechanism of their anticancer properties. It is noteworthy that there is no available report on their CK2 inhibitory potential. The molecular docking-based virtual screening process, along with increasing the data about the structure of CK2 alone or in complex with various inhibitors, could become of particular relevance in the discovery of new lead compounds as CK2 inhibitors [41,42]. In continuation of our interest in exploring the bioactivities of fungal metabolites, the present work focuses on the in silico assessment of CK2 inhibitory capacity of 33 phenalenone derivatives reported from various fungal sources (Table 1, Figures 1 and 2).

**Figure 1.** Structures of phenalenone derivatives **1**–**20**. **Figure 1.** Structures of phenalenone derivatives **1**–**20**.

**Figure 2. Figure 2.** Structures of phenalenone derivatives Structures of phenalenone derivatives **2121**––**3333**.

.

Computer-aided drug design/discovery (CADD) are useful tools for screening and identifying drug-like molecules in silico and thereby reducing the number of compounds to be tested experimentally. Several software and programs are used to filter and generate a group of compounds based on specified criteria, predict their physicochemical properties, predict suitable targets, and evaluate the binding affinity of the compounds to the predicted targets. One of the drug design and discovery approaches is structure-based drug design (SBDD). This approach relies on the knowledge of the 3D structure of the targets of interest, and it includes two common methods: molecular docking and molecular dynamic simulation. Molecular docking evaluates how tight the compound binds the target, as determined by the predicted binding affinity, while molecular dynamic (MD) simulations assess the behavior of the ligand-protein complex in terms of binding interactions and 3D conformation in aqueous conditions to mimic the physiological environment [43]. Several CADD methods and tools are used for investigating the phenalenone derivatives.

**Table 1.** List of phenalenone derivatives and their fungal source.

#### **2. Results and Discussion**

### *2.1. AI (Artificial Intelligence)-Based Target Prediction for Phenalenone Derivatives*

Choosing the appropriate target to investigate the inhibitory potential of these phenalenone derivatives relied on performing ligand-based-in silico target prediction [38]. The prediction webserver, SuperPred was the tool of choice to perform ATC (anatomicaltherapeutic chemical) code and predict the potential targets for the investigated phenalenones [57]. After analyzing the results of the predicted target proteins (for example, Cathepsin D, mineralocorticoid receptor, and thyroid hormone receptor-α), the kinase CK2α was selected for the study due to having a high percent of probability and model accuracy (Table 2). After selecting the target and proper crystal structure, the listed phenalenones were docked in the protein crystal structure, after which the docking method was validated by redocking the co-crystallized ligand. Prediction of ADMET properties of the listed metabolites in silico and MD (molecular-dynamic) simulation for the two metabolites with the highest docking scores were followed.

**Table 2.** Prediction of target probability and model accuracy for phenalenone derivatives against CK2 using SuperPred target prediction webserver.

\* The probability of the test compound binding to a specific target, as determined by the respective target machine learning model. \*\* The accuracy of the performance of the prediction model displaying the 10-fold cross-validation score of the respective logistic regression model, as the model performance varied between different targets.

#### *2.2. Ligands and Protein Preparation and Molecular Docking*

Target identification filtered out > 100 phenalenone derivatives. These derivatives were prepared for docking, where their energy-minimized 3D structures were generated, and all possible ionization and tautomeric states were created.

For docking, the human CK2α1 crystal structure (PDB ID: 7BU4) was chosen for the study due to the structural similarity of the co-crystallized ligand (**Y49**) to the selected phenalenones. The **Y49** (4-(6-aminocarbonyl-8-oxidanylidene-9-phenyl-7*H*-purin-2 yl)benzoic acid) is made of three aromatic rings: a purine ring with two phenyl moieties attached to it, and polar groups present at the rings, with polar groups at different positions. The selected phenalenones have a nucleus made of three-fused rings substituted with multiple OH and carbonyl groups. Based on their structures, both the phenalenones and **Y49** were expected to have a similar 3D conformation in the binding pocket. The PDB file of the 7BU4 crystal structure was downloaded from the protein data bank (PDB) [58], which was then prepared and minimized using Schrodinger's Protein Preparation wizard [59–61].

The docking process started by generating a grid box around the binding site of the co-crystallized ligand to locate the pocket where the docking of the compounds occurs. A receptor-Grid-Generation tool in Maestro [62] was utilized for that purpose.

Re-docking of the co-crystallized ligand, 4-(6-aminocarbonyl-8-oxidanylidene-9-phenyl-7*H*-purin-2-yl)benzoic acid (PDB: **Y49**), was performed to evaluate the docking method. The re-docked reference had an identical pose (Figure 3C) and binding interactions to the co-crystallized structure (Figure 3A,B). For both, the backbone of Val116 is H-bonded with the oxygen of the amide moiety, and the purinone nitrogen interacts through the water bridge with Val116, Asn118, as well as with the amide oxygen. On the opposite side of the molecule, the carboxylate makes an ionic interaction with the side chain of the adjacent Lys68 (Figure 3A,B). The RMSD (root-mean-square deviation) of the re-docked ligand was minimal, with a value of 0.0744 Å, indicating the docking method is valid (Figure 3C). The molecular surface display in Figure 3D shows the re-docked reference **Y49** occupying the binding pocket of the crystal structure.

After docking validation, docking the 3D structures of the > 100 phenalenones that proceeded from the target prediction using the extra-precision (XP) mode was followed. The docking produced derivatives that are ranked based on their score and approximated the free energy of binding; the more negative the value, the stronger the binding. Different docking scores were generated, including the gscore (best for ranking different compounds), emodel (best for ranking conformers), and XP gscore. Glide uses emodel scoring to select the best poses of the docked compounds; then, it ranks the best poses based on the given gscores. XP gscore ranks the poses generated by the Glide XP mode. In general, Glide uses gscore to sort and rank the docked compounds. The 33 derivatives listed in Table 3 are the ones with gscores close to or better than the gscore of the reference **Y49** (−9.049 kcal/mol), with the top two compounds, **19** and **31**, scoring −12.878 and −12.521 kcal/mol, respectively.

Compound **19**, in addition to interacting directly with Val116 and Lys68 in the protein's binding pocket like the reference ligand, had a long chain that extended along the surface of the protein allowing the terminal (R,6*E*,10*E*,14*E*)-2,6,10,14-tetramethylhexadeca-6,10,14 triene-2,3-diol group to bind a distant binding pocket (Figure 4). Besides, compound **31** seems to have similar interactions with the protein; however, the tetrahydropyran at the end of the aliphatic chain did not occupy the distant pocket like **19** and remained exposed to the solvent (Figure 5). Figure 6 showed compounds **19** and **31** simultaneously superimposed on the reference **Y49** inside the binding pocket in the molecular surface display.

**Figure 3.** Re-docking of the co-crystallized ligand to validate the docking method. The figure showed the 2D view of the binding interactions of the reference ligand **Y49** complexed with CK2α1; (**A**) after minimization of the crystal structure 7BU4, and (**B**) after re-docking of ligand **Y49** into the CK2α1 crystal structure. (**C**) 3D structure of the re-docked **Y49** (pink) superimposed on the co-crystallized Y49 (green). (**D**) Molecular surface display with electrostatic potential color scheme for CK2α1 complexed with ligand **Y49** after re-docking. After docking validation, docking the 3D structures of the > 100 phenalenones that **Figure 3.** Re-docking of the co-crystallized ligand to validate the docking method. The figure showed the 2D view of the binding interactions of the reference ligand **Y49** complexed with CK2α1; (**A**) after minimization of the crystal structure 7BU4, and (**B**) after re-docking of ligand **Y49** into the CK2α1 crystal structure. (**C**) 3D structure of the re-docked **Y49** (pink) superimposed on the co-crystallized Y49 (green). (**D**) Molecular surface display with electrostatic potential color scheme for CK2α1 complexed with ligand **Y49** after re-docking.

> proceeded from the target prediction using the extra-precision (XP) mode was followed. The docking produced derivatives that are ranked based on their score and approximated the free energy of binding; the more negative the value, the stronger the binding. Different docking scores were generated, including the gscore (best for ranking different compounds), emodel (best for ranking conformers), and XP gscore. Glide uses emodel scoring to select the best poses of the docked compounds; then, it ranks the best poses based on the given gscores. XP gscore ranks the poses generated by the Glide XP mode. In general, Glide uses gscore to sort and rank the docked compounds. The 33 derivatives listed in Table 3 are the ones with gscores close to or better than the gscore of the reference **Y49** (−9.049 kcal/mol), with the top two compounds, **19** and **31**, scoring −12.878 and −12.521

kcal/mol, respectively.

**Table 3.** In silico docking results of phenalenone derivatives with CK2α1 (PDB: 7BU4).

**Figure 4.** CK2α1 in complex with **19**. (**A**) Molecular surface display with electrostatic potential color scheme for CK2α1- **19** complex and the close-up view presented. (**B**) 3D presumed binding mode of **19** in the binding site of CK2 (PDB:7BU4). Compound **19** is displayed as green ball-and-sticks. The amino acids in the binding site are shown as grey sticks, and hydrogen bonds are represented in yellow dotted lines. (**C**) 2D depiction of the ligand-protein interactions. **Figure 4.** CK2α1 in complex with **19**. (**A**) Molecular surface display with electrostatic potential color scheme for CK2α1-**19** complex and the close-up view presented. (**B**) 3D presumed binding mode of **19** in the binding site of CK2 (PDB:7BU4). Compound **19** is displayed as green ball-and-sticks. The amino acids in the binding site are shown as grey sticks, and hydrogen bonds are represented in yellow dotted lines. (**C**) 2D depiction of the ligand-protein interactions.

**Figure 5.** CK2α1 in complex with **31**. (**A**) Molecular surface display with electrostatic potential color scheme for CK2α1- **31** complex and the close-up view presented. (**B**) 3D presumed binding mode of **31** in the binding site of CK2 (PDB:7BU4). Compound **31** is displayed as green ball-and-sticks. The amino acids in the binding site are shown as grey sticks, and hydrogen bonds are represented in yellow dotted lines. (**C**) 2D depiction of the ligand-protein interactions. **Figure 5.** CK2α1 in complex with **31**. (**A**) Molecular surface display with electrostatic potential color scheme for CK2α1-**31** complex and the close-up view presented. (**B**) 3D presumed binding mode of **31** in the binding site of CK2 (PDB:7BU4). Compound **31** is displayed as green ball-and-sticks. The amino acids in the binding site are shown as grey sticks, and hydrogen bonds are represented in yellow dotted lines. (**C**) 2D depiction of the ligand-protein interactions.

**Figure 6.** Molecular display with electrostatic potential color scheme for CK2α1 (PDB: 7B4U) showing **19** (orange) and **31** (cyan) superimposed on **Y49** (green) inside the binding pocket. **Figure 6.** Molecular display with electrostatic potential color scheme for CK2α1 (PDB: 7B4U) showing **19** (orange) and **31** (cyan) superimposed on **Y49** (green) inside the binding pocket.

#### *2.3. In Silico ADMET Properties of Selected Ligands 2.3. In Silico ADMET Properties of Selected Ligands*

ble 4.

The drug-likeness and ADMET properties of the processed compounds were predicted using Maestro's QikProp Schrodinger module in terms of absorption, distribution, metabolism, excretion, and toxicity, among others [63]. The module can quickly and reliably predict many physicochemical properties and other descriptors, such as the number of possible metabolites and number of reactive functional groups, in order to detect and filter compounds that can be problematic during the late stages of drug discovery and development. Therefore, it can eliminate unnecessary tests and experiments that will ultimately fail in clinical trials [64]. The ADMET prediction evaluates the usefulness of the examined compounds by describing and determining their drug-likeness, physicochemical properties, and expected toxicity profiles. Several descriptors were predicted for these derivatives, and most of the predicted values of ADMET descriptors fell within the recommended range. The predicted ADMET properties and descriptors are presented in Ta-The drug-likeness and ADMET properties of the processed compounds were predicted using Maestro's QikProp Schrodinger module in terms of absorption, distribution, metabolism, excretion, and toxicity, among others [63]. The module can quickly and reliably predict many physicochemical properties and other descriptors, such as the number of possible metabolites and number of reactive functional groups, in order to detect and filter compounds that can be problematic during the late stages of drug discovery and development. Therefore, it can eliminate unnecessary tests and experiments that will ultimately fail in clinical trials [64]. The ADMET prediction evaluates the usefulness of the examined compounds by describing and determining their drug-likeness, physicochemical properties, and expected toxicity profiles. Several descriptors were predicted for these derivatives, and most of the predicted values of ADMET descriptors fell within the recommended range. The predicted ADMET properties and descriptors are presented in Table 4.

**Table 4.** Predicted in silico ADMET properties of the phenalenone derivatives.

**Table 4.** *Cont.*

and vice versa; Dipole: computed dipole moment; SASA: Total solvent accessible surface area; DonorHB: estimated number H+ to be donated in HB; AcceptHB: estimated number H+ to be accepted in HB; QLogPo/w: predicted octanol/water partition coefficient; QPlogS: Predicted aqueous solubility; QPlogKhsa: Prediction of binding to human serum albumin; #Metab: number of possible metabolic reactions; QPlogBB: Predicted brain/blood partition coefficient; % Human Oral Absorption: Predicted human oral absorption on 0 to 100% scale; QPlogHERG: Predicted IC50 value for blockage of HERG K+ channels; CNS: Predicted central nervous system activity; #RtvFG: Number of reactive functional groups.

#### *2.4. Molecular Dynamic (MD) Simulation*

The MD simulations are performed using Desmond software [65,66] to simulate the aqueous physiological environment and assess the changes in protein conformation and binding affinity during the simulation time compared to the original affinity and confirmation of the crystal structure [67]. Only the two top-scoring compounds from the docking study, i.e., compounds **19** and **31** along with reference **Y49**, were analyzed by MD. The root mean square deviation (RMSD) is a calculated value that compares the poses of investigated compounds to that of the co-crystalized ligand [43]. RMSD plots of the selected compounds complexed with the CK2α1 measure the average change in the positions of the atoms of the protein and ligand inside the binding pocket at the end of the simulation period (100 ns) compared to their starting positions before the simulation at 0 ns. The RMSD plot of **Y49** showed that both the protein and the reference **Y49** were stable, and the observed fluctuations were insignificant since they were within the acceptable range of 1–3 Å (Figure 7A). For compound **19**, the RMSD of the protein and **19** laid over each other, indicating increased binding affinity of **19** to the protein and stability of the CK2α1-**19** complex. Additionally, the fluctuation seen for both over the 100 ns was within the range as well (Figure 8A). A similar RMSD pattern was observed for **31** and CK2α1 complex, despite the sudden, non-significant fluctuation of **31** at around 90 ns, which is potentially a result of the compound adjusting its pose in the pocket (Figure 9A). When calculating the RMSD for the compounds, it is not uncommon to observe fluctuation in the plot for some time at the beginning of the simulation, as observed in Figure 7A, Figure 8A, and Figure 9A within the first 20 ns of the run. This expected fluctuation happens as the compound keeps adjusting its conformation inside the pocket to assume a pose that has the least free energy.

The secondary structure of the CK2α1 protein (PDB ID: 7BU4) was also evaluated throughout the simulation while it was complexed with each ligand. Figure 7B represented the protein evaluation while it was complexed with ligand **Y49**. The top plot showed the distribution of the SSE (α-helices and β-sheets) with the protein represented by the residue index. The middle plot summarized the SSE composition for each trajectory frame throughout the simulation, while the bottom plot monitored each residue and its SSE assignment over the simulation time. Both plots indicated that the overall %SSE of the protein was maintained, and each SSE was stable over the course of the simulation. Comparable results were obtained when **19** (Figure 8B) and **31** (Figure 9B) were complexed with the protein.

The MD study also evaluated the binding interactions of a protein-ligand complex. For ligand **Y49**, the interactions between the **Y49** and protein are presented in Figure 10A; the interaction types are color-coded. The stacked bar chart is normalized over the course of the trajectory: for example, a value of 0.8 suggested that the specific interaction was maintained during 80% of the simulation time. Values over 1.0 are possible and indicate that some protein residue may make multiple interactions of the same subtype with the ligand. As indicated in Figure 10A, Val116 made direct H-bonding as well as through water bridges with **Y49** and had a normalized value of ~1.9. The value >1 represented the combined value of >1 type of interaction, and it indicated that these interactions were maintained for ~190% of the simulation time. The other key interactions were with Glu114, Asn118, Lys68, and Asp175, having values of ~0.9, ~0.7, ~1.1, and ~1.5, respectively. Figure 10B showed only the interactions between **Y49** and the protein that occurred ≥ 30% of the simulation time. Figure 10C displayed the total specific interactions between ligand **Y49** and the protein (top plot), whilst the bottom panel demonstrated the protein residues that interacted with the ligand at each time point. As mentioned earlier, Val116 made > 1 interaction with the ligand, which was represented by the dark orange color in the plot throughout the trajectory. Other residues: Lys86, Glu114, and Asp175, also made specific interactions with the ligand.

*2.4. Molecular Dynamic (MD) Simulation*

energy.

The MD simulations are performed using Desmond software [65,66] to simulate the aqueous physiological environment and assess the changes in protein conformation and binding affinity during the simulation time compared to the original affinity and confirmation of the crystal structure [67]. Only the two top-scoring compounds from the docking study, i.e., compounds **19** and **31** along with reference **Y49**, were analyzed by MD. The root mean square deviation (RMSD) is a calculated value that compares the poses of investigated compounds to that of the co-crystalized ligand [43]. RMSD plots of the selected compounds complexed with the CK2α1 measure the average change in the positions of the atoms of the protein and ligand inside the binding pocket at the end of the simulation period (100 ns) compared to their starting positions before the simulation at 0 ns. The RMSD plot of **Y49** showed that both the protein and the reference **Y49** were stable, and the observed fluctuations were insignificant since they were within the acceptable range of 1–3 Å (Figure 7A). For compound **19**, the RMSD of the protein and **19** laid over each other, indicating increased binding affinity of **19** to the protein and stability of the CK2α1- **19** complex. Additionally, the fluctuation seen for both over the 100 ns was within the range as well (Figure 8A). A similar RMSD pattern was observed for **31** and CK2α1 complex, despite the sudden, non-significant fluctuation of **31** at around 90 ns, which is potentially a result of the compound adjusting its pose in the pocket (Figure 9A). When calculating the RMSD for the compounds, it is not uncommon to observe fluctuation in the plot for some time at the beginning of the simulation, as observed in Figures 7A, 8A, and 9A within the first 20 ns of the run. This expected fluctuation happens as the compound keeps adjusting its conformation inside the pocket to assume a pose that has the least free

**Figure 7.** (**A**) The RMSD plot was obtained for the reference **Y49** complexed with CK2α1 protein (PDB-ID:7BU4). The simulation time (100 ns) reaffirmed the stability of the complex with no significant changes in the protein structure. (**B**) Stability of the secondary structure of CK2α1 protein (PDB ID: 7BU4) was evaluated by monitoring its SSE distribution (top plot), SSE composition (middle plot), and SEE assignment (bottom plot) over the 100 ns of MD simulation when complexed with **Y49. Figure 7.** (**A**) The RMSD plot was obtained for the reference **Y49** complexed with CK2α1 protein (PDB-ID:7BU4). The simulation time (100 ns) reaffirmed the stability of the complex with no significant changes in the protein structure. (**B**) Stability of the secondary structure of CK2α1 protein (PDB ID: 7BU4) was evaluated by monitoring its SSE distribution (top plot), SSE composition (middle plot), and SEE assignment (bottom plot) over the 100 ns of MD simulation when complexed with **Y49**.

**Figure 8.** (**A**) The RMSD plot was obtained for compound **19** complexed with CK2α1 protein (PDB-ID:7BU4). The simulation time (100 ns) reaffirmed the stability of the complex with no significant changes in the protein structure. (**B**) Stability of the secondary structure of CK2α1 protein (PDB ID: 7BU4) was evaluated by monitoring its SSE distribution (top plot), SSE composition (middle plot), and SEE assignment (bottom plot) over the 100 ns of MD simulation when complexed with **19**. **Figure 8.** (**A**) The RMSD plot was obtained for compound **19** complexed with CK2α1 protein (PDB-ID:7BU4). The simulation time (100 ns) reaffirmed the stability of the complex with no significant changes in the protein structure. (**B**) Stability of the secondary structure of CK2α1 protein (PDB ID: 7BU4) was evaluated by monitoring its SSE distribution (top plot), SSE composition (middle plot), and SEE assignment (bottom plot) over the 100 ns of MD simulation when complexed with **19**.

**Figure 9.** (**A**) Obtained RMSD plot for compound **31** complexed with CK2α1 protein (PDB-ID:7BU4). The simulation time (100 ns) reaffirmed the stability of the complex with no significant changes in the protein structure. (**B**) Stability of the secondary structure of CK2α1 protein (PDB ID: 7BU4) was evaluated by monitoring its SSE distribution (top plot), SSE composition (middle plot), and SEE assignment (bottom plot) over the 100 ns of MD simulation when complexed with **31. Figure 9.** (**A**) Obtained RMSD plot for compound **31** complexed with CK2α1 protein (PDB-ID:7BU4). The simulation time (100 ns) reaffirmed the stability of the complex with no significant changes in the protein structure. (**B**) Stability of the secondary structure of CK2α1 protein (PDB ID: 7BU4) was evaluated by monitoring its SSE distribution (top plot), SSE composition (middle plot), and SEE assignment (bottom plot) over the 100 ns of MD simulation when complexed with **31**.

Figure 11 shows the amino acid residues of the protein binding pocket that interacted with compound **19**. The fused ring system of **19** made similar interactions with the pocket residues as **Y49**, where Val116 and Lys86 interacted through the H-bond with the ring system (Figure 11B). As previously seen in the molecular surface display (Figure 4A), the extended aliphatic chain occupied a distant pocket and created new interaction points between the two OH groups at the end of the chain and Asp120, where they occurred > 85% during the simulation (Figure 11B). This interaction was not present with **Y49** (Figure 3B,D). It might be safe to assume that the enhanced binding affinity and stability of the complex were due to this new interaction with Asp120, which can also be inferred from the RMSD plot (Figure 8A). *J. Fungi* **2022**, *8*, x FOR PEER REVIEW 19 of 30 The secondary structure of the CK2α1 protein (PDB ID: 7BU4) was also evaluated throughout the simulation while it was complexed with each ligand. Figure 7B represented the protein evaluation while it was complexed with ligand **Y49**. The top plot showed the distribution of the SSE (α-helices and β-sheets) with the protein represented

> Compound **31** also created new interacting points with amino acids in the main binding pocket: the chiral OH of the fused ring system made a strong H-bonding with His160 and Asn161 through bridging water molecules with a value of ~1.18 and 0.6, respectively. An enhanced interaction with Arg47 was observed as well (~0.98) (Figure 12B). The tetrahydropyran ring at the end of the aliphatic chain of **31** also extended along the protein surface but did not occupy the distant pocket, as did compound **19** (Figure 5A). The reason for that might be the fact that the chain in compound **31** is 6-carbon shorter than that of **19**, so the group could not reach the second pocket. Another explanation could be the large size of the substituted tetrahydropyran hindered the group from occupying the pocket. Additionally, there is a high probability that the fluctuation observed in the RMSD of **31** towards the end of the simulation time (Figure 9A) might be a result of the inability of this group to bind to the second pocket. The L-RMSF (ligand-root-mean-square fluctuation) represents how the atoms of the ligand interact with the protein and the changes in the positions of the ligand atoms. As seen in the L-RMSF plot for compound **31** (Figure 13), the positions of atoms 29–45 were dramatically changed because of the free rotation around the aliphatic chain, which in turn decreased the interaction between this part of the molecule with the protein and was reflected by > 3 Å fluctuation in the RMSF plot. The time-depended representation of the CK2α1-**31** interactions showed that residues Arg47, His160, and Asp175 were the ones making specific interactions with the ligand, as indicated by the darker color in the plot (Figure 12C). by the residue index. The middle plot summarized the SSE composition for each trajectory frame throughout the simulation, while the bottom plot monitored each residue and its SSE assignment over the simulation time. Both plots indicated that the overall %SSE of the protein was maintained, and each SSE was stable over the course of the simulation. Comparable results were obtained when **19** (Figure 8B) and **31** (Figure 9B) were complexed with the protein. The MD study also evaluated the binding interactions of a protein-ligand complex. For ligand **Y49**, the interactions between the **Y49** and protein are presented in Figure 10A; the interaction types are color-coded. The stacked bar chart is normalized over the course of the trajectory: for example, a value of 0.8 suggested that the specific interaction was maintained during 80% of the simulation time. Values over 1.0 are possible and indicate that some protein residue may make multiple interactions of the same subtype with the ligand. As indicated in Figure 10A, Val116 made direct H-bonding as well as through water bridges with **Y49** and had a normalized value of ~1.9. The value >1 represented the combined value of >1 type of interaction, and it indicated that these interactions were maintained for ~190% of the simulation time. The other key interactions were with Glu114, Asn118, Lys68, and Asp175, having values of ~0.9, ~0.7, ~1.1, and ~1.5, respectively. Figure 10B showed only the interactions between **Y49** and the protein that occurred ≥ 30% of the simulation time. Figure 10C displayed the total specific interactions between ligand **Y49** and the protein (top plot), whilst the bottom panel demonstrated the protein residues that interacted with the ligand at each time point. As mentioned earlier, Val116 made > 1 interaction with the ligand, which was represented by the dark orange color in the plot throughout the trajectory. Other residues: Lys86, Glu114, and Asp175, also made specific interactions with the ligand.

**Figure 10.** *Cont*.

**Figure 10.** (**A**) Stacked bar graph for CK2 interactions with reference **Y49** throughout the simulation. (**B**) Schematic diagram shows the detailed 2D atomic interactions of **Y49** with CK2 that occurred > **Figure 10.** (**A**) Stacked bar graph for CK2 interactions with reference **Y49** throughout the simulation. (**B**) Schematic diagram shows the detailed 2D atomic interactions of **Y49** with CK2 that occurred > 30% of the simulation time in the selected trajectory. (**C**) A timeline representation of CK2-**Y49** interactions presented in (**A**). The top panel presents the total number of specific interactions the protein made with the ligand over the course of the trajectory. The bottom panel presents the residues interacting with the ligand in each trajectory frame. The dark orange color indicates more than one specific interaction is made between some residues and the ligand.

It was also noticed that the reference ligand, **Y49,** as well as the compounds **19** and **31,** all interacted with Asn118 through H-bonding; however, the contact points are different. While the residue interacted with **Y49** at the purine carbonyl oxygen (Figure 10B), it acted as an H-bond donor to the OH at the end of the aliphatic chain of **19** as well as to the OH at the fused ring system of **19** and **31** (Figures 11B and 12B). The reason for the different contact points of Asn118 with the compounds was probably attributed to the 3D conformation of the compounds inside the binding pocket, which is affected by the nature of the substitutions on the nucleus. Each compound assumed a pose that had the lowest possible free energy when interacting with the pocket's residues. Therefore, that pose with the different substitutions from one compound to the other created the unique binding interactions with the pocket amino acids. Figure 11 shows the amino acid residues of the protein binding pocket that interacted with compound **19**. The fused ring system of **19** made similar interactions with the pocket residues as **Y49**, where Val116 and Lys86 interacted through the H-bond with the ring system (Figure 11B). As previously seen in the molecular surface display (Figure 4A), the extended aliphatic chain occupied a distant pocket and created new interaction points between the two OH groups at the end of the chain and Asp120, where they occurred > 85% during the simulation (Figure 11B). This interaction was not present with **Y49** (Figure 3B,D). It might be safe to assume that the enhanced binding affinity and stability of the complex were due to this new interaction with Asp120, which can also be inferred from the RMSD plot (Figure 8A).

30% of the simulation time in the selected trajectory. (**C**) A timeline representation of CK2-**Y49** interactions presented in (**A**). The top panel presents the total number of specific interactions the protein made with the ligand over the course of the trajectory. The bottom panel presents the residues interacting with the ligand in each trajectory frame. The dark orange color indicates more than one

*J. Fungi* **2022**, *8*, x FOR PEER REVIEW 21 of 30

specific interaction is made between some residues and the ligand.

**Figure 11.** *Cont*.

**Figure 11.** (**A**) CK2 interactions with compound **19** throughout the simulation. (**B**) Schematic diagram shows the detailed 2D atomic interactions of **19** with CK2 that occurred > 30% of the simulation time in the selected trajectory. (**C**) A timeline representation of CK2-**19** interactions presented in (**A**). The top panel presents the total number of specific interactions the protein made with the ligand over the course of the trajectory. The bottom panel presents residues interacting with the ligand in each trajectory frame. The dark orange color indicates that more than one specific interaction is made between some residues and the ligand. Compound **31** also created new interacting points with amino acids in the main bind-**Figure 11.** (**A**) CK2 interactions with compound **19** throughout the simulation. (**B**) Schematic diagram shows the detailed 2D atomic interactions of **19** with CK2 that occurred > 30% of the simulation time in the selected trajectory. (**C**) A timeline representation of CK2-**19** interactions presented in (**A**). The top panel presents the total number of specific interactions the protein made with the ligand over the course of the trajectory. The bottom panel presents residues interacting with the ligand in each trajectory frame. The dark orange color indicates that more than one specific interaction is made between some residues and the ligand. *J. Fungi* **2022**, *8*, x FOR PEER REVIEW 23 of 30 around the aliphatic chain, which in turn decreased the interaction between this part of the molecule with the protein and was reflected by > 3 Å fluctuation in the RMSF plot. The time-depended representation of the CK2α1-**31** interactions showed that residues Arg47, His160, and Asp175 were the ones making specific interactions with the ligand, as indicated by the darker color in the plot (Figure 12C).

**Figure 12.** *Cont*.

around the aliphatic chain, which in turn decreased the interaction between this part of the molecule with the protein and was reflected by > 3 Å fluctuation in the RMSF plot. The time-depended representation of the CK2α1-**31** interactions showed that residues Arg47, His160, and Asp175 were the ones making specific interactions with the ligand, as indi-

cated by the darker color in the plot (Figure 12C).

**Figure 12.** (**A**) CK2 interactions with compound **31** throughout the simulation. (**B**) Schematic diagram shows the detailed 2D atomic interactions of **31** with CK2 that occurred > 30% of the simulation time in the selected trajectory. (**C**) A timeline representation of CK2-**31** interactions presented in (**A**). The top panel presents the total number of specific interactions the protein made with the ligand over the course of the trajectory. The bottom panel presents residues interacting with the ligand in each trajectory frame. The dark orange color indicates more than one specific interaction is made between some residues and the ligand. **Figure 12.** (**A**) CK2 interactions with compound **31** throughout the simulation. (**B**) Schematic diagram shows the detailed 2D atomic interactions of **31** with CK2 that occurred > 30% of the simulation time in the selected trajectory. (**C**) A timeline representation of CK2-**31** interactions presented in (**A**). The top panel presents the total number of specific interactions the protein made with the ligand over the course of the trajectory. The bottom panel presents residues interacting with the ligand in each trajectory frame. The dark orange color indicates more than one specific interaction is made between some residues and the ligand.

**Figure 13.** Ligand RMSF shows the fluctuations of **31** broken down by atom as represented by the compound's 2D structure. It provides ideas on how ligand atoms interact with the protein and their entropic role in the binding event. The 'Fit Ligand on Protein' line presents the ligand fluctuations, with respect to the protein. The CK2α1-**31** complex was first aligned on the protein backbone, and then the ligand RMSF was measured on the atoms of the ligand. It was also noticed that the reference ligand, **Y49,** as well as the compounds **19** and **Figure 13.** Ligand RMSF shows the fluctuations of **31** broken down by atom as represented by the compound's 2D structure. It provides ideas on how ligand atoms interact with the protein and their entropic role in the binding event. The 'Fit Ligand on Protein' line presents the ligand fluctuations, with respect to the protein. The CK2α1-**31** complex was first aligned on the protein backbone, and then the ligand RMSF was measured on the atoms of the ligand.

#### **31,** all interacted with Asn118 through H-bonding; however, the contact points are differ-**3. Conclusions**

ent. While the residue interacted with **Y49** at the purine carbonyl oxygen (Figure 10B), it acted as an H-bond donor to the OH at the end of the aliphatic chain of **19** as well as to the OH at the fused ring system of **19** and **31** (Figures 11B and 12B). The reason for the different contact points of Asn118 with the compounds was probably attributed to the 3D conformation of the compounds inside the binding pocket, which is affected by the nature of the substitutions on the nucleus. Each compound assumed a pose that had the lowest possible free energy when interacting with the pocket's residues. Therefore, that pose with the different substitutions from one compound to the other created the unique binding interactions with the pocket amino acids. **3. Conclusions**  CK2 was related to many human illnesses, not only cancer, but also multiple sclerosis, cardiac hypertrophy, neurodegenerative and inflammatory disorders, cystic fibrosis, and virus infections [68]. It is noteworthy that the CK2 role is best recognized and investigated in cancer, where CK2 is almost positively upregulated, resulting in tumor progression because of its role in regulating nearly all the essential processes for developing apoptosis suppression [5,69]. It was reported that cancer cells rely on CK2 high levels compared to normal cells, which supports that the CK2 inhibitors can have a crucial contribution to cancer therapy development [5]. Recently, several compounds have been discovered and optimized via rational drug design approaches. Various structure-based drug design (SBDD) tools have been utilized for CK2 drug discovery for predicting possible compound and target interactions and their affinity. Various classes of natural metabolites, such as anthraquinones, benzoimidazoles, coumarins, pyrazolotriazines, and flavonoids, are recognized as CK2 inhibitors [70,71]. Fungal phenalenones are a fascinating class of CK2 was related to many human illnesses, not only cancer, but also multiple sclerosis, cardiac hypertrophy, neurodegenerative and inflammatory disorders, cystic fibrosis, and virus infections [68]. It is noteworthy that the CK2 role is best recognized and investigated in cancer, where CK2 is almost positively upregulated, resulting in tumor progression because of its role in regulating nearly all the essential processes for developing apoptosis suppression [5,69]. It was reported that cancer cells rely on CK2 high levels compared to normal cells, which supports that the CK2 inhibitors can have a crucial contribution to cancer therapy development [5]. Recently, several compounds have been discovered and optimized via rational drug design approaches. Various structure-based drug design (SBDD) tools have been utilized for CK2 drug discovery for predicting possible compound and target interactions and their affinity. Various classes of natural metabolites, such as anthraquinones, benzoimidazoles, coumarins, pyrazolotriazines, and flavonoids, are recognized as CK2 inhibitors [70,71]. Fungal phenalenones are a fascinating class of fungal metabolites with diverse bioactivities that could be lead metabolites for drug discovery. With the aid of computational methods, i.e., ADMET, docking, and MD simulation, compounds **19** and **31** were identified as promising drug-like phenalenone derivatives that have better binding interactions and protein stability in a simulated aqueous physiological environment. The current work highlights the usefulness of these metabolites as lead for anticancer discovery. One of the important issues that require attentiveness is that several mechanistic studies are directed to the in silico methods because they provide information that cannot be obtained by other models and are less time-consuming. However, in vivo and in vitro investigations are warranted to strengthen the findings of in silico studies and provide opportunities for observing other mechanisms of the anticancer potential of these metabolites.

fungal metabolites with diverse bioactivities that could be lead metabolites for drug discovery. With the aid of computational methods, i.e., ADMET, docking, and MD simulation, compounds **19** and **31** were identified as promising drug-like phenalenone derivatives that have better binding interactions and protein stability in a simulated aqueous

#### **4. Materials and Methods**

#### *4.1. Target Prediction*

The webserver SuperPred is a knowledge-based method that uses machine learning models for ATC code and target prediction of investigated compounds [57]. The machine learning model uses logistic regression and Morgan fingerprints of length 2048. The drugs approved by the WHO are classified by a drug classification system that connects the drugs' chemical properties and therapeutic properties and indications, where each classification is given a code called an Anatomical Therapeutic Chemical (ATC) code. Therefore, if a drug has more than one therapeutic indication, it is given an ATC code for each indication. The WHO has 6300 approved drugs that are linked to over 600,000 targets. Based on the hypothesis that compounds that have similar physiochemical properties exhibit similar biological effects, the webserver translates a user-defined compound into a structural fingerprint and compares this fingerprint to that of the WHO-approved drugs. When similarity is found, the webserver predicts the ATC code, the possible therapeutic target(s), and the putative therapeutic indication(s) for that compound. In other words, if an investigated compound is structurally similar to an approved drug, the compound is predicted to have biological activity on all possible targets of that drug. After targets are predicted, a probability score and a model accuracy score are reported. The probability represents the chance that the investigated compound will bind to a specific predicted target. The model accuracy reflects the performance accuracy of the used machine-learning model when predicting that specific target for the compound since the model performance differs between targets [57,72]. The targets and ATC codes for a library of investigated compounds were predicted using the SuperPred tool. The compounds that did not have the common target(s) of interest were excluded from further analysis. The ones sharing the common target(s) were advanced for the docking and further studies.

#### *4.2. Preparation of PDB Structures*

#### 4.2.1. Ligand Preparation

Phenalenone derivatives were processed and prepared for docking using Schrodinger's LigPrep tool [40]. The 2D structures were converted to 3D and energy-minimized using OPLS3 force-field. After adding hydrogens, all possible ionization states and tautomeric forms were created at pH of 7.0 ± 0.2 by Epik; desalt option was also chosen. H-bonds were optimized by predicting the pKa of ionizable groups suing PROPKA [73].

### 4.2.2. Protein Preparation

CK2 crystal structure (PDB: 7BU4) was prepared using the Protein Preparation Wizard, added hydrogens to residues, changed covalent bonds to metal ions to zero-order, and created disulfide bonds. Water molecules > 5 Å from protein residues were deleted. Using Epik, the protonation state of residues was generated, and the formal charge on metal ions was adjusted. After removing the extra protein subunits of multi-subunit proteins and additional ligands, processing of the protein was refined by predicting the pKa of ionizable residues using PROPKA [73], and water molecules > 3 Å (not involved in water bridge) were removed. Finally, restrained minimization of the protein was applied using the OPLS4 force field.

#### *4.3. Grid Generation and Docking*

A grid box was generated around the co-crystallized ligand **Y49** in the protein crystal structure (PDB: 7BU4) binding site using Glide's Receptor-Grid-Generation tool [62]. Inside this box is where the docking of the phenalenone compounds was performed. The nonpolar atoms were set for the VdW radii scaling factor by 1.0, and the partial charge cutoff was 0.25. Docking was then performed by the Schrodinger suite "Ligand Docking" tool [62,74]. The selected docking protocol was standard precision (SP), and the ligand sampling method was flexible. All other settings were default. Re-docking of the cocrystallized ligand (PDB: **Y49**) was performed to evaluate the docking method and docking of the investigated phenalenones followed.

#### *4.4. ADMET Properties Prediction*

The processed compounds were subjected to ADMET prediction using the QikPropmodule of the Schrodinger suite [63]. The descriptors: molecular weight (mol\_MW), drug-likeness (#Stars), dipole moment (dipole), total solvent accessible surface area (SASA), number of hydrogen bond donors and acceptors (donorHB and acceptHB), predicted octanol-water partitioning (QPlogPo/w), predicted aqueous solubility (QPlogS), estimated binding to human serum albumin (QPlogKhsa), number of the possible metabolites (# metab), predicted blood-brain partitioning (QPlogBB), percentage of human oral absorption, predicted IC50 for inhibiting HERG-K+ channels (QPogHERG), central nervous system activity (CNS), and number of reactive functional groups present (#rtvFG), were predicted for these derivatives. The predicted values are compared to the recommended range derived from values determined/observed for 95% of known drugs.

#### *4.5. MD Simulation*

MD simulations were performed using Desmond software in the Schrodinger suite [65,66]. The protein-ligand complexes of interest were retrieved from the docking results where the force field was OPLS4. The complexes were tuned through the "System-Builder" tool to generate the solvated system for simulation. The solvent model was set as TIP3P, the selected box shape was orthorhombic, and the box dimensions were 10 Å. Na ions were added to neutralize the system. The simulation parameters were set up in the Molecular Dynamic tool, where the protein-ligand complexes were evaluated at pH 7.0 ± 0.2 over the 100 ns simulation time. The ensemble class was set as NPT in order to maintain the temperature and pressure constant during the run at 300 K and 1.01325 bar, respectively. After running the MD simulation, the generated results were analyzed.

**Author Contributions:** Conceptualization, G.A.M., A.M.O., and S.R.M.I.; methodology, G.A.M., A.M.O., S.R.M.I., and Y.A.M.; validation, A.A.B., R.M.D., A.O.N., and H.T.B.; resources, A.A.B., R.M.D., A.O.N., and H.T.B.; data curation, G.A.M., A.M.O., S.R.M.I., and Y.A.M.; software, A.M.O. and Y.A.M.; writing—original draft preparation, A.M.O., S.R.M.I., and Y.A.M.; writing—review and editing, A.A.B., R.M.D., A.O.N., and H.T.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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1. Introduction

Antenna measurement techniques are devoted to obtaining the main radiation parameters (radiation pattern, antenna gain, polarization, etc.) in the antenna far-field (FF) region1 from the acquisition of the fields radiated by the antenna under test (AUT). Novel methods for antenna measurement [1] and postprocessing techniques [2] are constantly emerging to cope with the requirements needed to provide efficient and accurate characterization of new types of antennas, mainly at high frequency bands. Additionally, antenna diagnostics enables nondestructive inspection of the antennas for detection of design or fabrication failures by means of the analysis of their extremely near fields or their equivalent currents [3–6].

First, antenna measurements were performed in outdoor ranges at FF distances. Those tests were highly affected by weather conditions, interference, and multipath from multiple reflections mainly caused by the floor. Anechoic chamber testing was sooner adopted as the standard method for antenna metrology. Anechoic chambers have an electromagnetic absorber lining to reduce electromagnetic reflections and to control the measurement environment [7].

Advances in fabrication technologies have contributed to the development of new components and antennas at millimeter (mm-) and submillimeter (submm-) wave frequency bands.2 At these frequencies, measurement of directive antennas would require extremely large anechoic chambers to fulfill the FF condition. Hence, other types of measurement ranges such as nearfield (NF) measurement ranges have been developed to avoid the previous shortcoming [1].

In NF measurement systems, the field is acquired over a surface in the vicinity of the AUT. Planar, cylindrical, or spherical surfaces are the most common acquisition surfaces, with recent extensions to arbitrary geometry [9] or noncanonical domains [10, 11]. The acquired NF can be employed to obtain the FF radiation pattern of the antenna by means of mathematical NF-FF transformations based either in wave expansions [1, 12, 13] or integral equation methods such as the sources reconstruction method (SRM) [3, 9]. Diagnostics applications can also be developed from NF data using backpropagation techniques toward the AUT aperture [1, 13] or the SRM [3, 9]. After several decades of research and development, NF ranges have become the preferred approach for antenna testing.

Special attention must be given to the probe pattern and positioning accuracy [1] as well as to the effects that error sources in NF acquisitions, such as truncation of the measurement plane, cable flexing, stray signals, leakage, etc., can introduce in the FF pattern of the AUT [1, 2, 13, 14].

1 The far-field distance is defined by R ¼ 2D2=λ (R >> λ), being D the maximum dimension of the antenna and λ the wavelength [1].

2 The mm-wave band is defined according to the IEEE Standard 521-2002 from 110 to 300 GHz. This standard is a review of the standard published in 1984 that also considered the lower bands defined from 30 to 110 GHz (Ka, V, and W bands) as part of the mm-wave band. This older definition is still commonly accepted. Frequency bands above 300 GHz are not included in the standard; the submm-wave or Terahertz band corresponds, depending on the author, to the fraction of the spectrum from 300 GHz to either 3 or 10 THz in the lower limit of the far-infrared spectrum [8].

NF techniques for both NF-FF transformation and antenna diagnostics generally require the knowledge of amplitude and phase of the radiated electric field by the AUT [1–5]. Nevertheless, phase acquisition, particularly at mm- and submm-wave bands, is a challenging task that requires sophisticated and expensive equipment due to the high thermal stability requirements and the effect of the errors, mostly resulting from thermal drift and cable flexing [1, 13–16].

1. Introduction

244 Holographic Materials and Optical Systems

preferred approach for antenna testing.

[1, 2, 13, 14].

wavelength [1].

1

2

Antenna measurement techniques are devoted to obtaining the main radiation parameters (radiation pattern, antenna gain, polarization, etc.) in the antenna far-field (FF) region1 from the acquisition of the fields radiated by the antenna under test (AUT). Novel methods for antenna measurement [1] and postprocessing techniques [2] are constantly emerging to cope with the requirements needed to provide efficient and accurate characterization of new types of antennas, mainly at high frequency bands. Additionally, antenna diagnostics enables nondestructive inspection of the antennas for detection of design or fabrication failures by means

First, antenna measurements were performed in outdoor ranges at FF distances. Those tests were highly affected by weather conditions, interference, and multipath from multiple reflections mainly caused by the floor. Anechoic chamber testing was sooner adopted as the standard method for antenna metrology. Anechoic chambers have an electromagnetic absorber lining to reduce electromagnetic reflections and to control the measurement environment [7]. Advances in fabrication technologies have contributed to the development of new components and antennas at millimeter (mm-) and submillimeter (submm-) wave frequency bands.2 At these frequencies, measurement of directive antennas would require extremely large anechoic chambers to fulfill the FF condition. Hence, other types of measurement ranges such as nearfield (NF) measurement ranges have been developed to avoid the previous shortcoming [1]. In NF measurement systems, the field is acquired over a surface in the vicinity of the AUT. Planar, cylindrical, or spherical surfaces are the most common acquisition surfaces, with recent extensions to arbitrary geometry [9] or noncanonical domains [10, 11]. The acquired NF can be employed to obtain the FF radiation pattern of the antenna by means of mathematical NF-FF transformations based either in wave expansions [1, 12, 13] or integral equation methods such as the sources reconstruction method (SRM) [3, 9]. Diagnostics applications can also be developed from NF data using backpropagation techniques toward the AUT aperture [1, 13] or the SRM [3, 9]. After several decades of research and development, NF ranges have become the

Special attention must be given to the probe pattern and positioning accuracy [1] as well as to the effects that error sources in NF acquisitions, such as truncation of the measurement plane, cable flexing, stray signals, leakage, etc., can introduce in the FF pattern of the AUT

The far-field distance is defined by R ¼ 2D2=λ (R >> λ), being D the maximum dimension of the antenna and λ the

The mm-wave band is defined according to the IEEE Standard 521-2002 from 110 to 300 GHz. This standard is a review of the standard published in 1984 that also considered the lower bands defined from 30 to 110 GHz (Ka, V, and W bands) as part of the mm-wave band. This older definition is still commonly accepted. Frequency bands above 300 GHz are not included in the standard; the submm-wave or Terahertz band corresponds, depending on the author, to the fraction of the

spectrum from 300 GHz to either 3 or 10 THz in the lower limit of the far-infrared spectrum [8].

of the analysis of their extremely near fields or their equivalent currents [3–6].

Nowadays research is focused on the development of new measurement systems [17, 18] and techniques that allow reducing the acquisition time and costs and preventing or correcting the effect of errors in NF measurements [2–7, 19]. Among these techniques, amplitude-only measurements, commonly referred to as phaseless or scalar measurements (in contrast to vector, also referred to as complex measurements involving amplitude and phase), are frequently employed due to their multiple advantages such as the use of simpler and less expensive receivers and robustness to errors related to phase acquisition. Amplitude-only techniques can be indistinctly applied to antenna measurements and diagnostics and are divided into two main groups depending on the implementation approach: iterative and noniterative techniques.

On the one hand, most of the iterative techniques [3, 19, 10] are based on the acquisition of the field intensity in two or more surfaces. Then, an iterative process is employed to propagate the field from one surface to another after guessing an initial phase, until certain condition is satisfied for all the surfaces. This kind of technique is popular because they involve minor changes in the measurement setup, nevertheless they can suffer from stagnation and their convergence is strongly related to the first guess solution. On the other hand, and belonging to noniterative techniques, most of the interferometric approaches [5, 20–23] rely on the use of a reference field, previously known in amplitude and phase, used to interfere the field of the AUT and allowing an easy and iteration-free phase retrieval by means of a filtering process in the spectral domain.

Indirect off-axis holography, also known as Leith-Upatnieks holography [24], is an interferometric technique adapted from optical holography to amplitude-only antenna metrology in the early 1970s [25, 26]. During the last years, great efforts have been made to improve aspects such as sampling [22] and overlapping reduction [27] or reference signal calibration [28, 29]. The rest of the chapter is divided as follows: Section 2 contains an introduction to conventional off-axis holography techniques applied to antenna metrology. Novel techniques that allow for the use of synthesized reference waves with mechanical phase shifts [5, 30] will be introduced in Section 3. A new efficient method for amplitude-only characterization of broadband antennas [23] compatible with nonredundant sampling techniques [31] will be described in Section 4. Finally, main conclusions regarding the advantages and disadvantages of the proposed methods will be drawn in Section 5. Numerical validation of the proposed techniques in Sections 3 and 4, performed in Planar NF (PNF) measurement ranges [32, 33], will be given for each method and, thus, although easily translatable to other geometries, formulation will be particularized for planar acquisition systems.


*2.2. Selection of the Powertrain Components*

While the set of internal combustion engines to be employed in the studied powertrains was defined (i.e., the diesel and two gas engines), the electrical components were to be selected or designed. Considering the available technical resources and the objectives of the study, units available "from the shelf" were preferred over theoretical ones. In particular, the prototype traction electric drive was acquired from one of the commercially available hybrid units intended for HD vehicles. When used in an HEV with the gross weight considered in this work (35–44 tons), the power and torque characteristics of the electric drive (see Section 3.4 for details) correspond to an intermediate solution between the full and mild hybrids.

Two options for the engine control at vehicle stops were considered, namely idling and switching the engine off and starting it back when the vehicle resumes moving (i.e., the start–stop feature). The latter option was assumed to be implemented using an "enhanced" starter rather than the traction electric drive to prevent impairing the vehicle dynamics.

The energy storage system (ESS) is one of the key components in a hybrid powertrain, which defines the amount of regenerated braking energy and the vehicle performance in the pure electric driving mode. The prevailing ESS technology in the field of hybrid and pure electric vehicles are accumulator cells, which are lithium-ion for the most part [19]. Their specific energy capacity and power, which have noticeably increased over the years [20])], along with their moderate prices make them well-suited for passenger and light-duty commercial vehicles. Their known vulnerability to high and low temperatures (capacity and efficiency drop, accelerated degrading) can be alleviated using appropriate temperature management [19], at least in hybrid vehicles, where engine heat can be utilized for that purpose. The cycle life of typical lithium-ion cells, although relatively short (a typical value is around 3000 cycles, but may be lower), is nevertheless admissible for electric vehicles since they employ large battery packs that allow for traveling up to a few hundred kilometers per charge–discharge cycle. Hybrid vehicles, especially non-plugin vehicles, have significantly smaller batteries, which compels developers and producers to resort to more advanced (and expensive) accumulator cells that have higher power densities and longer cycle lives.

When it comes to the hybridization of heavy-duty vehicles, the following specifics of long-haul vehicle applications have to be taken into account while selecting the ESS type. Due to the large mass of such vehicles, the ESS should be able to deliver and consume high amounts of power (over 100 kW) continuously. An HD vehicle usually has a long service life and is operated intensively (on an everyday basis), which entails a large mileage from hundreds of thousands to even millions of kilometers. Throughout the service period, the number of overhauls should be minimal. The replacement of powertrain components, especially expensive ones, is undesirable (the operating life of the powertrain and its major components is to be equal to that of the vehicle). Additional expenses brought about by introducing advanced powertrain technologies should be (at least) compensated for by the economic effect provided by those technologies (e.g., reduced fuel consumption). Climatic operating conditions of the heavy-duty vehicle fleet vary greatly, including both extremely cold and warm regions.

To provide a longer cycle life of accumulator-based solutions, one should use "shallow" charge–discharge cycles. Together with the requirement for higher power, this implies that large batteries are to be used in HD vehicles. As a result, even for hybrid applications, which offer a relatively small pure electric driving range, the battery tends to be oversized due to the necessity in meeting both the power and cycle life requirements.

A known alternative for high-power ESSs are supercapacitors (SCs), which the literature claims as a promising technology for heavy-duty vehicles [11,21–24]. One has to admit that the characteristics of supercapacitors include both substantial advantages and adversities. Among the former, one can provide high operating currents and, consequently, a high power density [25,26]. A single SC cell having a nominal voltage of 3 V can operate continuously with currents up to 300 A and, for a limited time, over 1000 A. The cycle life of supercapacitors is outstandingly higher than that of lithium-ion accumulators and exceeds 1 million cycles [25,26]. Additionally, supercapacitors have a wide operating range of low temperatures, which can reach −40 ◦C. For example, when used in engine-cranking applications, an SC can start an engine smoothly in a −25 ◦C ambient temperature [26]. Thus, supercapacitors do not impose the same strict requirements regarding the low-temperature management as accumulators do. On the other hand, the following shortcomings of supercapacitors should be taken into account. Their energy density is far lower (about 95% lower on average) than that of lithium accumulators. The prices for a kWh of supercapacitors are at least 20 times higher than those of the typical lithium cells. For advanced, high-power, long-life accumulators used in compact batteries of hybrid vehicles, this price ratio may be smaller, although not drastically. Like lithium-ion accumulators, supercapacitors are vulnerable to high-temperature degradation; therefore, they require effective cooling systems [25]. Yet another feature may be counted as both positive and negative, namely the proportionality between the supercapacitor voltage and its state of energy. On the one hand, this allows an ESS management system to determine the state of energy using simple voltage monitoring. In contrast, lithium-ion accumulators, especially the LiFePO4-type accumulators, require battery management systems to have sophisticated algorithms for the indirect determination of the state of charge [27] due to its substantial independence from the accumulator voltage. On the other hand, the said proportionality results in a wide operating range of the supercapacitor voltage is much wider than that of lithium-ion accumulators, which raises the question of matching this range with the operating voltage of the traction electric drive. One known solution is employing a DC–DC converter that keeps the input voltage of the electric drive at a reference level, while the supercapacitor voltage travels through its operating range [24,28,29]. This ensures that the traction drive will be able to deliver its rated power independently (to a certain extent) of the ESS voltage. The complication of this approach is, obviously, the need for a high-power buck–boost converter, which entails additional costs, weight, occupied space, and finally, yet importantly, power losses due to voltage transformation. One can expect a 95% peak efficiency at most from such a converter, which is rather noticeable for the powertrain energy balance considering that the major power flow will be transmitted through this converter. Another solution is a direct DC connection between the supercapacitor and the traction drive inverter [29]. This makes the operating characteristics of the drive variable and needs to be addressed in the control algorithm of the powertrain. In the described study, both solutions were compared in terms of the resulting fuel economy and ESS efficiency.

For commercial vehicles, all the mentioned virtues of supercapacitors—high power, long cycle life, and wide operating temperature span—are particularly advantageous. When considering the drawback of low energy density, one can conclude that unlike for pure electric vehicles, for non-plugin hybrids, this is not a critical issue, although the large weight of HD vehicles, of course, does require a proportional energy content of the ESS that can recuperate the bulk of the braking energy. The supercapacitor cost, however, is an issue that raises concerns regarding the additional expenses entailed by hybridization. Since the amount of regenerated energy that can be stored within the ESS is the decisive factor of fuel economy (in the case of HD vehicles), the ESS capacity is a result of a trade-off between lower fuel expenses and higher ESS costs. Therefore, establishing the influence of the ESS energy content on the fuel economy becomes an additional objective of the study.

The prototype of the supercapacitor-based ESS used for this study has been taken from the powertrain of a hybrid city bus that belonged to a limited series produced earlier. The ESS in that bus has an electric capacitance of 28 F and a maximum voltage of 650 V, providing an energy content of 1.6 kWh. The maximum continuous current is 300 A for both discharging and charging. Considering the voltage operating range of 300–640 V, the maximum power delivered by the SC amounts to 90–195 kW. To obtain the characteristics of the prototype supercapacitor, several field experiments were conducted involving the mentioned hybrid bus. During those tests, the supercapacitor current and voltage were being measured and logged while the bus was being driven through predetermined velocity patterns.


**1. Introduction**

Autoimmune pancreatitis (AIP) is an emerging disease, recognized with an increasing frequency in the whole world. Autoimmune factors have been known since long time to participate in the etiology of some cases of chronic pancreatitis [1]; however, their importance was somewhat marginal, no more than 3–5% of the patients of chronic pancreatitis [2, 3]. In addition, pancreatic involvement is relatively rare in the major autoimmune diseases: while described, chronic pancreatitis is only exceptionally found in lupus erythematosus [4] and Sjögren's syndrome [5, 6]. Conversely, AIP while described before [7, 8] was identified as an independent entity only in 1995 [9], and it is associated with specific IgG4-related autoimmune disease (type 1) and with inflammatory bowel disease (type 2). Their histology is characteristic and quite different when compared to pancreatic involvement in SLE or Sjögren's syndrome. This fact is very similar to the case of the liver, hepatitis associated with lupus and autoimmune hepatitis being also the two distinct diseases [10].


*2.9. Secondary Structure of Nucleotides Interacting with DOT Residues*

Further, we have classified the nucleotides based on location and contacts with DOT residues and preference of amino acids in a protein and the results are presented in Table 4 and Table S3. Among all secondary structures formed by nucleotides, unpaired bases are most likely to bind with DOT residues. Specifically, we observed that A and U in unpaired regions prefer to interact with DOT residues, whereas C and G in unpaired and base-paired positions interact with DOT residues with a similar preference. G and C also interact with DOT residues in pseudoknot secondary structure, whereas A and U are least likely to exist in pseudoknot form when bound to DOT regions.

Percentage is mentioned in parenthesis. Relative contacts in DOT regions are calculated by *Nidt*/*Nprot* × 100.

#### *2.10. Interaction Energy of DOT Residues with Nucleotides*

We have computed the interaction energy between amino acids and nucleotides in DOT and ordered regions at the binding interface and the results are presented in Table 5. Most of the amino acids have stronger interactions with nucleotides in ordered regions than DOT regions. However, we noticed that some combinations of amino acid–nucleotide pairs have favourable energy when

interacting with DOT regions. For example, Arg, His, Ile, Leu, Val, and Phe interact with G, His, Ser, and Val with C, and Asn, Asp, Gly, Ile, Leu, and Ser with U. In addition, hydrophobic residues Ile, Leu, and Val have more favourable interactions with G at DOT regions than others. Since Arg and Lys are important for protein–RNA complex formation through electrostatic interactions these residues have stronger energies in ordered regions than DOT regions. On the other hand, His in the DOT region has favourable energy with G and C. These differences in energy could be important to understand the interactions between DOT regions and the RNA molecule, which might also be used to distinguish the RNA binding residues of proteins in DOT and other regions.

**Table 5.** Interaction energy between amino acids and nucleotides in DOT regions.

Interaction energy for non-DOT residues is mentioned in the parenthesis. Amino acid–nucleotide pairs with favourable interaction energies in DOT regions are shown in bold.

We have compared the interaction energy of amino acid–nucleotide pairs in the interface of DOT and other regions and two typical examples are shown in Figure 8. We noticed a wide range of interactions such as stacking, cation-π, electrostatic, and van der Waals interactions at the interface. Most favourable energy is observed for Asn and His with U (−3.26 kcal/mol) and G (−5.44 kcal/mol), respectively, in DOT regions (Figure 8a). On the other hand, Arg and Phe have favourable energy with A (−8.49 kcal/mol) and C (−4.88 kcal/mol), respectively, in non-DOT regions.

**Figure 8.** Amino acid showing (**a**) strong interaction in DOT and weak interaction in non-DOT regions and (**b**)weak interaction in DOT and strong interaction in non-DOT regions.

### **3. Materials and Methods**

We adopted the following protocol to obtain a set of protein–RNA complexes with disorder-to-order transition (DOT) regions: (i) Downloaded the protein–RNA complexes from PDB and NDB databases (www.rcsb.org) [37–39]; (ii) Clustered all the protein–RNA complexes with 30% sequence identity cut-off using CD-Hit suite [40]; (iii) Performed BLAST search (using 99% identity cut-off) of protein sequences to obtain free proteins corresponding to each protein–RNA complex [41,42]. The free proteins have the same sequences as the protein part of protein–RNA complexes but crystallized without RNA. Note that free proteins contain unique PDB IDs, which is distinct from the protein–RNA complex; (iv) Disordered residues are obtained from missing residues information in the protein–RNA complex and free protein pairs by locating "REMARK 465" statement in the protein structure file; (v) DOT residues are isolated by comparing the disorder residues of free and protein–RNA complex pairs such that the residue is ordered in the protein–RNA complex but disordered in free protein. Note that only the regions having 3 or more continuous DOT residues are considered. The final dataset contains 101 DOT regions in 52 proteins and complete data are given in supplementary information. The representation of DOT and ordered region in a typical protein–RNA complex (PDB ID: 4H4K) is shown in Figure 9.

**Figure 9.** Representation of disorder-to-order mediated interactions. Free protein, RNA, and complex (CRISPR-Cas RNA Silencing Cmr Complex) are shown in cyan, orange and green, respectively. The PDB IDs are 4H4K:A (free protein), 3XIL:I (RNA of protein–RNA complex) and 3XIL:B (RNA-bound protein). The disorder-to-order transition (DOT) region can be clearly seen in green with a missing overlapping region of free protein.


**6. Irrigation scheduling**

Irrigation scheduling simply means application of water to crops at the required time and in the required quantity. Irrigation scheduling is one of the most effective way to increase water productivity in fertile crop production. Marketable yields for most shallow rooted vegetables can be easily damaged by short-term moisture stress of two to three days. Deficit irrigation generally results yield loss and inadequate quality in vegetables, while excess irrigation increases susceptibility to diseases, irrigation energy cost and environmental pollution risk from the nutrient leaching [31].

Different techniques of irrigation scheduling in irrigation of vegetable crops are used. They can be classified as monitoring of soil water status, water balance approach from crop water demand and observing of plant traits. Continuously monitoring soil moisture throughout crop growing period is very crucial and also requires accurate measurement with precision-based devices [32]. Soil moisture sensors can be used to regulate the interval of irrigation and, possibly, the water quantity by continuously monitoring water content or tension of the soil [31]. Technological advances in automatic soil water sensor-based irrigation systems are aimed to save an optimum soil water range in the root zone for high-quality plant growth. These algorithms are? used in automated irrigation management and scheduling agricultural activities. Furthermore, these algorithms are developed to observe water content and ensure irrigation with automated activation when necessary [33]. Smart irrigation automation systems can be less used in open field agriculture, while they are used increasingly in greenhouse production with soil or without soil to save considerable amounts of water and nutrients that are heavily applied.

Irrigation scheduling in crop water demand method consists of supplying the crop evapotranspiration (ETc) (daily, five or ten days' averages) for each crop growing stage. Thus, this method is known as crop evapotranspiration method. The ETc value of a fully-irrigated vegetable crop can be calculated either empirically by multiplying daily reference of evapotranspiration (ETo) by crop coefficient (Kc) or experimentally (2). However empirical way is commonly preferred to save time, cost and labor.

$$\mathbf{ETc = ETo \times Kc} \tag{2}$$

ETo is calculated by well-known Penman-Monteith (FAO) equation using daily or daily average (of five or ten days) air temperature, relative humidity, wind speed and solar radiation data [22, 34]. Kc values are selected from the tables prepared for different growth stages of vegetable crops [34]. Irrigation scheduling programs such as CROPWAT can be used as the model-based scheduling. This program uses Penman-Monteith (FAO) method with collected soil, crop and climatic data in the region [22, 35]. The precision of ET-based scheduling method depends strongly on the accuracy of the ETo estimation value, a correct Kc value determined with site-specific calibration approach, correct determination of the soil's available water holding capacity, and measuring site-specific precipitation [35, 36].

Irrigation interval can. be calculated by the ratio of readily available water (RAW) to the crop daily net irrigation water requirement (Inet) which are calculated as:

$$\text{Int}\left(\text{mm}\,\text{day}^{-1}\right) = \text{ETc} - \text{Effective Precipitation},\tag{3}$$

$$\text{Irrigation interval} \left( \text{day} \right) \text{=RAW} / \text{Inet.}\tag{4}$$

RAW is calculated by, below equation [35].

$$\mathbf{RAW} = \left(\theta \mathbf{fc} - \theta \mathbf{w} \mathbf{p}\right) \times \mathbf{D} \times \mathbf{MAD} \tag{5}$$

where RAW is the readily available water content (mm), θfc is the volumetric water content at field capacity (m3 m−3), θwp is the volumetric water content at the permanent wilting point (m3 m−3), D is the effective rooting zone depth or the soil layer depth considered (mm) and MAD is the fraction of the total available water that is allowed to be depleted. MAD value should be kept low in vegetable irrigations to protect plants from water stress. RAW value is also equal to the net irrigation quantity applied to the soil.

Plant-based scheduling techniques have been improved from the relationship between crop water stress and soil moisture deficit to define an optimal moisture content level for crop growth. Measuring crop water stress for irrigation scheduling has been also recommended considering the variations in plant species, tissues, and phenological stages [35, 37]. The approaches have been categorized as the measurements of tissue water potential and the measurements with plant physiology-based (sap flow, stomatal conductance, thermal sensing with infrared thermometers).

Stomatal conductance is a good indicator in determination of irrigation need in many plants sensitive to water insufficiency, thus improvement of this technique among plant-based irrigation scheduling approaches has drawn increaasing attention [37]. In recent years, the use of irrigation scheduling based on the crop water stress index (CWSI), which is calculated based on the canopy temperature measured with an infrared thermometer, has gained importance. Many researchers have reported that the CWSI value can be used for preparation of irrigation scheduling [38]. This approach argues that significant increases in canopy temperature exceeding air temperature has been a good indicative for stomatal closure and water deficit stress [37].

Furthermore, a systematic method can be applied as a practical scheduling approach. In this method, water applications are managed on a time or volume basis applying every day for the same duration or in the same quantity. Moreover, it is quite practical to base irrigation scheduling on evaporation from a Class A pan as a result of the combined effect of climatic factors. This approach requires a correction coefficient (kp) (mostly changed between 0.6–0.8) to convert potential evaporation value measured in pan to the ETo value. The Kp coefficient is also expressed as Kcp when it includes the crop coefficient. Water use from fully developed vegetation can be about 75–80% of the amount of water evaporated from the pan, in other words, Kcp = 0.75–0.80. When plants do not completely cover the soil surface, actual water consumption will be less than 75% of pan evaporation. Water use for vegetable crops can be considered as 10–15% of pan evaporation during the first 1/3 of the season, 40–50% of the pan evaporation during the mid-season, and 60–80% of the pan evaporation during the last 1/3 of the growing season [39].

#### **7. Irrigation methods**

In irrigated agriculture, when operating an area for irrigation, firstly the most suitable irrigation method under the conditions should be selected, then the system required by this method must be planned, installed and operated. In general, the irrigation method to be selected must meet some conditions such as to provide uniform water distribution, to minimize deep percolation and run-off losses, not cause soil erosion, not prevent agricultural mechanization, help leaching the salt from soil.

Due to the shallow rooting depth of most vegetables and their high response to lack of water, irrigation is frequently required in small amounts. This situation is more important in greenhouses with intensive production. Vegetable growers consider drip irrigation method as an effective way to save water and that plant needs, as well as to reduce weeds, fungi and diseases. Drip irrigation minimizes water loss from run-off and deep percolation, decreases evaporation losses. It has been determined that water savings of 50–80% are achieved when compared to conventional surface irrigation methods [27]. Drip irrigation method also provides more efficient water and fertilizer usage than the sprinkler method. It also reduces disease problems because leaves are not wetted. Drip irrigation lowers energy need because of the low pump pressures required and provides more applicable opportunity of automation. However, compared to sprinkler nozzle sizes, drip system emitters have very small openings, emitters gets clogged. Therefore, it requires water quality control and some preventive solutions such as filtration and dilute acid applications. Many researchers have declared considerable benefits of drip irrigation method over other conventional irrigation methods to improve yield and water productivity (WP) of fruits and vegetables [40]. The water application efficiency is about 80–90% in drip irrigation systems [39]. Maximizing the water productivity with decreased water loss and increased yield in drip irrigation is a practical way to manage finite water supplies. Plants use large amount of the water applied from increased water efficiency. This also minimizes leaching of agrochemicals out of the field or vegetable growing containers into the environment. In the last few decades, water productivity of vegetable crop values has been improved with the use of efficient micro irrigation techniques such as micro sprinkler and drip irrigation [41]. Jha et al. [40] determined that drip irrigation method resulted higher water productivity with more than five-folds increase in potato and cauliflower compared to the furrow method. It was also observed that drip irrigation method conserves approximately 70–80% water compared to conventional flood irrigation method.

In drip irrigation systems, to avoid possible plant stress, irrigations are usually scheduled to start when allowable percentage of usable water in the soil has been consumed. This level ranges from 30% in drought-sensitive plants to 70% in droughtresistant plants. In drip irrigation, this value is usually taken as 30% (MAD value) [39].

Irrigation volume in drip irrigation system considering soil available water depletion approach can be calculated with equation below.

$$\text{Irrigation volume} \left(\text{L}\right) = \left(\theta \text{fc} - \theta \text{wp}\right) \times \text{D} \times \text{MAD} \times \text{P} \times \text{A} \tag{6}$$

where P is the wetting factor, A is the irrigated area (m2 ), and other terms are as mentioned before. Wetting ratio are considered minimum %30 in semi-arid regions, and it is 35% and 25% in arid and humid regions, respectively [42]. Wetting factor is less than 1 because especially during irrigation of plants with wide row spacing, a dry area remains between the laterals that is not wetted. In some cases, the plant covering ratio is also considered instead of this value in order to apply water according to the plant growth rate.

Irrigation volume can be also determined using the Class A pan evaporation with following equation [43].

$$\text{Irrigation volume} \left(\text{L}\right) = \text{Ep} \times \text{Kcp} \times \text{P} \times \text{A} \tag{7}$$

*Principles of Irrigation Management for Vegetables DOI: http://dx.doi.org/10.5772/intechopen.101066*

where Ep is the cumulative pan evaporation measured using a standard Class A pan at considered duration (mm), Kcp is the coefficient of crop-pan evaporation, P is the wetting factor and A is the irrigated area (m2 ).

Due to (Ep x Kcp) is equal to the ETc (ETc = Ep × Kcp), bunun yerine (7) de can be also used to calculate irrigation volume from the ETc values determined using other approaches empirical (e.g. Penman-Monteith) or experimental.


*1.2.1. Relevance of medicinal plants*

Medicinal plants are gaining popularity in usage due to a large number of people in search of health remedies with little or no side effect which is the problem of most chemically synthesized drugs. Considerable attention is presently given to the use of eco-friendly and biofriendly products from plant origin for the prevention and cure of human and animal health challenges (diseases) [9, 10]. This problem of side effects of most chemically based drugs has spurred the Western world to looking into natural products that are safe, effective, and affordable. It has been documented that 80% of the world's population has a strong belief in traditional medicine, especially drugs from plant origin for their primary health care [9, 10]. Medicinal plants, for example, neem leaves and stem bark (*Azadirachta indica*), pawpaw leaves (*Carica papaya*), mango leaves and stem bark (*Mangifera indica*), and Cinchona bark have been in use in one form or the other traditionally. No doubt, the plant kingdom is rich in diverse array of plants whose medicinal attributes (potencies) are yet to be unraveled [9, 10]. The various uses of some common medicinal plants from Nigeria used for treating various diseases highlighting the parts of the plants used are represented in **Table 1**.


*4.3. Final Energy and Cost Considerations*

This section has considered best available technologies (BAT), which are innovative and economically viable [48]. Hydronic technologies are compatible with radiant systems, such as WFG and radiant floors and walls. Air-to-air heat pumps are used to compare the final energy consumption and cost of different cooling systems. WFG can be a part of hydronic HVAC systems, and it is compatible with water-to-water heat pumps. Tables 6 and 7 illustrate the final energy consumption with different energy generators. It takes into account the effect of the operative temperature of the system [63]. The performance of water-to-water heat pumps (WWHP) depends on the inlet temperature of the WFG (θ*IN*), and the source inlet temperature (*Ts,i*) in the heat pump. A typical value of *Ts,i* ranges from 20 ◦C in ground source heat pumps (GSHP) to 35 ◦C in other WWHPs. The source and load sides are relevant when it comes to calculating the performance of the cooling device. Air-to-air heat pumps (AAHP) for heat recovery on ventilation are also analyzed. The parameters that influence air-to-air heat pumps' performance are the dry bulb exterior air temperature (*Te\_db*) and the dry bulb interior return air temperature (*Tri\_db*).

1 Energy efficiency ratio (ERR) values are taken from Appendix A in [63].

1 ERR values are taken from Appendix A in [63].

PEF stands for the primary energy factor from final energy (FE) to non-renewable final energy (NRFE). The Spanish code for thermal systems in buildings (RITE) recommends a value of 1.954. The factor of CO2 emissions for electricity was 0.331 [64]. The RITE aims to establish primary energy factors and CO2 emission factors, for each final energy consumed by buildings in Spain and for each geographic area with a different electricity generation source.

Table 6 shows that the best performance belongs to WWHP when the inlet temperature (θ*IN*) is close to 18 ◦C, and the source inlet temperature (*Ts,i*) in the heat pump is 20 ◦C. Figure 16 shows that it is possible to keep the cabin's indoor temperature within the comfort range by setting θ*IN* between 18 ◦C and 22 ◦C. Other systems, such as fan-coils, need lower operating temperatures. The lower the difference between *Ts,i* and θ*IN* the higher the EER coefficient. The NRFE consumption of GSHP is 0.065 kWh per m2 of WFG, and the average NRFE use of air-to-air heat pumps is 0.155 kWh per m2 of WFG. When it comes to CO2 emissions, air-to-air heat pumps generate an average of 0.027 KgCO2, twice as much as the CO2 emitted by GSHP.


**6. Conclusions**

It has been shown that the first and second kind Chebyshev polynomials play an important role in separating the even part from the odd part of several polynomials and special functions, which include the Appell polynomials, the first kind Bessel functions and the recently introduced Appell–Bessel functions [2]. This is another remarkable property of Chebyshev's classic polynomials within Function theory, which seems to be the counterpart of another, highlighted in [1], which showed its role in separating the real from the imaginary part of Appell's polynomials.

**Author Contributions:** Review and editing, P.N.; investigation, original draft preparation, P.E.R.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare that they have not received funds from any institution and that they have no conflict of interest.


**Karsten Klingberg, Adrian Stoller, Martin M ¨uller, Sabrina Jegerlehner, Adam D. Brown and Aristomenis Exadaktylos et al.**

Asylum Seekers and Swiss Nationals with Low-Acuity Complaints: Disparities in the Perceived level of Urgency, Health Literacy and Ability to Communicate—A Cross-Sectional Survey at a Tertiary Emergency Department

Reprinted from: *Int. J. Environ. Res. Public Health* **2020**, *17*, 2769, doi:10.3390/ijerph17082769 . . . **421**