**2. Methodology**

#### **2.1 Density functional theory calculations**

The Kohn-Sham (KS) methodology approach to Density Functional Theory (DFT) involves the determination of the electronic density, the molecular energy, and the orbital energies of a specific system, in particular, the HOMO and LUMO frontier orbitals which are intrinsically related to the chemical reactivity of the molecules [47–50]. The definitions for the global reactivity descriptors that form the core of Conceptual DFT are [30–35]:

$$\text{Electromagnetic} \quad \chi \approx \frac{1}{2} (\varepsilon\_L + \varepsilon\_H) \tag{1}$$

$$\text{Global Hardness} \quad \eta \approx (\varepsilon\_L - \varepsilon\_H) \tag{2}$$

*Computational Chemistry Study of Natural Apocarotenoids and Their Synthetic Glycopeptide… DOI: http://dx.doi.org/10.5772/intechopen.103130*

$$\text{Electropibility} \qquad \boldsymbol{\omega} \approx (\boldsymbol{\varepsilon}\_{\rm L} + \boldsymbol{\varepsilon}\_{\rm H})^2 / 4(\boldsymbol{\varepsilon}\_{\rm L} - \boldsymbol{\varepsilon}\_{\rm H}) \tag{3}$$

$$\text{Electrodonating Power} \quad \text{o} \,\text{"} \approx \left( \text{3} \varepsilon\_{\text{H}} + \varepsilon\_{\text{L}} \right)^{2} / \text{16} \eta \tag{4}$$

$$\text{Electroaccepted Power} \qquad o^+ \approx (\varepsilon\_H + \mathfrak{A}\varepsilon\_L)^2 / \mathfrak{16}\eta \tag{5}$$

$$\text{Net Efficiency} \quad \Delta o^{\pm} = o^{+} + o^{-} \tag{6}$$

being *ε<sup>H</sup>* and *ε<sup>L</sup>* the frontier orbital energies related to the molecular systems considered in this research. These global reactivity descriptors that arise from Conceptual DFT [30–35], have been complemented by the estimation of the Nucleophilicity Index N [51–55] that takes into account the value of the HOMO energy obtained using the KS scheme using an arbitrary shift of the origin with tetracyanoethylene (TCE) as a reference.

Conformational analysis of the studied molecules has been achieved using MarvinView 17.15 from ChemAxon [http://www.chemaxon.com], which was applied to undertake Molecular Mechanics calculations considering the MMFF94 force field [56–60]. This was followed in each case by a geometry optimization and frequency calculation using the Density Functional Tight Binding (DFTB) methodology [61]. This last step was required for the verification of the absence of imaginary frequencies as a confirmation of the stability of every optimized structure as being a minimum in the energy surface. The determination of the electronic properties and the Conceptual DFT reactivity descriptors of the studied molecules was addressed through the MN12SX/Def2TZVP/H2O model chemistry [62–64] because it has been previously shown that it verifies the KID procedure fulfiling the Ionization Energy Theorem, with the help of the Gaussian 16 software [61] and the context of the SMD solvation model [65]. The charge of all the molecules was taken as equal to zero whereas the radical anion and cation were considered in the doublet spin state. The SMD solvation model was chosen because it has been shown that it provides atomic charges of the Hirshfeld kind that are almost independent of the basis set and which are usually recommended for calculations within Conceptual Density Functional Theory.

#### **2.2 Computational pharmacokinetics and ADMET report**

The SMILES notation of each studied molecule was generated through the Online SMILES Translator and Structure File Generator [https://cactus.nci.nih.gov/translate/], and then was fed into the online program Chemicalize from ChemAxon [http://www. chemaxon.com], which was considered to get a glimpse of the potential therapeutic properties of the studied molecular systems (accessed: January 2022).

A similarity search in the chemical space of compounds with molecular structures that could be compared to the ones being studied, with already known biological and pharmacological properties, was achieved through the online Molinspiration software from Molinspiration Cheminformatics [https://www.molinspiration.com/] (accessed, January 2022).

Pharmacokinetics is a procedure that involves determining the likely fate of a medicinal molecule in the body, which is critical information in the creation of new medicine. Individual indices named Absorption, Distribution, Metabolism, Excretion, and Toxicity (ADMET) factors have typically been used to analyze the associated consequences. Chemicalize and the internet available pkCSM, a software for the prediction of small-molecule pharmacokinetic properties using SMILES, was also used to obtain additional information regarding the Pharmacokinetics parameters and ADMET indices [45].

## **3. Results and discussion**

#### **3.1 Conceptual DFT-based computational peptidology**

The optimized molecular structures of the three apocarotenoid glycopeptide conjugates considered through this research through the methodology presented before are displayed in **Figure 1**:

The quality of the chosen density functional may be realized by comparing its results with results from high-level computations or experiential values. Nevertheless, this comparison is not always computationally practicable because of the large size of the molecules or the lack of experimental results for the chemical methods being explored. Our research group has developed a methodology known as KID [20–24], as an aid to evaluating a particular density functional about its internal coherence. It is evident that within the Generalized Kohn-Sham (GKS) version of DFT, some relationships exist between the KID methodology and the Ionization Energy Theorem, which is a corollary of Janak theorem [25–29]. This is done by connecting *ε<sup>H</sup>* to -I and *ε<sup>L</sup>* to -A, through

$$J\_I = \varepsilon\_H + E\_{\mathbb{g}^\flat}(N-1) - E\_{\mathbb{g}^\flat}(N) \tag{7}$$

$$J\_A = \varepsilon\_L + E\_{\mathfrak{g}^\sharp}(\mathbf{N}) - E\_{\mathfrak{g}^\flat}(\mathbf{N} + \mathbf{1})\tag{8}$$

#### **Figure 1.**

*Optimized molecular structures of three apocarotenoid glycopeptide conjugates (Brown: C, blue: N, red: O, green: Cl, and white: H).*

*Computational Chemistry Study of Natural Apocarotenoids and Their Synthetic Glycopeptide… DOI: http://dx.doi.org/10.5772/intechopen.103130*

$$J\_{\rm HL} = \sqrt{{J\_I}^2 + {J\_A}^2} \tag{9}$$

Another KID descriptor ΔSL related to the difference in energies between the SOMO and the LUMO of the neutral system has been devised to aid in the verification of the accuracy of the methodology.

The MN12SX density functional has been shown to have a Koopmans-compliant behavior in earlier studies of the chemical reactivity of diverse molecular systems. However, for further validation of this model chemistry in the prediction of the chemical reactivity properties of the apocarotenoid glycopeptides conjugates considered here, additional research is necessary. The CDFT software tool was used to make this determination, and the findings are shown in **Table 1**:

The results from **Table 1** are very interesting because they show that there is an almost perfect fulfillment of the Janak and Ionization Energy theorems for the MN12SX/Def2TZVP/H2O model chemistry employed in this work.

Having verified that the MN12SX/Def2TZVP/H2O is the most adequate one for obtaining accurate results for the Conceptual DFT global reactivity descriptors, the estimated values for the Global Reactivity Descriptors (including the Nucleophilicity N) for the three molecular systems acquired utilizing the mentioned CDFT tool are displayed in **Table 2**:

The electronegativity (*χ*) and global hardness (*η*) are absolute values for the chemical reactivity that have not a known experimental counterpart. Indeed, they can be estimated by resorting to the experimental vertical ionization energy (I) and vertical electron affinity (A) but these values are not known for the molecule under study. A different thing can be said about electrophilicity *ω* and Nucleophilicity (N). The electrophilicity *ω* index involves a compromise between the tendency of an electrophile to acquire extra electron density and its resistance to exchange electron


*1: Teicoplanin-Bixin; 2: Teicoplanin-Methylcrocetin; 3: Teicoplanin-β-apo-8*<sup>0</sup> *-Carotenoic Acid.*

#### **Table 1.**

*Frontier orbital energies, H-L gap and the KID indices (all in eV) were used for the verification of the ionization energy theorem behavior of the MN12SX density functional in the study of the chemical reactivity of the synthetic conjugates of the glycopeptide Teicoplanin with several apocarotenoids.*


**Table 2.**

*Global reactivity descriptors for the synthetic conjugates of the glycopeptide Teicoplanin with several apocarotenoids: Electronegativity (χ), hardness (η), Electrophilicity (ω) (all in eV), softness S (in eV*�<sup>1</sup>*), Nucleophilicity N, Electrodonating power (ω*�*), Electroaccepting power (ω*þ*) and net Electrophilicity (*Δ*ω*�*) (also in eV).*

density with the environment [55]. By considering a group of Diels-Alder reactions and the electrophiles involved in them [53, 66, 67], classification of organic compounds as strong, moderate, or marginal electrophiles, that is an electrophilicity *ω* scale, was established, with *ω* larger than 1.5 eV for the first instance, with *ω* between 0.8 and 1.5 eV for the second case, and *ω* smaller than 0.8 eV for the final case [53, 66, 67]. By checking **Table 2**, it can be said that the three molecules may be regarded as strong electrophiles. Domingo and his collaborators [51–55] have also proposed a Nucleophilicity index N through the consideration of the HOMO energy obtained through the KS scheme with an arbitrary shift of the origin taking the molecule of tetracyanoethylene (TCE) as a reference. An analysis of a series of common nucleophilic species participating in polar organic reactions allowed them to establish a further classification of organic molecules as strong nucleophiles with N > 3.0 eV, moderate nucleophiles with 2.0 < N < 3.0 eV and marginal nucleophiles with

N < 2.0 eV. By checking again **Table 2**, it can be concluded that the three molecular systems may be considered also as strong nucleophiles.

It is interesting to see that in comparison with similar research with peptides [20–24], the MN12SX/Def2TZVP/H2O model chemistry retains its predictive ability even when the glycopeptides are conjugated with carotenoids, as in the present case. An important point is that the conjugates are predicted to be strong nucleophiles and electrophiles while the computed behavior for isolated peptides depicts them as moderate or even marginal nucleophiles and electrophiles.

#### **3.2 Computational pharmacokinetics and ADMET report**

The majority of medicinal drugs work by attaching to target protein molecules while at the same time modifying their functions. The Bioactivity Scores, which are a measure of the capacity of the molecules to act or coordinate with distinct receptors, are listed in **Table 3** for the three apocarotenoid glycopeptide conjugates:

These bioactivity scores for organic molecules can be interpreted as active (when the bioactivity score is greater than 0), moderately active (when the bioactivity score lies between 5.0 and 0.0) and inactive (when the bioactivity score is lower than 5.0).

The pharmacokinetics of a drug is evaluated through ADMET research, which is acronymous for Absorption, Distribution, Metabolism, Excretion, and Toxicity. If absorption is unsatisfactory, the distribution and metabolism of the drug would be changed, potentially resulting in nephrotoxicity and neurotoxicity. As a result, ADMET analysis is one of the most important aspects of computational drug design. In addition to the previous Conceptual DFT-based Computational Peptidology and Pharmacokinetics results, we are complementing this study with a report of the computed ADMET features as shown in **Table 4**:


#### **Table 3.**

*Bioactivity scores of the synthetic conjugates of the glycopeptide Teicoplanin with several apocarotenoids.*

*Computational Chemistry Study of Natural Apocarotenoids and Their Synthetic Glycopeptide… DOI: http://dx.doi.org/10.5772/intechopen.103130*


#### **Table 4.**

*Computed ADMET features of the synthetic conjugates of the glycopeptide Teicoplanin with several apocarotenoids.*

It is important to note that all the members of the group of studied molecules display positive values for the Human Gastrointestinal Absorption (HI), in particular for MOL3, and negative values for the AMES toxicity and Hepatotoxicity. All the molecular systems will be P-glycoprotein inhibitors (P-gp), being also P-gp substrates. None of the apocarotenoid glycopeptide conjugates will be inhibitors of the molecules related to cytochrome P450, displaying also a negative behavior as substrates of the CYP2D6 and CYP3A4 variants. Finally, all the molecular systems considered here will display a negative result regarding their behavior as hERG inhibitors. These results are comparatively similar to those presented within the study of the structural and biochemical properties of lipophilic apocarotenoid conjugates of Teicoplanin and its pseudoaglycone that inspired this research [14].

### **4. Conclusions**

The chemical reactivities of three apocarotenoid glycopeptide conjugates have been thoroughly investigated by optimizing their structures using the DFTB methodology and calculating their electronic properties using high-quality model chemistry, namely MN12SX/Def2TZVP/H2O. This model chemistry was already used in previous research, demonstrating its utility for this type of calculation. However, an involved estimation of the KID descriptors for all the molecules demonstrated the ability of the MN12SX density functional for the accurate estimation of the frontier orbital energies based on the KID procedure methodology. The fact that the energy of the LUMO and the SOMO (or the HOMO energy of the anion) are almost the same, which is reflected in the KID accuracy descriptor ΔSL being very close to zero, is an indication that the derivative discontinuity is negligible for the chosen density functional. This is translated as the ability of the LUMO energy to reflect with precision the Electron Affinity of the molecule, implying that the chemical reactivity parameters obtained by considering this density functional will be very accurate. This is a very important result because it allowed the estimation of the accuracy of the results based only on the fulfillment of some intrinsic requirements (like the Janak and Ionization Energies) without the need to resort to the comparison with experimental results that could not be available, as in the present case.

By considering our suggested Conceptual DFT-based Computational Peptidology methodology, the three apocarotenoid glycopeptide conjugates have been studied by applying certain techniques generally used in the procedure of drug discovery and development, showing that these molecular systems may be regarded as potential therapeutic drugs. The biological targets, physicochemical attributes, and ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) indices associated with their bioavailability and pharmacokinetics were forecasted and analyzed as descriptors that could be useful in future drug development research.

It may be concluded that the results coming from the present study may be of importance for the pharmaceutic industry because they show that the proposed three apocarotenoid glycopeptide conjugates fulfilled the objective of increasing the lipophilicity while at the same time avoiding the risk of the associated toxicity.

### **Acknowledgements**

NFH and DGM are researchers of CIMAV and CONACYT (Mexico) and want to thank both institutions for partial support.

*Computational Chemistry Study of Natural Apocarotenoids and Their Synthetic Glycopeptide… DOI: http://dx.doi.org/10.5772/intechopen.103130*
