Comparative analysis of the trypanocidal activity and chemical properties of E-lychnophoric acid and its derivatives using theoretical calculations

E-Lychnophoric acid 1, its derivative ester 2 and alcohol 3 killed 100% of trypomastigote blood forms of Trypanosoma cruzi at the concentrations of 13.86, 5.68, and 6.48 μg/mL, respectively. Conformational distribution calculations (AM1) of 1, 2 and 3 gave minimum energies for the conformers a, b, c, and d, which differ from each other only in the cyclononene ring geometry. Calculations (DFT/ BLYP/6-31G*) of geometry optimization and chemical properties were performed for conformers of 1, 2, and 3. The theoretical results were numerically compared to the trypanocidal activity. Calculated values of atomic charge, orbital population, and vibrational frequencies showed that the C-4–C-5 π-endocyclic bond does not affect the trypanocidal activity of the studied compounds. Nevertheless, the structure of the group at C-4 strongly influences the activity. However, the theoretical results indicated that the intraring (C-1 and C-9) and π-exocycle (C-8 and C-14) carbons of caryophyllene-type structures promote the trypanocidal activity of these compounds.


Introduction
Chagas' disease (American trypanosomiasis) is a major cause of cardiomyopathy in South America.During the last years, the search for new chemical strategies to eliminate bloodstream forms of Trypanosoma cruzi has led to several compounds with trypanocidal activity [1], such as anfotericin B, tricomicin, β-carbolinic alkaloids, flavonoids, naphthoquinones, sesquiterpene lactones, triterpenes, and steroids [1][2][3][4].Although some of them show in vitro and in vivo activities, they often can not be used, because they present low solubility in water or toxicity in active doses [5].Gentian violet is able to kill T. cruzi trypomastigotes and sterilize blood at 4 o C, but there are some restrictions to its use, for instance potential mutagenicity and microaglutination [6].Additionally, gentian violet changes blood color and this fact promotes its rejection by patients [7].
The carboxylic group in 1 raises the question about the possible influence of the chemical function at C-4 on the trypanocidal activity of the caryophillene-type structures.In order to identify the major trypanocidal substances, two E-lychnophoric acid derivatives were prepared in this work: E-lychnophoric acid methyl ester 2, methyl bicycle[7.

Preparation of 1 and its derivatives
Thin Layer Chromatography for analytical (TLC) and preparative (PTLC) purposes was carried out on silica gel G. Anisaldehyde/H 2 SO 4 was used as spraying reagent.GC-MS was performed using a Hewlett-Packard HP5890 Series 2 gas chromatograph coupled to a mass spectrometer HP5989A.The analyses were carried out in duplicate using a BP-5 column.Analysis conditions: column temperature gradient: 150 o C (1 min) and 290 o C (10 min); injection volume: 2 µL of hexane solution.The temperature of the injector was the same of the detector: 300 o C. IR spectra were measured in a KBr disc using a Shimadzu IR-408 apparatus.NMR spectra (400 MHz) were measured using a Bruker AM-400, and TMS as internal standard.

In vitro trypanocidal test
Test samples were dissolved in DMSO (0.2 mL) plus Krebs-Ringer-glucose (1.8 mL) and mixed with infected blood (0.2 mL).Control tubes with DMSO and gentian violet (125 µg/mL) were run in parallel.After incubation at 4 o C for 24 h, the suspensions were microscopically examined.Only samples that killed 100% of the parasites were considered active [8].
Comparative analyses of the trypanocidal activity (TA) were made based on the variation of the necessary concentration of 1, 2 and 3 to kill 100% of trypomastigotes in vitro.For convenience, TA values of ester 2 and alcohol 3 were determined relative to the concentration of the acid 1.Thus, the TA value was always considered to be the unity (TA = 1.00) for this compound.

Theoretical Methodology
Theoretical studies were carried out using the software packages TITAN [15] and Gaussian03W [16].Geometries optimized by the semi-empirical AM1 [17] were used as an initial model for the optimizations by the Density Functional Theory (DFT) [18] with the functional BLYP [19,20] and the 6-31G* [21][22][23][24][25] (BLYP/6-31G*) set of bases.The geometries obtained by theoretical calculations were characterized as true minimal energy only when all the calculated frequencies (PES) were positive, considering the absence of intermolecular interactions in the gaseous state.
Calculations (DFT/BLYP/6-31G*) of energy and atomic contributions (orbital population) of the occupied and the virtual molecular orbitals (MO's) were made after geometry optimization on the same calculation level.Calculations (DFT/BLYP/6-31G*) of atomic charge were made by the Mulliken method with unities in electrons.
Calculated chemical properties were appropriately presented with average values.These averages were determined from chemical property values of the conformers of 1, 2, and 3 that presented higher populations.Thus, the values of chemical properties of conformers with relatively small populations were disregarded.
Similar to the trypanocidal activity analysis, average values of chemical properties of 1, 2 and 3 were presented a function of acid 1.Thus, for this compound, the average values were considered to be the unity.At the point corresponding to ester 2, a multiplying factor X was applied to make the average values of chemical properties equal to the TA value this compound.The same multiplying factor X was also used to establish the average values of chemical properties for alcohol 3. The better congruence between average chemical property and TA values obtained for 3 must probably indicate a better relationship with the alleged chemical activity.

In vitro trypanocidal test
At the test conditions, 1, 2 and 3 were able to kill 100% of bloodstream form T. cruzi at concentrations of 13.86, 5.68 and 6.48 µg/mL, respectively.Although the compounds had shown significantly different activities (3 and 2 are about two times more active than 1), they are chemically related.This fact suggests some influence of the groups at C-4 on the trypanocidal activity.By comparative analysis of trypanocidal activity between these compounds as a function of concentration for the activity of acid 1, the TA relative values for 1, 2 and 3 are 1.00, 2.44 and 2.13, respectively.Thus, for all cases, ∆TA = 2.13 was considered as a congruence factor between biological activity and chemical properties.

Conformational analysis
Initially, conformational distribution calculations (AM1) for 1, 2, and 3 were made.The obtained geometries were submitted to geometry optimization calculations (DFT/BLYP/6-31G*).For each compound, four conformers a, b, c, and d were generated from these calculations as minimal energies.Figure 2 shows the geometries of the conformers of 1, which are different from each other only in the skeleton conformation of the cyclononene ring.Table 1 presents the results of thermodynamic calculations (DFT/BLYP/6-31G*) of the conformers of 1, 2 and 3.For each compound, conformer a presents relatively lower enthalpy, with a value close to those of conformers b and ñ.The largest enthalpy of conformer d could indicate its smaller contribution to the conformational populations of 1, 2, and 3. Nevertheless, in the case of structurally simple cycloalkanes, conformational analyses based only on enthalpy calculations, can differ from those experimentally observed [26][27][28][29][30] .Therefore, the conformational population of these caryophillenetype structures can be better investigated by enthalpy and free energy calculations.According to Table 1, the enthalpy variation between the conformers of each compound is not very significant.The results in free energy values follow the same order of stability of the conformers proposed by enthalpy.
For cycloalkanes, conformational stability depends on the total tension of the ring, which is made up of angular, torsional and bond tensions, as well as van der Waals compressions.In medium rings (C 8-11 ), van der Waals compressions are due mainly to transannular tensions involving hydrogen atoms of adjacent methylene groups.When determined experimentally, the total tension of the cyclononane in relation to the n-nonane is of the order of 12.6 kcal/mol [31].In many cases, the transannular tensions can significantly influence the conformational stability of cyclic structures similar to those of caryophyllene-type structures.Theoretical studies carried out by Molecular Mechanics show that the angular deformations caused by transannular tensions in cyclononanes favor geometries with bond angles of 124 degrees [31,32].
The average angles (θ av ) of the cyclononene C-C-C bonds obtained by DFT/BLYP/6-31G* optimized geometries of the conformers of 1, 2 and 3 are presented in Table 1.For each compound, conformer a, which presents the lowest energy¸ also has the smallest value of θ av (≈ 116.7 degrees).In contrast, conformer d, which presents the highest energy, has a larger value of θ av (≈ 119.1 degrees).These results demonstrate a relation between the enthalpy and the θ av angles in cyclononane rings.Calculations (DFT/BLYP/6-31G*) of geometry optimization of non-substituted cyclononane were performed and gave a value of θ av (116.20 degrees) very close to those of conformers a (Table 1).Therefore, smaller van der Waals compressions are expected for 1a, 2a e 3a.
As in Table 1 the values of ∆G of conformers a, b, and c of each compound are very close and significantly smaller in relation to those of conformer d (≈ 7.6 kcal/mol).It is expected that its contribution to the conformational distribution of 1, 2, and 3 is not significant.exocyclic system in the trypanocidal activities of these compounds.As demonstrated by the larger atomic charge on C-14 in relation to C-8 (q 14 〉〉 〉〉 〉〉 〉〉 〉〉 q 8 ), if there are effects of electrostatic interactions of the π exocyclic system on the biological activity, the electrophilic character of C-8 and/or the nucleophilic character of C-14 must be considered.Table 3 list the DFT/BLYP/6-31G* calculated average orbital population for occupied (∆c o ) and virtual (∆c v ) MO's of 1, 2, and 3 as function of 1, considering only the results closer to ∆TA.The larger congruencies in relation to the .Thus, the results of these calculations suggest a more significant involvement of both the exocyclic π system and the cyclobutane ring in the trypanocidal activity of these caryophyllene compounds.

Conclusions
According to the trypanocidal tests carried out, the alteration of caryophillene structure due to the substituent group in C-4 can affect the potential activity of 1, 2, and 3.The geometry optimization calculations (DFT/BLYP/6-31G*) do not show any effect of these substituents in the conformational analysis of the caryophillene skeleton.Thus, the trypanocidal action of 1, 2 and 3 cannot be related to the spatial changes on the caryophillene skeleton given by the different substituent groups in C-4.
However, theoretical calculations show an effect of the substituent on the chemical properties related to the C-1-C-9 bond and the exocyclic π (C-8-C-14) and the endocyclic π (C-4-C-5) systems.Comparing the results of the trypanocidal test with the chemical properties calculated for 1, 2, and 3 lead us to conclude that the activity may be determined by the chemical properties of the exocyclic π bond and the C-1-C-9 bond of both the cyclobutane ring.Despite the spatial proximity of the substituent group to the endocyclic π system, the theoretical calculations performed did not allow an inference about the relation between the chemical properties of this π system and the trypanocidal activities of 1, 2, and 3.

Figure 2 .
Figure 2. Geometries of conformers from 1a to 1d generated by the conformational search (AM1) and optimized by calculations (DFT/BLYP/6-31G*).Conformers corresponding to 2 and 3 present the same geometries of the cyclononen ring, showed in that figure for 1

, b, c and d of 1, 2 and 3
# 298.15K and 1 atm

Table 2 .
Calculated average energies (DFT/BLYP/6-31G*) of occupied and virtual frontier MO's between conformers of 1, 2 and 3, and comparative analyses as function of the correspondent values of 1 a

Table 3 .
Calculated average of atomic charge (∆q) and orbital populations (DFT/BLYP/6-31G*) of occupied (∆c o ) and virtual (∆c v ) frontier molecular orbitals of the conformers of 1, 2 and 3 by comparative analyses as function of the corresponding values obtained for 1