Title (srp)

Komparativno ispitivanje molekulskih deskriptora zasnovanih na sopstvenim vrednostima

Author

Redžepović, Izudin, 1993-

Contributor

Furtula, Boris, 1978-
Gutman, Ivan, 1947-
Marković, Svetlana, 1959-
Arsić, Biljana B.

Description (srp)

Molekulski deskriptori su brojevi ili nizovi brojeva koji se koriste za kvantifikovanjemolekulske strukture. Posebna klasa molekulskih deskriptora su grafovske invarijante. Poznatesu i kao topoloski molekulski deskriptori. Izvo ˇ denje ovih deskriptora omoguceno je zamenom ´molekula molekulskim grafom. Mnoge korisne matematicke veli ˇ cine mogu se izra ˇ cunati iz ˇmolekulskog grafa, npr. sopstvene vrednosti. Stoga je postalo moguce konstruisati molekulske ´deskriptore koji se zasnivaju na sopstvenim vrednostima. Oni se nazivaju topoloski molekulski ˇdeskriptori zasnovani na sopstvenim vrednostima. Danas ih ima mnostvo. Samo nekoliko ˇnjih koristi sopstvene vrednosti dobijene iz klasicne matrice susedstva. Me ˇ du njima se isticuˇenergija grafa, Estradin indeks i rezolventna energija. U okviru ove doktorske disertacijeizvrseno je uporedno ispitivanje ovih deskriptora. ˇPrvi deo poglavlja Rezultati i diskusija izvestava o rezultatima u vezi sa istra ˇ zivanjem rela- ˇcija izmedu energije grafa, Estradinog indeksa i rezolventne energije. Tri topoloska molekulska ˇdeskriptora zasnovana na sopstvenim vrednostima uporedena su pomocu nekoliko skupova ´alkana i benzenoidnih ugljovodonika. Otkrivene su i diskutovane relacije medu njima. Identifikovani su strukturni parametri koji upravljaju ovim odnosima i dobijene su odgovarajuce´formule zasnovane na visestrukoj linearnoj regresiji. Pokazalo se da sva tri istra ˇ zena indeksa ˇkodiraju gotovo iste strukturne informacije o molekulu. Oni se razlikuju samo po stepenuosetljivosti na grananje molekula i po broju nevezivnih molekulskih orbitala.Dalja analiza energije grafa, Estradinog indeksa i rezolventne energije vezana je za degenerativnost ovih deskriptora. Da bi se testirao diskriminativni potencijal ovih deskriptora,korisˇceno je nekoliko klasa izomera hemijskih stabala. U ovim skupovima broj atoma ugljeni- ´ka se kretao od 9 do 20. Kvantifikovanje degenerativnosti je uradeno pomocu dobro utvr ´ denevelicine. Rezultati pokazuju da energija grafa i Estradin indeks imaju sli ˇ can nivo degenera- ˇtivnosti. Nagla promena degenerativnosti rezolventne energije u slucaju hemijskih stabala ˇzahtevala je dodatno ispitivanje. Dobijeni rezultati su pokazali da postoji mnogo hemijskihstabala sa istom rezolventnom energijom. Ona se zovu 푟–ekvienergetska hemijska stabla. Zatim su predstavljeni podaci vezani za pretrazivanje rezolventnih ekvienergetskih hemijskih ˇstabala.Treci deo poglavlja Rezultati i diskusija donosi rezultate o strukturnoj osetljivosti ener- ´gije grafa, Estradinog indeksa i rezolventne energije na nekoliko serija katakondenzovanihi perikondenzovanih izomernih benzenoidnih ugljovodonika. Strukturna osetljivost je jednood najvaznijih i najmanje istra ˇ zenih svojstava grafovskih invarijanti. Nedavno je predstavlje- ˇna nova metoda za procenu strukturne osetljivosti topoloskih molekulskih deskriptora. Ovaj ˇalgoritam se sastoji od nekoliko razlicitih koraka. Zasnovan je na Tanimoto indeksu i Morga- ˇnovim kruznim fingerprintovima. Utvr ˇ deno je da energija grafa, Estradin indeks i rezolventnaenergija imaju slicnu strukturnu osetljivost na katakondenzovane izomere. Energija grafa je ˇnajosetljivija na male promene u perikondenzovanim benzenoidnim ugljovodonicima. Poredtoga, osetljivost ovih deskriptora testirana je na katakondenzovanim izomerima sa razlicitim ˇbrojem zaliva, uvala i fjordova. Otkriveno je da se vrednost ovih deskriptora postepeno menja sa postepenim povecanjem broja ovih strukturnih detalja. Estradin indeks i rezolventna ´energija se slicno pona ˇ saju, i u nekim slu ˇ cajevima pokazuju istu strukturnu osetljivost. To se ˇmoze pripisati visokoj korelaciji izme ˇ du njih.U cetvrtom delu poglavlja Rezultati i diskusija predstavljeni su rezultati ispitivanja uticaja ˇcikla na vrednost energije grafa, Estradinog indeksa i rezolventne energije. Naime, pokazanoje da indeksi dobro opisuju fine strukturne detalje, te se moze pretpostaviti da ukoliko znamo ˇkako je deskriptor koreliran sa strukturom onda mozemo da saznamo i kako osobine zavise ˇod strukture. U cilju ispitivanja uticaja cikla na vrednost molekulskih deskriptora zasnovanihna sopstvenim vrednostima dizajnirana su tri in silicio eksperimenta .Poslednji deo ovog poglavlja predstavlja rezultate potencijalne hemijske primenljivostinasih deskriptora. Ta ˇ cnije, ispitan je potencijal predvi ˇ danja fizicko–hemijskih osobina. Ener- ˇgija grafa, Estradin indeks i rezolventna energija testirani su kao orude za predvidanje tacke ˇkljucanja, toplote obrazovanja i koeficijenta raspodele oktanol/voda alkana. Pokazano je da ˇse molekulski deskriptor zasnovan na sopstvenim vrednostima ne moze pojedina ˇ cno koristiti ˇza uspesno predvi ˇ danje ovih fizicko–hemijskih osobina. Prvi zagreba ˇ cki indeks, broj nula u ˇspektru i broj metil grupa, takode, moraju biti ukljuceni u modele. Dobijene statisti ˇ cke ve- ˇlicine pokazuju da su modeli konstruisani pomo ˇ cu Estradinog indeksa i rezolventne energije ´znatno bolji od modela sa energijom grafa. Takav trend je jos izra ˇ zeniji u slu ˇ caju koeficijenta ˇraspodele oktanol/voda alkana

Description (srp)

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Description (eng)

Molecular descriptors are numbers or series of numbers used for quantification of molecular structure. A special class of molecular descriptors are graph invariants. They are alsoknown as topological molecular descriptors. The derivation of these descriptors has beenenabled by the substitution of molecule by a molecular graph. Many useful mathematicalquantities may be calculated from a molecular graph, e.g., eigenvalues. Therefore, it became possible to construct molecular descriptors that are using eigenvalues. These are calledeigenvalue–based topological molecular descriptors. Today, there are plethora of them. Onlyfew of them are using eigenvalues obtained from the ordinary adjacency matrix. The graphenergy, Estrada index, and resolvent energy are the most prominent among them. Within thisdoctoral dissertation comparative investigation of these descriptors have been performed.The first part of Results and discussion chapter reports results regarding investigation ofrelationships among graph energy, Estrada index, and resolvent energy. Three eigenvalue–based topological molecular descriptors are compared using several datasets of alkanes andbenzenoid hydrocarbons. The relations among them are found and discussed. Structural parameters that govern these relations are identified and the corresponding formulae based onmultiple linear regression have been obtained. It has been shown that all three investigatedindices are encoding almost the same structural information of a molecule. They differ onlyby the extent of the sensitivity on a structural branching of a molecule and on the number ofnon–bonding molecular orbitals.Further analysis of the graph energy, the Estrada index, and the resolvent energy isconcerned with the degeneracy of these descriptors. To test discriminative potential of thesedescriptors, several classes of chemical-tree-isomers have been employed. In these sets numberof carbon atoms ranged from 9 up to 20. The quantification of degeneracy has been done usingwell–established measure. The results show that graph energy and Estrada index exert similardegeneracy level. The specious degeneracy of the resolvent energy in the case of chemicaltrees is discussed. Obtained results indicated that there are many chemical trees with thesame resolvent energy. These are called 푟–equienergetic chemical trees. Then, the results onsearching for resolvent equienergetic chemical trees are given.The third part of Results and discussion chapter brings results on structural sensitivityof the graph energy, the Estrada index, and the resolvent energy on several series of catacondensed and pericondensed isomeric benzenoid hydrocarbons. Structural sensitivity is oneof the most important and the least investigated property of graph invariants. Recently, anovel method for assessing the structural sensitivity of topological molecular descriptors wasput forward. This algorithm consists of several different steps. It is based on Tanimoto indexand Morgan circular fingerprints. It was found that graph energy, Estrada index, and resolvent energy exert similar structural sensitivity on catacondensed isomers. The graph energyshowed best performance on pericondensed molecules. Additionally, the sensitivities of thesedescriptors were tested on the catacondensed isomers with the increasing number of bays,coves, and fjords. It was revealed that these descriptors gradually change with the increasingnumber of these structural features. The Estrada index and resolvent energy perform similarlyand in some cases with the same structural sensitivity. This may be attributed to the highcorrelation between them.The fourth part of the Results and discussion chapter presents the results of the examinationof the influence of the cycle on the value of the graph energy, the Estrada index, and thevresolvent energy. Namely, it has been shown that indices describe fine structural details well,so it can be assumed that if we know how the descriptor correlates with the structure thenwe can also find out how the properties depend on the structure. In order to examine theinfluence of a cycle on the value of molecular descriptors based on the eigenvalues, three푖푛 푠푖푙푖푐표 experiments were designed.The last part of this chapter presents results of potential chemical applicability of ourdescriptors. More precisely, predictive potential of eigenvalue–based topological moleculardescriptors was examined. The graph energy, the Estrada index, and the resolvent energy weretested as parameters for the prediction of boiling points, heats of formation, and octanol/waterpartition coefficients of alkanes. It was shown that an eigenvalue–based molecular descriptorcannot be individually used for successful prediction of these physico–chemical properties.The first Zagreb index, the number of zeros in the spectrum and the number of methyl groupsmust be also involved in the models. Performed statistics showed that the models constructedusing the Estrada index and the resolvent energy are significantly better than ones withthe graph energy. Such trend is even more noticeable in the case of octanol/water partitioncoefficients of alkanes.

Object languages

Serbian

Date

2021

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