The molecular design of biologically active acridine derivatives using the graph theory

The problem of modeling the relationship between the structure and the biological activity of organic compounds is one of the urgent mathematical problems of chemistry. To find quantitative correlations of the structure - anti-inflammatory activity in the isostructural series of substituted 9-thioacridone, acridinyl-9-thioacetic acids and 9-hydrazine acridine the molecular connectivity indices calculated for the given molecular structures have been used. The correlation equations of lgA - f (xr) relationship with the convincing statistical characteristics have been determined. They will be used for the molecular design of active pharmacophores.

Determination of the quantitative relationship between the structure and its biological activity is one of the most important tasks of designing pharmacologically active substances. Formation of this relationship is the only reasonable alternative to the very expensive total screening. As a tool the graph theoretical and topological representations playing an increasing important role in various chemical and pharmaceutical studies can be used [1-3].

Molecular structures of organic compounds are in fact graphs, in which atoms are vertices, and covalent chemical bonds are edges. Such a graph describes the connectivity of atoms in the molecular skeleton regardless of metric features, i.e. the equilibrium internuclear distances, valence angles, etc., corresponding

to the chemical structure. Therefore, graph theoretical description reflects those features of the molecular structure that depend on the connectivity as opposed to properties conditioned by the precise geometric arrangement of atoms constituting the molecule in space. It is in this meaning that chemical graphs are topological (but not geometrical) values of molecular structures. Thus, the chemical graph describes the topology of the molecule. Numeric indices derived from topological characteristics of the corresponding chemical graphs are called topological indices.

One of the most successfully used topological indices to determine quantitative relationships of the structure - biological activity is the molecular connectivity index ≡r introduced by Randic:

≡r = Σ (Vi ∙Vj)-1∕2 (1)

where Vi,Vj - are the vertex degrees of i and j in the graph; the summation is carried out for all edges of the graph.

or the reference drug (diclofenac sodium) were introduced intraperitoneally 40 min before induction of the pain response. The control group of mice received the same amount of saline solution with the emulsifier Tween-80. After the injection of formalin solution the mice were placed in a cage and observed for 40 min recording the time spent by the animals for licking the swollen limb. The antinociceptive activity was judged by the ability of the compounds under study to reduce the time of the swollen limb licking [5].

Correlation analysis was carried out according to the microstatistics [6].


  1. Correlation of the relationship of the anti-inflammatory activity of acridine derivatives with their molecular connectivity indices has been conducted.
  2. The correlation equations obtained will be used for the molecular design of more active pharmacophores in these isostructural series.



  1. Коваленко С.Н., Друшляк А.Г., Черных В.П. Основы комбинаторной органической химии. - Харьков: НФаУ «Золотые страницы», 2003. - 106 с.
  2. Виноградова М.Г., Папулова Д.Р., Артемьев А.А. Теория графов в исследовании корреляций «структура-свойства» // Успехи современного естествознания. - 2006. - №11. - С. 37-38.
  3. Иванов В.В., Спета Л.А. Расчетные методы прогноза биологической активности органических соединений. - Харьков: ХНУ, 2003. - 71 с.
  4. Химические приложения топологии и теории графов. - М.: Мир, 1987. - 560 с.
  5. Tjolsen A., Berge D., Hunskaar S. et al. The formalin test: an evaluation of the method // Puin. - 1992. - Vol. 51. - P. 5-17.
  6. Львовский Е.Н. Статистические методы построения эмпирических формул. - М.: Высш. шк., 1988. - 239 с.
Year: 2017
City: Almaty
Category: Medicine