Non-commutative Geometrical Drug Discovery<br/>—The Principle of Geometrical Regulation—

Abstract

We developed a theoretical framework for the regulation of biological macromolecules using the logically designed compounds. According to the cohomology theory, algebraic objects can be translated into geometrical ones. Successfully established quantum theory at 20th century, which essentially deals with the non-commutative nature of the space, also suggests the non-commutative topology of biological space. Arithmetic geometrical representation of the molecules as well as the macroscopic membranous structures would uncover their structural groups in Hilbert space. In order to construct the concrete image of biological space, here we combined quantum chemical (QC) model, all-atom (AA) model and coarse grained (CG) model, into one program designated 'NAGARA'. These three models can be arranged in an arbitrary manner to yield the desired statistical ensemble. For example, QC model was applied to the optimization of the chemical structure of anti-prion lead compound GN8. Arithmetic geometrical representation of these algebraic models is in progress.