Mathematical Description of Biological Structures and Mechanisms

A new formalism and approach to describing cellular and molecular processes and structures is introduced, designed to support the creation of knowledge bases of molecular and cellular mechanisms, structures, and states in which all structural information about the entities, at all levels of detail, is represented formally. Structure is formalized via specification of n-ary relationships, as in mathematical logic. New mathematical formulations of complexity and structural similarity are introduced, that take into account differences in composition and structure at all levels of detail and apply equally to structures, mechanisms, and states. A recursive formula for calculation of structural similarity is derived. The formalism and the mathematical similarity definition enable several new mathematical and computational capabilities, such as searching a knowledge bank for processes or structures similar to a specified one or with specified structural or compositional deviations.