Elementary vectors are fundamental objects in polyhedral geometry. In metabolic pathway analysis, elementary vectors rangefrom elementary flux modes (of the flux cone) and elementary flux vectors (of a flux polyhedron) via elementary conversion modes (of the conversion cone) to minimal cut sets (elementary vectors of a dual cone) in computational strain design.
Given the mixed audience of the seminar, I first introduce standard models of metabolism and related optimization problems (for growth or production rate). Most importantly, all feasible solutions (optimal or suboptimal) can be written as conformal sums of elementary vectors (sums without cancellations). In fact, for certain problems, optimal solutions are elementary vectors themselves.
In my latest work, I introduce new classes of elementary vectors for more refined models of cellular growth, where individual synthesis reactions for macromolecules replace the traditional ''biomass reaction’’. For general growth models (kinetic or constraint-based), I define elementary growth modes, for constraint-based models (aka RBA models), I further define elementary growth vectors, and I present the corresponding conformal sum theorems. Finally, I illustrate definitions and results in examples of minimal networks.