Systems biology and deviation curvature tensor

In this article, we study the robustness of biological systems by means of the eigenstructure of the deviation curvature tensor. This is the differential geometric theory of the variational equations for deviation of whole trajectories to nearby ones. We apply this theory to the Van der Pohl equations and some biological models, and examine the relationship between the linear stability of steady-states and the stability of transient states. The main application is the G(1)-model for the cell cycle, where Jacobi stability reveals the robustness and fragility of the cell arrest states and suggests the existence of more subtle checkpoints. (c) 2005 Elsevier Ltd. All rights reserved.