Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal vs. Immortal Trees

The generalized Fibonacci numbers arise in models of growth and death [15], with interesting applications in medical sciences and statistics, such as dose escalation strategies in clinical drug trials [21]. Bronchial airway segments follow a Fibonacci pattern of bifurcation [7]. Experimental growth of tumor nodules can follow Fibonacci ratios related to dynamics of intratumoral pressure [20]. The associations of plant phyllotaxis and patterns of invertebrate growth with the Fibonacci series remain charming but puzzling connections to biology. Mechanistically, dislodgement, diffusion, and contact pressure models can be successfully applied to describe macroscopic growth patterns [17,23], but specific cellular rationales for such recursive patternings have been wanting.