title: Global dynamics of two-compartment models for cell production systems with regulatory mechanisms.
abstract: We present a global stability analysis of two-compartment models of a hierarchical cell production system with a nonlinear regulatory feedback loop. The models describe cell differentiation processes with the stem cell division rate or the self-renewal fraction regulated by the number of mature cells. The two-compartment systems constitute a basic version of the multicompartment models proposed recently by Marciniak-Czochra and collaborators [25] to investigate the dynamics of the hematopoietic system. Using global stability analysis, we compare different regulatory mechanisms. For both models, we show that there exists a unique positive equilibrium that is globally asymptotically stable if and only if the respective reproduction numbers exceed one. The proof is based on constructing Lyapunov functions, which are appropriate to handle the specific nonlinearities of the model. Additionally, we propose a new model to test biological hypothesis on the regulation of the fraction of differentiating cells. We show that such regulatory mechanism is incapable of maintaining homeostasis and leads to unbounded cell growth. Potential biological implications are discussed.
authors.affiliation: BCAM-Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain; TU Dresden, Fachrichtung Mathematik, Institut für Analysis, 01062 Dresden, Germany.
authors.forename: Philipp
authors.initials: P
authors.lastname: Getto
authors.forename: Anna
authors.initials: A
authors.lastname: Marciniak-Czochra
authors.forename: Yukihiko
authors.initials: Y
authors.lastname: Nakata
authors.forename: Maria dM
authors.initials: Md
authors.lastname: Vivanco
mesh_terms: D053687:Adult Stem Cells / Q000166:cytology*; D002454:Cell Differentiation; D049109:Cell Proliferation; D019295:Computational Biology; D025461:Feedback, Physiological; D006413:Hematopoietic System / Q000166:cytology; D006706:Homeostasis; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics
keywords: Cell production system; Global stability; Lyapunov function; Regulatory mechanism