## Emergent Properties of Feedback Regulation and Stem Cell Behavior in a Granulopoiesis Model as a Complex System

Yutaka Saikawa
To identify the internally generative theoretical relationship between microscopic mechanisms and the macroscopic behavior of hematopoietic processes as a complex system, a computer simulation of granulopoiesis was exploited by developing a cellular automaton (CA) model. Hematopoietic stem cells (HSCs) distribute themselves to proliferate and differentiate in a three-dimensional analytical space. The number of mitotic events of the cells in a proliferating phase, the transit times (T) of each of 15 differential stages progressing from a HSC to a mature cell, the duplication times ($T dup$) of HSCs, and the neighborhood rules for cell proliferation were all incorporated as analytical parameters in this space. Homeostatic granulopoiesis originating from a single HSC was successfully achieved. An important part is the stabilization of cell production induced by way of negative feedback following external perturbation of the peripheral granulocyte numbers. Single-cell kinetic analyses describe the behavior of differentiating cells and HSCs as fluctuating their T and self-renewal time ($T dup$) in response to the feedback dynamics. Stochastic cell divisions of HSCs were recruited in a transitional manner resulting in the generation of a regulatory effect on the differentiation--commitment processes. The concept that local cellular interaction produces global dynamics in a granulopoietic system was reified by CA modeling. This approach will provide a framework for analyzing the behavior of HSCs and enable an understanding of the abnormal kinetics of hematopoietic diseases.