  Identifying the mechanism of intercellular feedback regulation is critical
for the basic understanding of tissue growth control in organisms. In this
paper, we analyze a tissue growth model consisting of a single lineage of two
cell types regulated by negative feedback signalling molecules that undergo
spatial diffusion. By deriving the fixed points for the uniform steady states
and carrying out linear stability analysis, phase diagrams are obtained
analytically for arbitrary parameters of the model. Two different generic
growth modes are found: blow-up growth and final-state controlled growth which
are governed by the non-trivial fixed point and the trivial fixed point
respectively, and can be sensitively switched by varying the negative feedback
regulation on the proliferation of the stem cells. Analytic expressions for the
characteristic time scales for these two growth modes are also derived.
Remarkably, the trivial and non-trivial uniform steady states can coexist and a
sharp transition occurs in the bistable regime as the relevant parameters are
varied. Furthermore, the bi-stable growth properties allows for the external
control to switch between these two growth modes. In addition, the condition
for an early accelerated growth followed by a retarded growth can be derived.
These analytical results are further verified by numerical simulations and
provide insights on the growth behavior of the tissue. Our results are also
discussed in the light of possible realistic biological experiments and tissue
growth control strategy. Furthermore, by external feedback control of the
concentration of regulatory molecules, it is possible to achieve a desired
growth mode, as demonstrated with an analysis of boosted growth, catch-up
growth and the design for the target of a linear growth dynamic.
