  There is considerable theoretical and experimental support to the proposal
that tissue homeostasis in the adult skin can be represented as a critical
branching process. The homeostatic condition requires that the proliferation
rate of the progenitor (P) cells (capable of cell division) is counterbalanced
by the loss rate due to the differentiation of a P cell into differentiated (D)
cells so that the total number of P cells remains constant. We consider the
two-branch and three-branch models of tissue homeostasis to establish
homeostasis as a critical phenomenon. It is first shown that some critical
branching process theorems correctly predict experimental observations. A
number of temporal signatures of the approach to criticality are investigated
based on simulation and analytical results. The analogy between a critical
branching process and mean-field percolation and sandpile models is invoked to
show that the size and lifetime distributions of the populations of P cells
have power-law forms. The associated critical exponents have the same
magnitudes as in the cases of the mean-field lattice statistical models. The
results indicate that tissue homeostasis provides experimental opportunities
for testing critical phenomena.
