  The two-dimensional cell-sorting problem is found to be mathematically
equivalent to the one-dimensional random walk problem with pair creations and
annihilations, i.e. the adhesion probabilities in the cell-sorting model relate
analytically to the expectation values in the random walk problem. This is an
example demonstrating that two completely different biological systems are
governed by a common mathematical structure. This result is obtained through
the equivalences of these systems with lattice spin models. It is also shown
that arbitrary generation operators can be written by the spin operators, and
hence all biological stochastic problems can in principle be analyzed utilizing
the techniques and knowledge previously obtained in the study of lattice spin
systems.
