  In a recent letter, a simple method was proposed to generate solvable models
that predict the critical properties of statistical systems in hyperspherical
geometries. To that end, it was shown how to reduce a random walk in $D$
dimensions to an anisotropic one-dimensional random walk on concentric
hyperspheres. Here, I construct such a random walk to model the
adsorption-desorption transition of polymer chains growing near an attractive
cylindrical boundary such as that of a cell membrane. I find that the fraction
of adsorbed monomers on the boundary vanishes exponentially when the adsorption
energy decreases towards its critical value. When the adsorption energy rises
beyond a certain value above the critical point whose scale is set by the
radius of the cell, the adsorption fraction exhibits a crossover to a linear
increase characteristic to polymers growing near planar boundaries.
