  Experimental mechanisms that yield the growth of homochiral copolymers over
their heterochiral counterparts have been advocated by Lahav and co-workers.
These chiral amplification mechanisms proceed through racemic
{\beta}-sheet-controlled polymerization operative in both surface crystallites
as well as in solution. We develop two complementary theoretical models for
these template-induced desymmetrization processes leading to multicomponent
homochiral copolymers. First, assuming reversible {\beta}-sheet formation, the
equilibrium between the free monomer pool and the polymer strand within the
template is assumed. This yields coupled nonlinear mass balance equations whose
solutions are used to calculate enantiomeric excesses and average lengths of
the homochiral chains formed. The second approach is a probabilistic treatment
based on random polymerization. The occlusion probabilities depend on the
polymerization activation energies for each monomer species and are
proportional to the concentrations of the monomers in solution in the constant
pool approximation. The monomer occlusion probabilities are represented
geometrically in terms of unit simplexes from which conditions for maximizing
or minimizing the likelihood for mirror symmetry breaking can be determined.
