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Experimental mechanisms that yield the growth of homochiral copolymers overtheir 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 crystallitesas well as in solution. We develop two complementary theoretical models forthese template-induced desymmetrization processes leading to multicomponenthomochiral copolymers. First, assuming reversible {\beta}-sheet formation, theequilibrium between the free monomer pool and the polymer strand within thetemplate is assumed. This yields coupled nonlinear mass balance equations whosesolutions are used to calculate enantiomeric excesses and average lengths ofthe homochiral chains formed. The second approach is a probabilistic treatmentbased on random polymerization. The occlusion probabilities depend on thepolymerization activation energies for each monomer species and areproportional to the concentrations of the monomers in solution in the constantpool approximation. The monomer occlusion probabilities are representedgeometrically in terms of unit simplexes from which conditions for maximizingor minimizing the likelihood for mirror symmetry breaking can be determined.

Models for Mirror Symmetry Breaking via {\beta}-Sheet-Controlled Copolymerization: (i) Mass Balance and (ii) Probabilistic Treatment