Dual cooperativity in twisted host and multiple chiral guest systems: Theoretical evidence of 'superamplification of asymmetry'

Chiral host-guest systems are of significant interest due to their applications in chiral separation, chiral sensing, asymmetric catalysis, and circularly polarized luminescence. Chiral interactions involving multiple guest molecules exhibit two cooperative effects: allosteric binding and amplification of asymmetry. When combined, these effects can lead to a phenomenon that surpasses conventional amplification of asymmetry, proposed to be termed 'superamplification of asymmetry'. Despite its potential, no established theoretical framework exists. In this work, we developed three models: a 1:2 twisted host-guest interaction model in general form; a 1:n model assuming independent binding events at multiple sites equivalent to the majority rule effect type host-guest interaction (MRHG) model for short polymers; and the MRHG model combined with allosteric binding (MRHG-AB model), we could distinguish superamplification of asymmetry from ordinary amplification of asymmetry. These models were applied to twisted macrocycles and triple-stranded metallohelicates, offering new insights into the amplification of asymmetry mechanisms.