Theoretical models of nonlinear effects in two-component cooperative supramolecular copolymerizations

Abstract

The understanding of multi-component mixtures of self-assembling molecules under thermodynamic equilibrium can only be advanced by a combined experimental and theoretical approach. In such systems, small differences in association energy between the various components can be significantly amplified at the supramolecular level via intricate nonlinear effects. Here we report a theoretical investigation of two-component, self-assembling systems in order to rationalize chiral amplification in cooperative supramolecular copolymerizations. Unlike previous models based on theories developed for covalent polymers, the models presented here take into account the equilibrium between the monomer pool and supramolecular polymers, and the cooperative growth of the latter. Using two distinct methodologies, that is, solving mass-balance equations and stochastic simulation, we show that monomer exchange accounts for numerous unexplained observations in chiral amplification in supramolecular copolymerization. In analogy with asymmetric catalysis, amplification of chirality in supramolecular polymers results in an asymmetric depletion of the enantiomerically related monomer pool.

General statistical-thermodynamical treatment of one-dimensional multicomponent molecular hetero-assembly in solution

“…If cooperativity of one-dimensional hetero-assembly is involved, such models as the N-STOCH approach or the models from Refs. [8,9] are still the alternative. Nevertheless a potential possibility to introduce cooperativity of hetero-assembly into the equations of the model developed in the present work seems real and is a matter of further publication.…”

“…[9,17] for review) and two-component hetero-assembly (see Refs. [8,18] for review) leading to formation of aggregates, containing one type or two different types of molecules, respectively, ordered along a certain axis. Recently, a focus has been given to assemblies containing higher numbers of different molecules (multicomponent hetero-assembly) and direct applications of such approaches have been reported in different fields of chemical science.…”

“…Non-covalent hetero-assembly of small molecules in solution is currently attracting great attention due to extensive use of this phenomenon in molecular electronics [1][2][3], laser physics [4,5], supramolecular chemistry [2,[6][7][8][9], advanced materials [10][11][12][13], numerous biochemical applications [2,14,15] etc. The key feature of this process is the formation of nanoscale aggregates, which modify the macroscopic physical properties of solute resulting in outcomes of practical importance ranging from discovering of new perspective materials to treatment of human diseases [16].…”

Binding polynomial in molecular self-assembly

“…Knowledge of Z b allows us to define all necessary equilibrium characteristics of the system, e.g., to evaluate the total number of molecules c 0 and to evaluate the total number of interfaces (contacts) between molecules, which are required to set up a link to experimental observables [10,11].…”

“…If the manual construction of Z b is difficult, special methods can be used to obtain Z b such as transfer-matrix formalism [6], the method of sequence-generating functions [7], an algorithmic approach [8], and some others [9,10]. Knowledge of Z b allows us to define all necessary equilibrium characteristics of the system, e.g., to evaluate the total number of molecules c 0 and to evaluate the total number of interfaces (contacts) between molecules, which are required to set up a link to experimental observables [10,11].…”