A Mathematical Formulation and Solution of the CoPhMoRe Inverse Problem for Helically Wrapping Polymer Corona Phases on Cylindrical Substrates

Abstract

Corona phase molecular recognition (CoPhMoRe) is a new technique that generates a nanoparticle-coupled polymer phase, capable of recognizing a specific molecule with high affinity and selectivity. CoPhMoRe has been successfully demonstrated using polymer wrapped single walled carbon nanotubes, resulting in molecular recognition complexes, to date, for dopamine, estradiol, riboflavin, and l-thyroxine, utilizing combinatorial library screening. A rational alternative design to this empirical library screening is to solve the mathematical formulation that we introduce as the CoPhMoRe inverse problem. This inverse problem seeks a linear function representing the position of monomers or functional groups along a polymer backbone that results in a 3-dimensional structure capable of recognizing a specific molecule when mapped to a nanoparticle surface. The potential solution space for such an inverse problem is infinite in general, but for the specific constraint of a helically wrapping polymer, mapped to a cyli...