Information-based measure of chirality for biomolecules

Homochirality is a common property of biomolecules such as DNA, RNA and proteins. In particular, {\scshape d}-ribose and {\scshape d}-deoxyribose enantiomers are found within living cells, while their mirror images, the {\scshape l}-enantiomers, are not known to occur naturally even though the configurations are highly stable. On the other hand, proteins are formed by {\scshape l}-amino acids, not by their mirror images. Why? In this work, we propose the use of Fisher Information (FI) $I$ as a measure of chirality or dissimilarity between enantiomers. We performed Hartree-Fock (HF) and Density Functional Theory (DFT) calculations to obtain the electronic wave function $\Psi (x,y,z)$ and corresponding density function $\rho(x,y,z)$ for each of the natural and synthetic forms of oligoribonucleotides and alanine amino acid. The four wave functions $\Psi (x,y,z)$ are used to compute the FI evaluated from two different view points: a coherent viewpoint, which includes the phase part of each $\Psi (x,y,z)$, and an incoherent or classical viewpoint, which ignores the phase. Our goal is to describe the extent to which the information content in chiral molecules ({\scshape d}- and {\scshape l}-) plays a role in selecting one or the other isomer in nature.