An exact and ubiquitous condition for solid-state deracemization in vitro and in nature

Solid-state deracemization refers to the amplification of an enantiomeric excess in suspensions of conglomerate-forming compounds, in the presence of racemization in solution. It is an attractive route to the manufacture of enantiopure products, and a possible pathway to the emergence of homochirality on Earth, which is linked to the origin of life. Numerous compounds are known to deracemize, including many of biological relevance, which suggests the existence of a general governing mechanism. Yet pinning down such mechanism has been difficult, controversial, and not conclusive. Here we use a simplified formulation of the classical population balance model of deracemization through temperature cycles that includes neither agglomeration, nor breakage, nor ripening, to prove an exact condition under which deracemization occurs: crystal dissolution must be faster than crystal growth. Such kinetic asymmetry is a fundamental principle of crystallization, which explains the general success of deracemization experiments in the literature. Our theoretical analysis allows predicting that deracemization occurs for any amplitude of the temperature cycles, however small, and even for random temperature fluctuations. Here we demonstrate through ad hoc experiments that these predictions are correct. Since the exact condition for deracemization is simple and ubiquitous, solid-state deracemization provides indeed both a technical route to enantiopure products and a natural pathway towards homochirality.