  RNA in extant biological systems is homochiral; it consists exclusively of
D-ribonucleotides rather than L-ribonucleotides. How the homochirality of RNA
emerged is not known. Here, we use stochastic simulations to quantitatively
explore the conditions for RNA homochirality to emerge in the prebiotic
scenario of an RNA reactor, in which RNA strands react in a non-equilibrium
environment. These reactions include the hybridization, dehybridization,
template-directed ligation, and cleavage of RNA strands. The RNA reactor is
either closed, with a finite pool of ribonucleotide monomers of both
chiralities (D and L), or the reactor is open, with a constant inflow of a
racemic mixture of monomers. For the closed reactor, we also consider the
interconversion between D and L monomers via a racemization reaction. We first
show that template-free polymerization is unable to reach a high degree of
homochirality, due to the lack of autocatalytic amplification. In contrast, in
the presence of template-directed ligation, with base pairing and stacking
between bases of the same chirality thermodynamically favored, a high degree of
homochirality can arise and be maintained, provided the non equilibrium
environment overcomes product inhibition, for instance via temperature cycling.
Furthermore, if the experimentally observed kinetic stalling of ligation after
chiral mismatches is also incorporated, the RNA reactor can evolve towards a
fully homochiral state, in which one chirality is entirely lost. This is
possible because the kinetic stalling after chiral mismatches effectively
implements a chiral cross-inhibition process. Taken together, our model
supports a scenario where the emergence of homochirality is assisted by
template-directed ligation and polymerization in a non equilibrium RNA reactor.
