Mirror symmetry breaking as a problem in dynamical critical phenomena

The critical properties of the Frank model of spontaneous chiral synthesis are discussed by applying results from the field theoretic renormalization group (RG). The long time and long wavelength features of this microscopic reaction scheme belong to the same universality class as multi-colored directed percolation processes. Thus, the following RG fixed points (FP) govern the critical dynamics of the Frank model for d<4: one unstable FP that corresponds to complete decoupling between the two enantiomers, a saddle-point that corresponds to symmetric interspecies coupling, and two stable FPs that individually correspond to unidirectional couplings between the two chiral molecules. These latter two FPs are associated with the breakdown of mirror or chiral symmetry. In this simplified model of molecular synthesis, homochirality is a natural consequence of the intrinsic reaction noise in the critical regime, which corresponds to extremely dilute chemical systems.Comment: 9 pages, 3 figure

Homochirality and the need of energy

The mechanisms for explaining how a stable asymmetric chemical system can be formed from a symmetric chemical system, in the absence of any asymmetric influence other than statistical fluctuations, have been developed during the last decades, focusing on the non-linear kinetic aspects. Besides the absolute necessity of self-amplification processes, the importance of energetic aspects is often underestimated. Going down to the most fundamental aspects, the distinction between a single object -- that can be intrinsically asymmetric -- and a collection of objects -- whose racemic state is the more stable one -- must be emphasized. A system of strongly interacting objects can be described as one single object retaining its individuality and a single asymmetry; weakly or non-interacting objects keep their own individuality, and are prone to racemize towards the equilibrium state. In the presence of energy fluxes, systems can be maintained in an asymmetric non-equilibrium steady-state. Such dynamical systems can retain their asymmetry for times longer than their racemization time.Comment: 8 pages, 7 figures, submitted to Origins of Life and Evolution of Biosphere

Chirality: spin and gravity give a helping hand

The handedness of supramolecular helices formed from achiral monomers has been controlled by applying rotational and gravitational forces, but at the start of the assembly process only. This demonstrates that a falsely chiral influence is able to induce absolute enantioselection