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Project Progress

In 1953, the British physicist Sir Charles Frank proposed that homochirality could be a consequence of chemical autocatalysis, presumably occuring very early on in the emergence of chemical evolution. He introduced a model in which the R and L-handed enantiomers of a chiral molecule are autocatalytically produced from an achiral molecule A through reactions

A + R —> 2R A + L —>2L

and consumed in a reaction that can be written in steady state as

R + L —> 2A

Frank’s model, as well as all others that followed with various degrees of elaboration, can be written down as a set of ordinary differential equations, and reduced to a single equation for the chiral order parameter w = (R-L)/(R+L) of the form

dw/dt = F(t) w (1-w^2)

showing that the chiral symmetry breaking is associated with the nonlinear term arising not from autocatalysis, but instead the chiral inhibition. The chiral inhibition reaction does not have evident biochemical relevance to early life, so the emergence of homochirality in Frank’s model is not in fact due to autocatalysis.

The question that we have been able to address with a significant technical advance is: can autocatalysis on its own, without supplementary reactions that force homochirality, generate homochirality? To tackle this issue, we formulated a fully stochastic version of Frank’s model, but with two significant emphases. First, because modern life is a far-from-equilibrium process, we have treated a system that is maintained in a non-equilibrium steady state by an external driving force. This could be, for example, the chemical and thermal gradients in the vicinity of a hydrothermal vent. Secondly, we have assumed that as life evolved to greater and greater levels of complexity, the efficiency of autocatalytic production compared to non-autocatalytic production increased.

The resulting stochastic model has some remarkable mathematical properties. In equilibrium it only has a racemic or achiral state as a solution. Nevertheless, the non-equilibrium system can exhibit fluctuations in chirality which drive the system towards a state where the fluctuations themselves become less important. The fluctuations can be shown to vanish as the system becomes more and more chiral. Thus, in the end, a fully homochiral state arises, not because it minimises the free energy in some potential, but because it minimises the effects of noisy fluctuations. This mechanism for homochirality really only uses two universal attributes of life: its far from equilibrium nature and the existence of death (ie. the decay of reactants).

Our main calculation was done assuming a well-mixed ecosystem, but we were able to solve mathematically the case of two coupled “patches”, and using computer simulation, a fully spatially-extended system in one or two dimensions. We discovered that our mechanism for homochirality is stable to spatial fluctuations, and in fact the dynamics leading to the emergence of one homochiral state over another is in the compact directed percolation universality class, familiar from phase transition theory.

The mechanism proposed differs in significant ways from other variants of Frank’s model in the literature, apart from the way in which the calculation was done. The most important is that the noise-induced mechanism does not require an initial enantiomeric excess to start the chiral symmetry breaking process. Copy number fluctuations of the molecules are all that are needed. Thus, the non-equilibrium dynamics of autocatalysis alone, without other model-specific choices of nonlinearity, is enough to generate homochirality at the 100% level. Because the assumptions of the theory are so general, using properties that are likely to be generic aspects of life, we can conclude that chiral symmetry breaking is a biosignature possessed by all life based on autocatalysis, replication and far-from-equilibrium dynamics.