Even after Apoptosis antagonist this reduction, the model is extremely complex to analyse due to the large number of cluster sizes retained in the model. Hence we construct two truncated models, one truncated at tetramers, which shows no symmetry-breaking and one at hexamers which shows symmetry-breaking under certain conditions on the parameter values. Alternative reductions are proposed: instead of retaining the concentrations of just a few cluster sizes, we retain

information about the shape of the distribution, such as the number of clusters and the total mass of material in clusters of each handedness. These reduced models are as simple to analyse as truncated models yet, since they more accurately account for the shape of the size-distribution than a truncated model, are expected to give models which more easily fit to experimental data. Of course, other ansatzes for the shape of the size distributions could be made, and will lead to modified conditions for symmetry-breaking; however, we believe that the qualitative results outlined here will not be contradicted by analyses of other macroscopic reductions. One noteworthy feature of the results shown herein is that the symmetry-breaking GSK1120212 supplier is inherently a product

of the two handednesses competing for achiral material. The symmetry-breaking does not rely on critical cluster sizes, which are a common feature of theories of crystallisation, or on complicated arguments about surface area to volume ratios to make the symmetric state unstable. We do not deny that these aspects of crystallisation are genuine, these features are present in the phenomena of crystal growth, but they are not the fundamental cause of chiral symmetry-breaking. More accurate fitting of the

models to experimental data could be acheived if one were to fit the generalised Becker–Döring model (Eqs. 2.11 and 2.12) with realistic rate coefficients. Questions to address include elucidating how the number and size distribution at the start Carnitine palmitoyltransferase II of the grinding influences the end state. For example, if one were to start with a few large right-handed crystals and many small left-handed crystals, would the system convert to entirely left- or entirely right-handed crystals ? Answers to these more complex questions may rely on higher moments of the size distributions, surface area to volume ratios and critical cluster nuclei sizes. Acknowledgements I would particularly like to thank Professors Axel Brandenburg and Raphael Plasson for inviting me to an extended programme of study on homochirality at Nordita (Stockholm, Sweden) in February 2008. There I met and benefited greatly from discussions with Professors Meir Lahav, Mike McBride, Wim Noorduin, as well as many others. The models described here are a product of the stimulating discussions held there. I am also grateful for funding under EPSRC springboard fellowship EP/E032362/1.