## Spontaneous asymmetric synthesis

F. C. Frank (see Enderby (1998) to learn more about Frank) envisioned the equations of spontaneous asymmetric synthesis as a means for the evolution of optimal activity in biological compounds. That is, the two types x and y in our equations are dynamically identical, but suppose that x rotated light clockwise andy rotated light counter clockwise. We could imagine a situation in which we go from a < 1 to a > 1 in Eq. (2.47); for example if temperature is inversely related to a, then as a system cools, the dynamics would change from (1,1) being a stable node (and a racemic mixture) to (1, 1) being a saddle point (and optically active). However, because of molecular fluctuations, when this change takes place we do not expect the system to be exactly at (1,1). Thus small deviations from (1,1) will become amplified if a > 1. This is what Frank meant by spontaneous asymmetric synthesis and when my first paper on this subject appeared (Mangel and Ludwig 1977) he wrote to me suggesting that I had developed methods for a problem that he was unable to solve, which was a great treat for a young scientist. This topic is still of great interest. I encourage you to read Frank's original paper (Frank 1953) and a one dimensional version that predates it by Max DelbrÃ¼ck (DelbrÃ¼ck 1940); some of the more recent work on this subject - which can also point you towards other literature -is found in Pincock et a/. (1971), Pincock and Wilson (1973), Soai et a/. (1990), Link et a/. (1997), Berger et a/. (2000), Blackmond et a/. (2001), Siegel (2002) and Singleton and Vo (2002).

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