Five simultaneous steady states in a flipping two-compartment-system with optical antipodes

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Abstract
The previously given systems-theoretic model for the synthesis of optical antipodes (AD and AL) in strongly asymmetric yield, which shows mono- or bistable behaviour depending on the degree of "openess" of the chemical reaction system is reconsidered for two equal compartments (subscripts 1 and 2 on A) with coupling by diffusion. In this configuration three threshold values, j123, for the influx j of the common precursor substance appear. For j1 only one steady state (s.s.) with no optical activity (A i D =A i L , i=1;2) and equal distribution of the antipodes in both compartments (A 1 D =A 2 D , A 1 L =A 2 L ) exists. For j2, this totally symmetric s.s. becomes unstable and a pair of s.s. with optical activity (A 1 D < A 1 L , A 2 D < A 2 L or A 1 D > A 1 L , A 2 D > A 2 L ) but no spatial asymmetry emerges (parallel flipping), i.e. both compartments behave as a whole, showing a preponderance of either the D- or the L-form. For j>j2 in addition two new s.s. are possible with antiparallel flipping (A 1 D < A 1 L , A 2 D > A 2 L or A 1 D > A 1 L , A 2 D < A 2 L ) i.e. in one compartment the D-form has the majority and in the other one the L-form, but these are stable only beyond a third threshold value j3. A third thinkable pair with no optical activity, but different sum concentrations in both cells, does not exist in this special circuitry, but can be obtained in a slightly changed arrangement. So for j>j3, 5 different (4 stable, 1 unstable) s.s. exist for the same set of parameters, one of which is chosen by the system.

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