Chiral Symmetry Breaking and Life

These are called the bifurcation equations. In fact, though (19.2.1) is an equation in its own right, it is also a bifurcation equation for systems that break a two-fold symmetry. The multiplicity of solutions to (19.2.6) corresponds to the multiplicity of solutions to the original equation (19.2.4). 

In this manner, instability, bifurcation, multiplicity of solutions and symmetry are all interrelated. We shall now give a few detailed examples of instability of the thermodynamic branch leading to dissipative structures. 

Biochemistry s hidden asymmetry was discovered by Louis Pasteur in 1857. Nearly 150 years later, its true origin remains an unsolved problem, but we can see how such a state might be realized in the framework of dissipative structures. First, we note that such an asymmetry can arise only under far-from-equilibrium conditions at equilibrium the concentrations of the two enantiomers will be equal. The maintenance of this asymmetry requires constant catalytic production of the preferred enantiomer in the face of interconversion between enantiomers, called racemization. (Racemization drives the system to the equilibrium state in which the concentrations of the two enantiomers will become equal.) Second, following the paradigm of order through fluctuations, we will presently see how, in systems with appropriate chiral autocatalysis, the thermodynamic branch, which contains equal amounts of L- and D-enantiomers, can become unstable. The instability is accompanied by the bifurcation of asymmetric states, or states of broken symmetry, in which one enantiomer dominates. Driven by random fluctuations, the system makes, a transition to one of the two possible states. 

In 1953 F. C. Frank [7] devised a simple model reaction scheme with chiral autocatalysis that could amplify a small initial asymmetry. We shall modify this 

Each enantiomer of X is produced directly from the achiral reactants S and T, as shown in (19.3.1) and (19.3.3) and autocatalytically, as shown in (19.3.2) and (19.3.4). In addition, the two enantiomers react with one another and turn into an inactive compound, P. Due to symmetry, the rate constants for the direct reactions, (19.3.1) and (19.3.3), as well as the autocatalytic reactions, (19.3.2) and (19.3.4), must be equal. It is easy to see that at equilibrium the system will be in a symmetric state, i.e.[XL] = [Xd] (exc. 19.3). Now let us consider an open system into which S and T are pumped and from which P is removed. For mathematical simplicity, we assume that the pumping is done in such a way that the concentrations [S] and [T] are maintained at a fixed level, and that due to removal of P the reverse reaction in (19.3.5) may be ignored. The kinetic equation, of this system are 

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Abstract Theoretical models and rate equations relevant to the Soai reaction are reviewed. It is found that in production of chiral molecules from an achiral substrate autocatalytic processes can induce either enantiomeric excess (ee) amplification or chiral symmetry breaking. The former means that the final ee value is larger than the initial value but is dependent upon it, whereas the latter means the selection of a unique value of the final ee, independent of the initial value. The ee amplification takes place in an irreversible reaction such that all the substrate molecules are converted to chiral products and the reaction comes to a halt. Chiral symmetry breaking is possible when recycling processes are incorporated. Reactions become reversible and the system relaxes slowly to a unique final state. The difference between the two behaviors is apparent in the flow diagram in the phase space of chiral molecule concentrations. The ee amplification takes place when the flow terminates on a line of fixed points (or a fixed line), whereas symmetry breaking corresponds to the dissolution of the fixed line accompanied by the appearance of fixed points. The relevance of the Soai reaction to the homochirality in life is also discussed. 

It was Pasteur, in the middle of the 19th century, who first recognized the breaking of chiral symmetry in life. By crystallizing optically inactive sodium anmonium racemates, he separated two enantiomers of sodium ammonium tartrates, with opposite optical activities, by means of their asymmetric crystalline shapes [2], Since the activity was observed even in solution, it was concluded that optical activity is due to the molecular asymmetry or chirality, not due to the crystalline symmetry. Because two enantiomers with different chiralities are identical in every chemical and physical property except for optical activity, in 1860 Pasteur stated that artificial products have no molecular asymmetry and continued that the molecular asymmetry of natural organic products establishes the only well-marked line of demarcation that can at present be drawn between the chemistry of dead matter and the chemistry... 

Finally, a possible discovery of chiral materials and primitive life in the universe might throw additional light on this question of the origin of mirror symmetry breaking at prebiotic times. 

In a certain sense, one can consider these asymmetries to be quasi-fossils in the evolution of the entire universe. If this is valid, then they contain coded information about the history of the universe from the start of time and matter up to the evolution of life. We shall see here that we are able to answer the first question about the nature of molecular chirality at least theoretically, even though important experimental confirmations are still missing. On the basis of this question, we shall explain also important common concepts of symmetry breaking in the following sections. 

The above example shows how a far-from-equilibrium chemical system can generate and maintain chiral asymmetry, but it only provides a general framework in which we must seek the origins of biomolecular handedness. The origin of biomolecular handedness, or life s homochirality, remains to be explained [11, 12]. Here we shall confine our discussion to how the theory of nonequilibrium symmetry breaking contributes to this important topic. We cannot yet say with confidence whether chiral asymmetry arose in a prebiotic (i.e. before life) process and facilitated the evolution of life, or whether some primitive form of life that incorporated both L- and D-amino acids arose first and subsequent evolution of this life form led to the homochirality of L-amino acids and D-sugars. Both views have their proponents. 

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