SPONTANEOUS BREAKING OF L - D SYMMETRY IN BIOCHEMICAL EVOLUTION

: A simple mathematical model is constructed to show that a minute difference A E in the activation energies of L +nd D isomers of biomolecules is sufficient to achieve optical stereoselection in biochemical evolution. Rate equa- tions describing the competition between self-replicating molecules of two types are shown to exhibit spontaneous breaking of right-left symmetry.


Introduction
The richness and diversity of the universe depends on lack of perfect symmetry. The most symmetric universe w~u l d be a time reversible homogeneous gravitating system of ~h o t o n s ?~ . 'Physics' would become meaningless in such a situation as intelligent beings cannot evolve in this world where there is no 'Chemistry'. In fact if matter is CP invariant a homogeneous photon universe is probably the only possible realization.
The major macroscopic asymmetries in the universe are (I) the arrow of time, ie, the general irreversibility of all natural processes, (2) the inhomogeneity of space, ie, the matter in the universe &lumped into galaxies placed far apart, f3) the chemical asymmetry, ie, nearly symmetric forms of matter allowed by microscopic laws of nature do not exist with equal abundance, either locally or globally.
Although, the macroscopic world is largely asymmetric, the fundamental interactions among elementary particles respect it t o a'much higher degree of accuracy, parity and time reversal invariance are only slight1 violated. Recent developments in nonequilibrium thennodynamics6-H indicate that in a system far from thermal equilibrium the minute asymmetries could get amplified t o generate large scale macroscopic asymmetries. Thus it is possible that macroscopic asymmetries in the universe are direct consequences of microscopic asymmetries. Current developments in elementary particle physics suggest that the observed baryon-antibaryon asymmetry in the universe is a result of small violations in CP and the baryon number conservation?* llSeveral authors have proposed that biochemical L -D stereoselection is caused by pariJy violations in weak interactions?, After the discovery of weak neutral currents much attention is given to this. idea:'4 as the neutral currents could give rise to minute but nonzero difference in the activation energies of the two enantiomers. of the same compound. In this work we present a simple exactly soluble model which clearly shows biochemicaI L -D stereoselection could result as a spontaneous breaking of symmetry in an nonequilibrium process.

Model
It is generally believed that life originated in primeval oceans containing dissolved organic compounds formed by the action of solar ultraviolet radiation or electrical discharges on the primitive atmosphere?*7 As there are no significant right-left distinguishing factors in the chemical or geophysical environment, we assume that the prebiotic medium was a racemic mixture of 'basic chemical building blocks of life' (eg, amino acids) and stereoselection occurred after the development of self-replicating molecules. At the initial stages both L and D isomers of primitive self-replicating molecules would have existed in comparable concentrations. These molecules use compounds in the prebiotic medium of the correct type (L or D) as food and-regenerate molecules of the same type.powever, because of the differenoe in activation energies resulting from neutral currents, the rate constants of replication KL and KD for the two types of molecules will not be exactly equal. Again the self-replicating molecules of one type could interact with the other type inhibiting growth mutually. Perhaps the mixed polymers formed withL and D molecules cannot undergo replication. If NL and-ND are the concentrations of the two types of self-replicating molecules, the rate equations governing their evolution can be written in the form, where, a = constant and KL, KD are the replication constants of the two types of molecules. In the presence of neutraI currents KL is not exactly equd t o KD and before considering the asymmetric equations with Kt + KD we consider the symmetric equations with KL = KD = K. If we impose the symmetric initial condition NL = ND , t -, .o , the equation (1) with KL = KD = K has a symmetric solubon, and two asjrmmetric solutions, where b is a constant.
The symmetric solution and the two asymmetric solutions are plotted in Figure 1 (1) is, The solution (5) is sketched in Figure 3. It is seen that once the concentration of L and D isomers reach a value comparable t o the equilibrium " concentration an unstability develops and N L + w , N D -f O a s t + @ .
We have ignrored the diffusion of interacting molecules. In the actual situation, diffusion plays a n important role in determining the spatiotemporal distribution of the reaction products. When diffusion is included into (1)  Kondepodi and el son' have shown that in models of the above type bifurcation takes place only if [K -K,, ] exceeds a lower limit and neutral current effects could produce a sukficiently large difference in KL and KD.