Spontaneous mirror symmetry breaking and origin of biological homochirality

Abstract

Recent reports on both theoretical simulations and on the physical chemistry basis of spontaneous mirror symmetry breaking (SMSB), that is, asymmetric synthesis in the absence of any chiral polarizations other than those arising from the chiral recognition between enantiomers, strongly suggest that the same nonlinear dynamics acting during the crucial stages of abiotic chemical evolution leading to the formation and selection of instructed polymers and replicators, would have led to the homochirality of instructed polymers. We review, in the first instance, which reaction networks lead to the nonlinear kinetics necessary for SMSB, and the thermodynamic features of the systems where this potentiality may be realized. This could aid not only in the understanding of SMSB, but also the design of reliable scenarios in abiotic evolution where biological homochirality could have taken place. Furthermore, when the emergence of biological chirality is assumed to occur during the stages of chemical evolution leading to the selection of polymeric species, one may hypothesize on a tandem track of the decrease of symmetry order towards biological homochirality, and the transition from the simple chemistry of astrophysical scenarios to the complexity of systems chemistry yielding Darwinian evolution.

Keywords: absolute asymmetric synthesis; asymmetric induction; autocatalysis; chemical evolution; chirality; coupled reaction networks.

Figure 1.

Thermodynamic and kinetic control in an enantioselective reaction , where A is achiral and D/L is an enantiomeric pair.

Figure 2.

Bifurcation enantioselective scenario. The racemic state may become unstable and chiral statistical fluctuations drive the racemic stationary state towards one of two degenerate enantiomeric stable stationary states. Weak chiral polarization acting at the bifurcation point transforms the stochastic bifurcation into a deterministic one.

Figure 3.

Scheme of the reaction network and thermodynamic system of Viedma deracemization [11]. (a) Viedma reaction network: free-energy aggregation diagram, according to the classical theory of primary nucleation showing a free energy profile of cooperative polymerization with the existence of critical cluster/oligomer size (i_crit). Cluster-to-cluster mechanisms of growth give a quadratic nonlinear kinetic dependence. The mutualistic effect that a specific size be formed by different cluster sizes may lead to exponential growth dynamics for SMSB [44]. (b) Thermodynamic system: crystal grinding in their saturated solution yields small clusters which are more soluble that the bigger ones, i.e. it maintains the crystal growth in a stationary state. The unidirectional cycle of matter flux through the crystal growth mechanisms reveal the potentiality of the reaction network for SMSB. The same effect can be created by the different supersaturations provided by permanent temperature gradients [49,50]. (Online version in colour.)

Figure 4.

Differentiation between reaction network and thermodynamic system in the case of the Soai reaction [10]. Adapted with permission from ref. [51]. (Online version in colour.)

Figure 5.

Simulation of SMSB in a CSTR of a six-member hypercycle, where A, B, C, E, F and G are the achiral resources of the replicators. The reaction network also includes the presence of the much slower direct non-catalytic replicator synthesis. Reproduced with permission from ref. [27].

Figure 6.

Limited enantioselective (LES) reaction network, which obeys the thermodynamic constraints of microreversibility. SMSB may be obtained in a system open to the reagents X and Y, by the formation of net unidirectional fluxes between the reactants (A, achiral) and the final enantiomeric products (D and L) [55].

Figure 7.

Stoichiometric flux analysis of the extreme currents of a simple Frank reaction network working in an open system with entry of the initial achiral reagent (A) and the exit of the mutual inhibition achiral compound P. The competition between extreme currents for a minimum entropy production (racemic composition for the currents on the left, and homochiral composition for the current on the right) may lead to the bifurcation scenario. Adapted with permission from ref. [54].

Figure 8.

Necessary elements for yielding SMSB. The reaction network should be able to show enantiomeric nonlinearity capable of achieving the hyperbolic growth necessary for the selection between enantiomers. The thermodynamic structure of the system able to reveal SMSB of a reaction network must generate a net flux between the ‘initial and final species’ of the transformation, either by the entry and exit of specific species in the reactor, or by creating a unidirectional flux in the case of enantioselective autocatalytic cycles. These features of unidirectionality or irreversibility in the cycles/flows are what lead to the generation of entropy.

Figure 9.

Example of the sensitivity of a SMSB system (enantioselective hypercyclic autocatalysis in an open flow reactor). A weak change on the enantioselective reaction constants of one replicator (seven orders of magnitude lower in the example) suffices to select the final chiral sign. The same effect is achieved when, instead of a chiral polarization, the enantiomeric reaction rate constants have an extremely low initial ee value. Adapted with permission from ref. [27].

Figure 10.

Scheme for chemical evolution from simple molecules (astrophysical scenarios) to the systems chemistry complexity of proto-cellular systems (terrestrial scenarios) indicating their relationship with the chirality question. Adapted with the author's permission from [66]. On the right (green colour) the current hypothesis that the formation of primordial biopolymers requires enantiopure pools of building blocks. On the left (blue) the hypothesis presented here on the role of chirality during the different stages of chemical evolution: SMSB appears at the onset of polymer formation and replicator selection and, due to residual ee values coming from former simple asymmetric inductions or singular SMSB syntheses, the stochastic chiral sign distribution transforms into a deterministic final chiral sign.