Application Of Differential Equation In Stereochemistry

Progressive accumulation; crystallization

Experimental approaches r

Asymmetric autocatalysis; non-linear effects

Polypeptide formation

Frank 1953 Kondepudi & Prigogine 1998

Yamagata 1966 Thiemann 1974 Klussmann et al. 2007

Soai et al. 1995 Girard & Kagan 1998

Wald 1957 Brack & Spach 1971, 1980

Fig. 10.1 Overview of amplification models for the generation of life's molecular homochirality. We distinguish between mathematically driven models such as bifurcating systems and the progressive accumulation as well as experimental approaches like, e.g., asymmetric autocatalysis and the enantioselective formation of polypeptides fine-tuned classification, we will then distinguish between approaches of different research teams working internationally on the amplification of enantiomeric enhancements as it is schematically depicted in Fig. 10.1.

In the field of amplification of small enantiomeric imbalances obtained by the above-described scenarios several theoretical model mechanisms have been proposed. Starting in 1953, F. C. Frank from Bristol University suggested an autocatalytic kinetic model for spontaneous asymmetric synthesis in which the presence of one enantiomer encourages the production of itself, but inhibits the production of its optical antipode. The Frank model was later modified by Decker (1973), Kondepudi and Nelson (1985), Kondepudi (1987), and Kondepudi and Prigogine (1998) with the help of the bifurcation theory predicting that a laboratory demonstration of this work may not be impossible. In modern thermodynamics the bifurcation theory is therefore highly discussed and exciting. It will be presented in the next section.

Since recently, also experimental trials to amplify a small enantiomeric excess of 1 or 2% e.e. towards nearly homochirality were performed successfully at 'real' systems in the laboratory. The required asymmetric amplification can involve enan-tioenriched auxiliaries showing catalytic (Fenwick and Kagan 1999) or even auto-catalytic (Shibata et al. 1998) function, as we will see later in this chapter.

Earlier experimental approaches stimulated by the theory of Wald (1957) predicting that the a-helical structure of a growing polypeptide chain allows the stepwise assembly of amino acid monomers in a way that small chains form with significant levels of stereoregularity (Bonner 1995a), were adequately discussed in Chap. 3.

10.1 Some Amplification Needed: The Bifurcation Theory

Traditional physico-chemical laws of thermodynamics have often been limited to the study of systems at their chemical equilibrium. Moreover, these systems involved idealized slow and reversible chemical reactions. Here, chemical kinetics were limited to first order reactions and second order reactions, easy to be treated. The term "thermostatic" might better describe the study of such systems than the grandiosely used term "thermodynamics".

Kondepudi and Prigogine (1998) outlined these limitations particularly when they tried to apply the laws of thermodynamics to biological systems (a) that are usually not at chemical equilibrium and (b) that do not involve exclusively first and second order kinetics. Kondepudi and Prigogine thus founded a new branch of physical chemistry, called "Modern Thermodynamics", allowing us now to better understand non-equilibrium phenomena such as the bifurcation and the breaking of symmetry. Moreover, advanced software programmes help us today to solve complex differential equations allowing thus the understanding of bifurcating systems. In former times, people even assumed that bifurcating systems resisted any scientific description by appropriate laws.

To introduce bifurcation theory we should visualize that bifurcation is a common phenomenon in macroscopic and microscopic scale: water streams on a flat horizontal surface at "non-equilibrium conditions" are capable of bifurcating into two or more flows. A river such as the source in the Swiss Oberengadin at Piz Lunghin bifurcates into streams serving simultaneously (a) the Rhein flowing into the Northern See, (b) the Inn flowing via the Danube towards the Black Sea, and also (c) the Italian Po flowing into the Mediterranean Ocean. To give another example: close to Detmold in Germany, where I was born, the small river Hase bifurcates into two streams. One serves the river Ems, the other serves the Weser.

Macroscopic bifurcations can be observed also in "cellular rotations" of the hy-drodynamic Benard instability (Forsterling and Kuhn 1985), in fractal structures such as the branching of trees towards leafs, and also in the hexagonal branches of snow crystals. A very impressive multiple bifurcating system is the so-called zinc metal-leaf, an often used practical-training experiment appreciated by students: here, a central carbon electrode in a zinc sulphate (ZnSO4) solution is surrounded by a cyclic zinc electrode of about 30 cm diameter. After applying a DC voltage of 3 to 10 V to the electrodes, beautiful metallic zinc-leafs grow in two dimensions showing a fractal structure (see e.g. Matsushita 1989). Due to their dendritic growth this is called a zinc-leaf or zinc-tree, showing bifurcations at various levels as depicted in Fig. 10.2. In a modified version of this experiment, a zinc-forest showing various bifurcations can be observed by the parallel orientation of two linear electrodes.

Having a closer look on bifurcating structures, the question arises, which general characteristics of systems are necessary to develop one or more bifurcations? Which parameters determine a bifurcation and how? And is the bifurcation a random or determinate driven ramification? In order to answer these questions we will now turn towards bifurcation theory by treating a simple mathematical system showing one bifurcation only.

Fig. 10.2 Zinc crystal "zinc-leaf of 25 cm diameter. The purely inorganic crystal shows multiple bifurcations; it is classified as fractal structure. The fractal dimension can be determined by the "Box-Counting" method

In general, bifurcation and symmetry breaking follow a non-linear differential equation, which is called the bifurcation equation or sometimes Langevin equation (10.1). In this equation, a simply gives the amplitude of an asymmetry and X is a parameter describing the distance of the system from chemical equilibrium. The higher a, the higher the asymmetry of the system; the higher X, the more the system is pushed away from equilibrium conditions. As we will see later, the parameters a and X are to be adapted to specific chemical systems.

Equation (10.1) is a homogeneous differential equation of first order. It contains a polynomial of third order and no quadratic summands.

Now, we will consider a simple chemical system described by the Langevin equation in its steady state conditions. In general, a steady state characterizes a system that allows the transport of matter into and out of the system in a way that the concentrations of chemical species within the system remain unaltered. Therewith, in the steady state da over dt in Eq. (10.1) becomes zero. With X < 0 we obtain one real solution for the asymmetry a (a = 0) and with X > 0 we obtain three solutions

Fig. 10.3 Bifurcation diagram including the solutions of the Langevin equation which are a = 0 for X < Xq and a = X for X > Xq. The thin line representing a = 0 for X > Xq corresponds to an instable solution

Fig. 10.3 Bifurcation diagram including the solutions of the Langevin equation which are a = 0 for X < Xq and a = X for X > Xq. The thin line representing a = 0 for X > Xq corresponds to an instable solution

(a = ±a/X and a = 0). One of the three solutions (a = 0) becomes unstable, which can be demonstrated by stability analysis. The system bifurcates at X = 0. More generally, it can be shown that the system bifurcates at a critical value for lambda which is X = XC. If we now plot a as a function of X, we obtain the bifurcation diagram with its bifurcation point as it is given in Fig. 10.3.

It is important to understand that if we shift the system away from the thermody-namic equilibrium by increasing values of X (i.e., moving in the bifurcation diagram from the left to the right), the system passes the bifurcation point and is thus - at a critical value of XC - forced to realize either the upper or the lower branch. The repetition of an experiment under ideal symmetric conditions can be assumed to realize 50% cases the upper branch and 50% cases the lower branch. Here, the evolution of a is not deterministic. 'Natural' and biological systems often develop in sequences by realizing multiple branching, meaning that one branch follows another (see for example the zinc-leaf).

The treated phenomenon presenting bifurcating solutions is by no means an exceptional case. It is a rather common phenomenon. It is valid for non-linear equations, which might be simple algebraic equations but also more complex coupled differential equations as well as partial differential equations. If this phenomenon is indeed regarded as a general one, does any chemical system show a chiral bifurcation? Can we imagine a chemical system that amplifies a small enantioenrichment towards homochirality just by increasing its X-value? The following kinetic reaction sequence was developed for these purposes.

10.2 Amplification by Kinetic Reaction Sequences

The amplifying model that will be presented here is a modern version of the Frank model (1953) that showed how enantioselective autocatalysis could amplify a small initial asymmetry. It was worked out by Dilip Kondepudi at the University of North Carolina in the US and Nobel Prize laureate Ilya Prigogine at the University of

Brussels (1998), modifying Frank's reaction scheme so that its non-equilibrium aspects, instability, and bifurcation of symmetry breaking states can be clearly seen.

The amplifying Kondepudi-Prigogine model assumes a chemical system, which is initially (a) close to chemical equilibrium and (b) in a symmetric state. The symmetric state can be expressed by chiral reactants furnished in a racemic mixture or still by achiral reactants. Here, we will introduce the achiral reactants S and T into the system. The chiral products XL and XD will be synthesized by specific reactions of the achiral reactants. Moreover, an inactive product P forms that will be taken out of the system. A schematic view of the Kondepudi-Prigogine model is given in Fig. 10.4.

The initial formation of the chiral enantiomers XL and XD by the achiral reactants S and T is described by Eq. (10.2). Please note that the rate constant k1f is identical for the formation of XL and for the formation of XD. The backwards reaction determined by rate constant k1r is also identical for the two enantiomers XL and XD. So far, no asymmetry is induced into the system. It remains highly symmetric.

k1r k1r

Moreover, we will allow - and this is of crucial importance - the chemical system to synthesize the chiral products XL and XD by an additional reaction in an auto-catalytic process. The characteristics for autocatalytic reactions are that a reactant (here XL or XD) increases its quantity in a reaction catalyzed by itself without being consumed. This behaviour is particular but not very exotic (neither in human society nor on the molecular level). The required autocatalytic step will be introduced into the reaction sequence as it is described in Eq. (10.3) for enantiomer XL and in Eq. (10.4) for enantiomer XD. Also here, the system remains highly symmetric since rate constants k2f and k2r remain again identical for the two enantiomers.

k2r k2f

Kondepudi-Prigogine model assumed an open system into which the achiral reactants S and T are introduced, forming chiral species Xl and Xd. The achiral product P is to be taken out of the system k2f

Kondepudi-Prigogine model assumed an open system into which the achiral reactants S and T are introduced, forming chiral species Xl and Xd. The achiral product P is to be taken out of the system

Finally, the inactive product P will form irreversibly by reaction of the two enan-tiomers with one another Eq. (10.5). Product P will be removed from the system by rate constant k3. Due to the irreversibility of this last reaction, the reverse reaction is ignored:

In this example of the Kondepudi-Prigogine reaction sequence we will also ignore a racemization reaction XL ^ XD that might be introduced into the chemical system as done by Kondepudi and Asakura (2001). This step is interesting from two viewpoints, (a) it introduces an evolutionary element into the chirally autocat-alytic scheme that takes into account (long-term) racemization processes and (b) it results that any batch scenario will evolve into a racemic equilibrium state, i.e., in this case an open system becomes essential. Moreover, the scheme can be extended to accommodate unequal reaction rates for the two enantiomers, to include thermal fluctuations, and other factors such as asymmetric destruction rates of the two enan-tiomers by P-radiolysis or other chiral environmental influences (MacDermott and Tranter, 1989).

In order to fully predict the evolution of an eventual enantiomeric excess within this system, we have to apply chemical kinetics by developing the related kinetic equations. We are particularly interested in the evolution of the concentrations of the individual enantiomers over time, denoted as d[XL] over dt and d[XD] over dt. With this information, we will be able to compare the two concentrations and to predict conditions under which an enantiomeric excess can be amplified by any reaction sequence following the Kondepudi-Prigogine system. According to rules in chemical kinetics, the kinetic equations (Eq. 10.6 for enantiomer XL and Eq. 10.7 for enantiomer XD) on the above system can be expressed as:

These kinetic differential equations, in which square brackets denote concentrations, were numerically solved with the help of the software programme Mathemat-ica®. We can now follow the evolution of the concentration for the two individual enantiomers over time starting with a very small excess of XL at t = 0 (see below) and as we surprisingly see in Fig. 10.5, the concentration of the L-enantiomer increases after about 5 min, whereas the concentration of the D-enantiomer decreases.

After temporal evolution of about 30 min, a highly significant enantiomeric excess evolved from the autocatalytic Kondepudi-Prigogine reaction sequence.

In this particular system the parameter X, which denotes the system's distance of its thermodynamic equilibrium, is defined as the product of the concentrations of

Time / min

Fig. 10.5 Spot the difference: time evolution of the concentration of Xl and Xd in the autocatalytic Kondepudi-Prigogine reaction sequence. A tiny excess in the Xl enantiomer is increased to a high enantiomeric excess after 30 min of reaction time. Please consider that the given figure is no bifurcation diagram

Time / min

Fig. 10.5 Spot the difference: time evolution of the concentration of Xl and Xd in the autocatalytic Kondepudi-Prigogine reaction sequence. A tiny excess in the Xl enantiomer is increased to a high enantiomeric excess after 30 min of reaction time. Please consider that the given figure is no bifurcation diagram the achiral reactants X = [S] • [T]. In order to push the system away from the ther-modynamical equilibrium (and to increase X), we used relatively high values for the concentrations of the achiral reactants. At thermodynamical equilibrium (i.e., with lower concentrations of S and T and thus a lower X-value) with X < XC the reaction sequence evolves symmetrically, resulting in [XL] = [Xq]. At thermodynamic equilibrium there can be no enantiomeric excess (Kondepudi and Asakura 2001). Here, each small asymmetry falls back to the symmetric state with a = 0. As the input concentrations of S and T are increased, the racemic process becomes metastable and switches spontaneously into the one or the other enantiomeric homochiral reaction sequence (Mason 1984).

Furthermore, we used a relatively high value of the rate constant k3 for the generation of product P. Precise values for rate constants and initial concentrations of the reactants are given below1 together with the Mathematical® commands (see also Kondepudi and Prigogine 1998). Summarizing, an inflow of S and T and an outflow of the product P maintained the system in non-equilibrium conditions.

The initial concentration of the L-enantiomer was selected as XL(t = 0) = 0.001 molL-1 and the initial concentration of the D-enantiomer is given by XD(t = 0) = 0molL-1. Therewith we introduced a tiny initial asymmetry into the system that

1 Mathematica® commands:

k1f=0.5;k1r=0.01;k2f=0.5;k2r=0.2;k3=1.5;S=1.25;T=1.25; Soln1=NDSolve[{XL'[t]==k1fxSxT-k1rxXL[t]+k2fxSxTxXL[t]-k2rx (XL[t])~2-k3xXL[t]xXD[t],XD'[t]==k1fxSxT-k1rxXD[t]+k2fxSxTxXD[t]-k2rx(XD[t])~2-k3 x XL[t] xXD[t],

XL[0]==0.001, XD[0]==0.0}, {XL, XD}, {t, 0, 100}, MaxSteps^500] Plot[Evaluate[{XL[t], XD[t]}/.Soln1], {t, 0, 30}]

successfully evolved to high enantiomeric excess after 30 min. Such systems are characterized by an extreme sensitivity - Stephen Mason entitled them "hypersensitive" (Mason 1984) - for tiny asymmetries that might be amplified, triggering a selection between two alternative outputs. Kondepudi (1987) calculated that such reaction sequence models might even amplify asymmetries originated from parity non-conserving energy differences to reach a significant effect on the selection of biomolecular chirality. More generally spoken, a tiny asymmetry that arose from one (or more) of the models that we have discussed in the preceding chapters has the potential to be noticeably amplified.

Asymmetries caused by external perturbations to the system but also intrinsic asymmetries are unified in the complete Langevin equation (10.8). Intrinsic asymmetries such as parity non-conserving energy differences AEPNC are represented in the g-term of this equation with g = AEPNC/kT, where k is the Boltzmann constant and T the temperature. Thermal fluctuations, which increase with a rise in temperature, offset the hypersensitivity of the reactions sequence at the bifurcation to chiral perturbations. An increase in temperature thus decreases g-values, being proportional to AE/kT.

The external chiral influence of the environment such as circularly polarized light or other macroscopic electric, magnetic, and gravitational chiral fields is expressed by the term C'nf2(t) where f2(t) is assumed to be a normalized Gaussian white noise. Furthermore, random thermodynamic fluctuations including the normalized Gaussian white noise f1 (t) given by i/efi(t) were respected in Eq. 10.8. A, B, and C are kinetic constants, and £ can also be calculated from the chemical kinetics (Kondepudi and Nelson 1985; Kondepudi and Asakura 2001).

— = -Aa3 + B(X -Xc)a + Cg + Cnf2(t)+ V£h(t) (10.8)

In principle, this equation allows the calculation of an asymmetry in a bifurcating system such as the biomolecular asymmetry that had fallen towards the L-enantiomers of amino acids. The analysis of Kondepudi and Nelson (1985) and Kondepudi and Asakura (2001) of this situation resulted in the counterintuitive result that even when the magnitude of the systematic asymmetry expressed in the g-term is smaller than the root-mean-square value of the random fluctuations, the systematic asymmetry factor could tip the balance to a preferred asymmetric state with high probability. A minute but systematic chiral preference, no stronger than the preference caused by the parity non-conserving energy differences, was proposed to have been amplified by this sequence reaction over a period of about 15 000 years to determine which enantiomer will dominate (Kondepudi and Nelson 1987). Unfortunately, this time scale remained difficult to reproduce in the laboratory for any experimental verification. A common criticism of the application of the complete Langevin equation is that such a unified calculation requires the precise knowledge of each of the Langevin parameters. Today, we are still far from that precise knowledge.

Since recently, only computer simulations of this sort of stereospecific autocata-lytic reaction sequences have produced promising results: Thomas Buhse, now at Morelos State University in Mexico, stimulated by the Kondepudi-Prigogine system, studied the autooxidation reaction of tetralin, a simple hydrocarbon molecule (Buhse et al. 1993a). Tetralin is achiral and well known to be oxidized under mild conditions in the liquid phase. The oxidation product tetralin hydroperoxide is chiral and partly decomposes to peroxyl radicals (ROO •) that are chiral as well and which react with tetralin forming the chiral tetralol. A computer analysis involving the kinetic equations predicted stereospecific and autocatalytic behaviour of the system resulted in a measurable enantiomeric excess. Experimental confirmation of the reaction sequence by investigation of the tetralin-system in the laboratory, however, had remained difficult to obtain (Buhse et al. 1993b).

The situation changed dramatically some years ago when experimental approaches successfully demonstrated the amplification of small enantiomeric excesses. These experiments will be outlined in Sect. 10.4. Before, Yamagata's accumulation principle that is based on a mathematical model will be presented.

10.3 Amplification by Progressive Accumulation

Yamagata (1966) proposed an amplification model which he called "accumulation principle". This model describes the progressive amplification of a small enan-tiomeric enhancement starting from an achiral or racemic substrate and terminating with enantiomerically enriched or even homochiral products corresponding to enantiomeric excesses of +1 or -1. Here, small differences between successive enantiomeric stages are progressively accumulated in a time-extended, uniformly cumulative process. The differences are manifested in activation parameters, for example of n enantiomeric monomers evolving towards polymers. The obtained enan-tiomeric excess of the favoured polymer depends on the degree of polymerization. Polypeptides (Mason 1984) but also DNA (Yamagata 1966) have been discussed as such polymers.

In a general criticism of the "accumulation principle" it is argued that the polymerization needs to be enantiospecific, but with no enantiomeric antagonism (MacDermott and Tranter 1989). The monomers are furthermore required to be optically labile, i.e., they undergo rapid racemization, otherwise the polymerization of an initially racemic mixture of monomers cannot result in the production of a ho-mochiral polymer. These conditions are usually not applicable to biopolymerization reactions often including enantiomeric antagonism and slowly racemizing chemical species such as amino acids.

Anyhow, the "accumulation principle" is ideally applicable to the resolution of racemic substances by crystallization. Here, the precipitate of racemic tartrate solution serves as example which was demonstrated to show a tiny but reproducible optical activity (Thiemann and Wagener 1970). Such kind of amplification we have moreover discussed in detail in Chap. 4 on the crystallization of quartz, sodium chlorate solutions, binaphthyl melts, and others. As we have seen, here the criterion of optical lability is often fulfilled as achiral monomer units were used for the construction of an enantiomorphous crystal. The implications of homochiral crystals for the origin of biomolecular asymmetry were sufficiently discussed in Chap. 4, including the distribution of d-(+)- and l-(-)-quartz on Earth.

10.4 Amplification by the Soai Reaction

Even if the theoretical basis for the amplification of minute chiral imbalances of enantiomers was founded more than half a century ago by Frank (1953), we had to wait for its experimental proof until 1995 and the landmark results of Soai et al. (1995). Organic chemist Kenso Soai from the University of Tokyo and coworkers studied an asymmetric autocatalytic reaction that used a catalyst with initial low enantiomeric excess. This reaction yielded the same catalyst as a product with very high enantiomeric excess. The first such system to be found was the asymmetric autocatalysis of 5pyrimidyl alkanol with 2% initial enantiomeric excess (Soai et al. 1995) proceeding without the need of any other chiral auxiliaries.

In this system the chiral initiator (5-pyrimidyl alkanol) showing low enan-tiomeric excess determined the absolute configuration of the product showing itself (5-pyrimidyl alkanol) overwhelming enantiomeric excesses close to enantiomeric purity of 99.5% (Soai et al. 2000, 2001). Since 1995, a wide variety of chiral 5-pyrimidyl, 3-pyrimidyl-, and 3-quinolyl alkanols have been shown to be asymmetric autocatalysts. In the enantioselective addition of diisopropylzinc (i-Pr2Zn) to an achiral aldehyde these compounds automultiply the initial enantiomeric excess of a chiral alkanol as it is illustrated in Fig. 10.6. Today, this kind of reaction is subsumed under the term "Soai reaction".

Thus, a small enantiomeric asymmetry in the chiral initiator was highly amplified by the above Soai reaction. Are other chiral initiators also able to tip the balance towards the products' S- or ^-configuration?

Pyrimidirie-5-carbaldehyde Diiso- S-pyrimidyl alkanol

Fig. 10.6 The chiral S-pyrimidyl alkanol with 2% enantiomeric excess is capable of autocataly-zing its own production in the Soai reaction between i-P^Zn and an aldehyde yielding a high enantiomeric excess of 88% and more (Soai et al. 1995)

Pyrimidirie-5-carbaldehyde Diiso- S-pyrimidyl alkanol

Fig. 10.6 The chiral S-pyrimidyl alkanol with 2% enantiomeric excess is capable of autocataly-zing its own production in the Soai reaction between i-P^Zn and an aldehyde yielding a high enantiomeric excess of 88% and more (Soai et al. 1995)

Yes, indeed. Four years after the discovery of the Soai reaction, Soai et al. (1999) tried enantiomorphous quartz crystals as chiral initiators. The inspected chemical reaction was - similar to the above system - the asymmetric addition of /-Pr2Zn to a heteroaromatic aldehyde chemically described as 2-(tert-butylethynyl)-pyrimidine-5-carbaldehyde in toluene. And indeed, the chiral product, a secondary alcohol, was formed in its ^-configuration by using (+)-d-quartz powder as chiral initiator. On the other hand, in the presence of (-)-l-quartz powder as chiral promoter the product was obtained in R-configuration. The determined enantiomeric excesses were significantly high with 93-97%. The authors concluded that chiral enantiomorphous quartz crystals might have been involved in the origin of the biomolecular homochi-rality through catalytic asymmetric synthesis. In addition to the use of quartz crystals as chiral initiators, the Soai reaction was reported to produce high enantiomeric enrichments with enantiomorphous sodium chlorate NaClO3 crystals (Sato et al. 2000) as well as chiral two-component crystals of tryptamine/para-chlorobenzoic acid (Kawasaki et al. 2005). This kind of reaction serves as an intriguing example of "chirality propagation" from an inorganic to an organic reaction system.

But not enough to the Soai reaction: instead of quartz crystals in high optical purity, an amino acid itself was tested in a set of experiments to serve as chiral initiator. The chosen amino acid leucine was introduced into the Soai reaction with a small e.e. of + 2% and — 2%. Asymmetric photochemical reactions with circularly polarized light are known to be capable of inducing an enantiomeric excess of this value into racemic mixtures of amino acids, particularly into leucine (Flores et al. 1977; Meierhenrich et al. 2005b). By adding the Soai reactants ¿-Pr2Zn and 2-methylpyrimidine-5-carbaldehyde to L-leucine with an 2% enantiomeric excess in a toluene solution, the product (^-2-methyl-1-(2-methyl-5-pyrimidyl) propan-1-ol) was reproducibly obtained in its R-configuration showing 21% enantiomeric excess. Conversely, in the presence of D-leucine with an 2% enantiomeric excess, enantios-elective alkylation under the same conditions gave the approx. opposite enantiomer-enriched S-pyrimidyl alkanol with 26% enantiomeric excess (Shibata et al. 1998). Similar results were obtained by use of the amino acid valine and also with methyl mandelate, 2-butanol or a chiral carboxylic acid as chiral initiator. All these chemical species serve as chiral initiators or chiral promoters in the Soai system due to which small amounts of the chiral autocatalyst, the pyrimidyl alkanol itself, form. It is important to understand that quartz, amino acids, methyl mandelate, 2-butanol, and chiral carboxylic acids cannot be considered themselves as autocatalysts in the Soai system.

The detailed chemical mechanism in particular for the autocatalytic step of the Soai reaction remained unknown, until the team of Thomas Buhse at Morelos State University in Mexico contributed to its kinetic understanding very recently. With the help of non-linear differential equations the chemical kinetics of the Soai reaction were modelled. And the results show indeed that a chiral amplification starting from an initial enantiomeric excess of < 10—6% to > 60% is feasible. The kinetic model used was based on the Frank model involving stereospecific autocatalysis and mutual inhibition (Rivera Islas et al. 2005). For further insights into the auto-catalytic kinetics of the Soai reaction, kinetic sequences were proposed by Lavabre et al. (2008), which were based on the Frank model, as well.

At the University of South-Paris in Orsay, France, Henri Kagan has been working on "surprising phenomena" on asymmetric amplification such as an enantiomer-ically impure chiral auxiliary or ligands that give a stereoselection higher than its own and even equivalent to the pure one. Kagan entitles these effects generally as "non-linear effects in asymmetric synthesis". A wide variety of different chemical systems showing this effect was summarized by Girard and Kagan (1998). These non-linear effects describe that the relation between the enantiomeric excess value of the chiral auxiliary and the enantiomeric excess value of the product deviates from linearity. This deviation might be caused by molecular aggregation or molecular organization in a particular environment reflecting molecular interactions and complexity in an eventual rather subtle reaction mechanism. Furthermore, Ryoji Noyori, Nobel laureate of Chemistry in 2001, contributed reflections on the possible reaction mechanisms of "non-linear effects" and concluded that the degree of nonlinearity is highly affected not only by the structures and purity of catalysts but also by various reaction parameters, all of them summarized in Noyori et al. (2001).

Despite of all these beautiful amplifications of small enantiomeric excesses by the Soai reaction or non-linear effects we should remain realistic, open our eyes and see that the dialkylzinc chemistry involved in the amplifying Soai reaction, however, is unlikely to have been of basic importance in an aqueous prebiotic environment.

Consequently, the area of amino acid catalysis moved recently into the center of scientific interest. Here, first experimental trials are promising, showing for example in the case of a proline-mediated reaction quite unexpectedly accelerating reaction rates and an amplified, temporally increasing enantiomeric excess of the product (Mathew et al. 2004). The authors were intrigued to find that when the reaction was carried out with non-enantiopure proline, the enantiomeric excess of the product was higher than that expected for a linear relationship and that enantiomeric excess increased during the course of the reaction.

10.5 Transfer, Memory, and Switching of Chiral Properties

In the general context of amplification of small enantiomeric enhancements it is reasonable to mention that some modern research activities focus on transfer, memory, and switching of chiral properties (see Huck et al. 1996). Chiral information can be transferred from chiral non-racemic organic molecules into liquid crystals and then amplified. Such a chirality propagation is usually based on a nematic to cholesteric phase transition of the liquid crystal which depends on the chiral information in the organic dopant (Solladie and Zimmermann 1984; Green et al. 1998; Irie 2000). It was even demonstrated that a chiral bicyclic ketone trigger can induce the reversible switching of a liquid crystal between its nematic and cholesteric form by irradiation with CPL followed by unpolarized light (Burnham and Schuster 1999). The other way round, the transfer from a structural chiral information stored in a liquid crystal can be transferred and amplified into chiral trioxalato chromate guest molecules (Teutsch 1988; Thiemann and Teutsch 1990).

In this context, Ben Feringa and his team at the University of Groningen, The Netherlands, made very recently furore by proposing an amplification of a low enantiomeric enhancement in amino acids by sublimation2 only (Fletcher et al. 2007). The amino acid leucine with an initial enantiomeric excess of up to 10% was partially sublimated from the solid into the gaseous phase. After condensation of the gas phase leucine molecules an enantiomeric excess of 82% was detected in the sublimate. The author assumed to have used "astrophysically-relevant conditions" and to have performed relevant work in order to better understand the origin of biomolecular's asymmetry.

Nevertheless, the reported results are not surprising. In the mentioned experiment, L-amino acid crystals were added to racemic D,L-amino acid crystals before sublimation. Thus two types of crystals were mixed having different lattice structures. This mixture of crystals can be separated under specific temperature/pressure conditions, since these crystals have very different physico-chemical properties such as melting points but also sublimation temperatures. Under the chosen conditions, L-amino acids sublimed preferably, whereas racemic crystals remained in the solid state. An enantiomeric excess of 82% in the sublimate is absolutely not surprising (and depends on the absolute amount of sublimate which is not given by the authors).

However, a more profound contribution to amino acid enantiomer enrichment would be an experiment in which one mixes L-amino acid crystals with their counterpart D-amino acid crystals in order to obtain the starting 10% enantiomeric excess to be sublimated. In this case, melting points and sublimation temperatures are identical. I predict that here the authors would have obtained only the same 10% enan-tiomeric excess also in the sublimate. The statement of Fletcher et al. (2007) to have applied "astrophysically-relevant conditions" requires thus a sound explanation and has to be taken cautiously.

10.6 Concluding Remarks

Mechanisms for the asymmetric amplification of small enantiomeric excesses are important for designing models of biogenesis which all demand a supply of sufficient enantioenrichments in precursor molecules, thus triggering self-organization far from thermodynamic equilibrium (Krueger and Kissel 1989). Such a mechanism being provided lets us assume that the required high enantiomeric excess of one chiral species would not proceed necessarily ab initio, because reaction sequences involving only one powerful autocatalytic step would suffice to select one stereoisomer (Eigen and Schuster 1978a, 1978b). Tipping the balance to the one or the other stereoisomer might have occurred just by chance or by one of the attractive determinate mechanisms presented in the above chapters. The mirror species not selected by the first living organisms for oligomer and polymer production could then be racemized, e.g., by ultraviolet radiation, simply decomposed, or consumed as "nutrient".

2 Sublimation describes the phase transition of a chemical compound from the solid state directly into the gaseous phase.

Was this article helpful?

0 0

Post a comment