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Homochirality and stereospecific activity: evolutionary aspects
BioSystems, 25 (1991) 141--149
141
Elsevier Scientific Publishers Ireland Ltd.
Homochirality and stereospecific activity: evolutionary aspects V l a d i k V. A v e t i s o v a n d Vitalii I. G o l d a n s k i i N.N. Semenov Institute of Chemical Physics, Academy of Sciences of USSR, 117334Kossygin st.4, Moscow (USSR) (Received September 4th, 1990) (Accepted March 8th, 1991)
The problem discussed in this paper is the connection between the unique property of biopolymers (proteins, DNA and RNA), i.e. homochirality, and their main functionalproperty, i.e. self-replication. Our approach is based on an analysis of the conditions for the origination of the mechanism of self-replication of chiral polymers. It is demonstrated that self-replication could originate only on the basis of homochiral structures, possessing stereospecific (enzymatic) activity. It is also shown that complete breaking of the mirror symmetry of the organic medium is required both at the stage of polymeric takeover and at the stage of formation of sl;ructures possessing stereospecific activity. This requirement is satisfied only in the framework of the mechanism of spontaneous symmetry breaking i.e. the mechanism of non-equilibrium phase transition from the racemic state of the organic medium to the chiraily pure one. The results obtained suggest that homchirality is a necessary condition for the origination of biological specificity and plays a fundamental role in the formation of structures capable of self-replication.
Keywords: Biopolymer,% Homochirality; Self-replication; Stereospecific activity; Symmetry breaking; Evolution.
1. Introduction It is well known that the organic compounds (nucleotides and amino acid residues) which make up polymeric chain units are chiral (except for glycine); their' spatial structure does not have mirror symmetry and therefore they may exist in two mirror-isomeric L and D forms. However, these biopolymers consist of fragments of a defini~e stereoisomeric form only. For example, all enzymes contain only Lisomers of amino e~id residues, whereas nucleic acids contain only D-isomers of ribose or deoxyribose. The existence of the property mentioned above means that the scenario of prebiological evolution either should include the step of the formation of homochiral polymers or make it possible at some subsequent stage of evolution. Some arguments for the formation of homochiral polymers during prebiological evolution
are presented in Sections 2 and 3. In Sections 4 and 5 we discuss conditions necessary for this step while the last section contains our main conclusions. 2. Is homochirality a consequence of specific features of polymeric takeover of the medium? Let us consider the conditions for the assembly of a polymeric chain, for instance of L-type, in a medium with chiral polarization = (XL - XD)/(XL + XD) (XL and XDbeing the concentrations of L- and D-isomers from which the chain is assembled). The quantity ~ describes the relative enantiomeric excess. If the probability of addition of a unit to the end portion of the chain does not depend on its isomeric form, the relative probability l) of assembly of a homochiral portion of the chain of the length N is equal to fl -- ¢~N _- exp[N In ~1,
0303-2647/91/$08.50 (9 1991 Elsevier Scientific Publishers Ireland Ltd. Published and Printed in Ireland
142
where co = (1+ 7)/2 is the relative concentration of L-isomers in the medium. The value decreases with N and becomes exponentially small when - N In co < 1. For this reason, the formation of homochiral polymers of length N is possible only when - l n w < N - 1, and consequently, chiral polarization of the medium must satisfy the condition 7 > 1 - 2N-1. This is a very rigid condition. For instance, for the formation of a homochiral chain of length N oc 100, the medium must be practically chirally pure (7 > 1--10-2). In a racemic medium (7 = 0) the probability of random assembly of a homochiral portion of the same length (fl a 2-100) is vanishingly small even for time periods of the order of the age of the Universe (~ 1017 s). However, this result, assuming no stereoselectivity, is an idealization: it is necessary to take into account not only the isomeric composition of the medium, but also stereoselectivity `/of the interaction of mirror antipodes with an active portion of the growing chain. Let col and COd -- 1 - COLbe the relative probabilities of addition of L- and D-isomers to the end fragment of L-type in the racemic environment. It is convenient to specify the value `/in the form `/ = 1 - 2ooD. If the chain growth is nonselective, ~0L ---- COD = 1/2 and `/ = 0, as considered above. If the chain growth is absolutely stereoselective, then COD ---- 0 and `/ = 1. The relative probability of assembly of a homochiral portion of length N is now equal to
Figure 1 shows the dependence of 7c on `/for N 100 (the area of values 7 satisfying condition (2) is hatched). At sufficiently large N the dependence 7c (`/) has the character of abrupt turnover. For almost all values of `/in the large 0 to 1 except the narrow area `/ > 1--10 -2, corresponding to absolute stereoselective growth of the polymer chain, the values of 7c change slightly, remaining in the neighborhood of the chirally pure state (7c ~ 1--10-2). However, near `/= 1, in the area of-/ > 1--10 -2, 7c drops sharply down to zero. Thus, the polymeric takeover of the organic medium by homochiral structures is possible either (A) in a chirally pure medium (7 > 1--10 -2) or (B) in the case of absolute stereoselectivity in the polymer assembly (`/ > 1--10-2). In the scenarios of prebiological evolution based on situation (A), the stage of polymeric takeover must be preceded by strong symmetry breaking of the organic medium. Therefore, the origin of homochiral polymers and their evolution along the path to almost absolute stereoselection (i.e. the formation of structures possessing stereospecific activity) must take place in a chirally pure medium. Steady maintenance of the chirally pure state throughout the stage of formation of specifically active structures is also necessary.
----(CO * 00L)N ----expIN In(co • COL)}
/L0"2
I
and it is not exponentially small when -ln(~ • COL) <~ N -1, i.e. when (1 - ~) (1 -`/)
< N -1
(1)
0.5-
From (1) it is easy to derive the condition for formation of homochiral polymers of length N taking into account the stereoselectivity `/:
0
2(1 + ,!`/)
2a
7/ >,Ic = 1 - - - ,
N+~
wherea--
i+7
1-`/
(2)
i
/.=
Fig. 1. The plot of ~c(7) in the case of assembly of a homochiral polymer. The area of the ~ and V values satisfying the condition of assembly of a homochiral chain is hatched.
143
In the scenarios based on situation (B), the organic medium is racemic, i.e. it does not possess any nontrivial properties. But the appearance of homochiral polymers must of necessity have been preceded by a stage of formation of heterochiral structures possessing stereospecific activity. In this case the origination of homochiral self-replicating systems is the result of evolution of their heterochiral precursors. This dilemma may be solved if one shows that only homochiral protoenzymes might be formed during the prebiological evolution. 3. should heteroclMral protoenzymes exist? It should be stressed at once that complete understanding of the process of selforganization of biological macromolecules has not been reached so far. Nevertheless, it is clear already that their main feature is their hierarchic structures (Grosberg and Khohlov, 1989), i.e. primary, secondary and tertiary structures. The role of the stereoisomeric composition of the polymeric chain in the formation of its second'ary and tertiary structures is thus of special interest. This important problem was investigated in detail in a number of studies (Lundberg and Doty, 1957; Brack and Spach, 1979; Brack and Spach, 1980; Goldanskii et al., 1986), where it was shown that chiral defects hinder the formation of both the double helix in polynucleic acids and the a-helix and/3-sheets in polypeptides, i.e. they hinder the formation of the main motifs of the secondary structure of the biomacromolecules. In heterochiral polymers with random disposition of mirror isomers along the chain there arise such strong steric hindrances that formation of these secondary-structure motifs proves to be impossible. However, one cannot exclude that a certain regular alternation of the L- and D-isomers in the chain could alh)w the formation of secondary structure (such heterochiral polymeric structures were discussed, for example, by Weber, 1989). Could such macromolecules play an essential role in the prebiological evolution? An
answer to this question may be obtained from an analysis of the conditions of takeover of the organic medium by polymers with a certain definite sequence of the L- and D-isomers. Let the primary structure of the heterochiral polymer of length N be a certain ordered alternation of m fragments of L-type and n fragments of D-type (m = n). A chiral defect here will be simply a violation of the order of alternation of the isomers in any pair of the units (see Fig. 2). Suppose also that the mechanism of stereodifferentiation of mirror antipodes at the end portion of the chain ensures a certain advantage for the addition of a correct isomer and, consequently, the stereoselectivity of ~ ffi 1 - 2¢0def > 0 (~def being the relative probability of the appearance of a chiral defect in racemic environment). Then the probability ON of the assembly of a defect-free chain of the length N -- m + n is fiN = (1-o~Lef)m (1-¢0Def)n ffi
exp[m ln(i-o~dief) + n ln(1-~Def)/
where (1+,1) ( l - v ) 2(1 + 'r/)
o)Le f _-
and o~Def= (1-7) (1-7) 2(1 + 'I~)
are the relative probabilities of formation of chiral defects of L- and D-types, respectively. The value fin is not exponentially small when I n ( l - ~Lef) + n In(1 - o~dDef)} < 1
-/m
---
II
---
~'.
---
I
---
O
""
U
---
O
.--
chain
defect-free
C]
---
(3)
II
---
II
---
•
---
O
---
I chiral
defect
Fig. 2. Chiral defect in heterochiral chain: • and [] are conventional designations of mirror antipodes.
144
From (3) it is not difficult to obtain the condition of takeover of the organic medium by defectfree polymeric structures: N-or
N+~
o/-i
< Y <
(4)
cz+N
where, as in (2), a = (1 + 7)/(1 - 7). It should be noted that condition (4) is fulfilled only for a > N, i.e. when 7 > 1 - 2 N -1. The region of the values (~,7), satisfying condition (4), is demonstrated in Fig. 3. When N ~ 100, it is a narrow peak (having a width oc 10-2), confined near the value 7 = 1. Thus, in the absence of almost absolute stereoselectivity in a chain assembly, takeover of the organic medium by heterochiral polymers with any sequence of the L- and D-isomers specified in advance is exponentially suppressed at all values ,1 of the chiral polarization. As a result, we come to the conclusion that the formation of heterochiral protoenzymes is impossible either because of strong structural limitations (when the disposition of the L- and Disomers in the polymeric chain is random) or because of strong kinetic limitation of the process of polymeric takeover (by structures with any unique sequence of the chiral fragments).
4. Two main stages of prebiological evolution
From the above analysis it follows that only situation (A) provides a consistent scenario for prebiological evolution. Within this, the stages of prebiological evolution may be represented by the scheme in Fig. 4. This scheme reflects two distinctive features which are, in our opinion, important. First of all, strong breaking of the mirror symmetry of the organic medium preceded the stage of polymeric takeover and, thus, predetermined the formation of homochiral polymers. This conclusion was derived earlier (Avetisov et ai., 1985) from the assumption that at the stage of polymeric capture an essential role in the formation of homochiral polymers might be played by the process of matrix oligomerization (Joyce et ai., 1984). However, as shown above, this conclusion may also be derived from more general consideration. Another specific feature of the prebiological evolution is that the chiral purity of the medium was maintained not only at the stage of z synthesis o f organic compounds
i V racemic organic medium (~=0, ¥<10"21
strong breaking of mirror symmetry V chirally pure organic medium { ~ > 1 - 1 0 -2,
o5
~<10 -2 }
q V homochiral polymers ( ~ > 1 - 1 0 "2 , ~<<1)
#--.40o
,
0
~
formation of stereospecific enzymatic activity
V homochiral "chemical automata" ( ~ > 1 - 1 0 "2 ) II V
Fig. 3. The plot of ,c(7) in the case of assembly of a heteroehiral (L,D)-polymer. The area of the ~/and 7 values satisfying the condition of assembly of heteroehiral chains is hatched.
polymeric takeover of medium
(
f.... tion of selfreproducin~ systems
Fig. 4. Scheme of the main stages of prebiological evolution.
145
polymeric takeover, but also in the next important stage: the formation of structures and functions of the biochemical level of complexity. It was only after the appearance of the stereospecific mechanism of the synthesis of homochiral polymers that chiral purity of the medium was no longer necessary. Thus, the specilSc feature of prebiological evolution is not oni[y strong breaking of mirror symmetry, but also stability of the chirally pure state of the medium throughout the stage of formation of protoenzymes. The latter requirement is stronger than the requirement of mirror symmetry breaking itself. This is due to the fact that the efflux of mirror isomers of predominantly one kind (and their incorporation into polymeric structures) is an asymmetric process, which may lead to a reduction of the chiral purity of the monomer medium. Indeed, let us consider a simple kinetic diagram of an asymmetric withdrawal of L- and D-isomers from a monomeric subsystem X into a polymeric subsystem Q (Fig. 5): L
kL
--
Q, D
kD
--
Q
(5)
(k L and kD being the effective values of the polymerization rate constants of the L- and D-
isomers, respectively). The contribution of processes (5) to the dynamic equation for the chiral purity of the monomeric subsystem has the form d~ dt
K~(l_~2)
(6)
where K = (kL + kD)/2 and ~ -- (kL - kD)/(k L + kD) is the stereoselectivity of the formation of polymeric chains (for the sake of definiteness we assume that chiral defects correspond to the incorporation of D-isomers into the L-chain, i.e. ~>0). It is easy to see that equation (6) describes the process of diminution of ~ to zero. Consequently, in the formation of homochiral polymers, the monomeric medium experience an additional asymmetric effect of racemizing type. This asymmetric kinetic factor, brought about by the interaction of the polymeric and monomeric subsystems, is called by us the stereoselective pressure and denoted as a = KT. In the course of polymeric takeover of the chiral medium and formation of stereospecific catalytic functions, the value of a increases because of the growth of ~/ from ~/ ~ 10 -2 to ~ ¢¢ 1 - - 1 0 -2 Therefore, a viable mirror symmetry breaking process must also be able to maintain chiral purity despite the growth of stereoselective pressure.
5. Strong breaking of mirror symmetry: evolutionary accumulation of asymmetric action or non-equilibrium phase transition?
I//,
/: J/ / / / )
x"
Fig. 5. Model presentation of the stage of polymeric takeover. Asymmetric efflux of L- and D-isomers from monomeric subsystem X into polymeric subsystem Q creates stereoselective pressure.
Finally, let us consider which processes of mirror symmetry breaking satisfy these conditions. Strong mirror symmetry breaking in the prebiological evolution has been the subject of recent extensive discussions (see the review of Goldanskii and Kuz'min, 1989 and references therein). There are two basic classes of symmetry breaking mechanisms; evolutionary or the bifurcation type. For each of them we investigate changes of chiral purity during the growth of stereoselective pressure.
146 In systems of the evolutionary type, the symmetry breaking is brought about by the asymmetry of the constants of mirror-conjugated channels of the transformations of the L- and Disomers, arising as a result of a certain (external) asymmetric effect (for example, circularly polarized radiation, an asymmetric mineral catalyst, etc. (Barron, 1986)). The change of chiral polarization (t) with time has the form d__~ = g (l_y2) _ KRrt dr
i +
[1 + (g/KR) 2] 1/2 ]-1
d,, -"
fir
= (g - roK'l) (1-7/2) - KRr/
The value Ymaxin this case may by derived from (7) through the replacement g -- (g -- r0Ky). Therefore, the condition of strong mirror symmetry breaking has a similar form:
(8)
(g - roK~l)/K R >> 1
where g = (kL(i) - kD(i))/(kb (i) + kn (/)) is the advantage factor (AF) (kL(0, kD(i) being the rate constants of mirror-conjugated reactions of i-th type), , -- 7o-1" t is the dimensionless time related to the scale ~'o o¢ (kL(i) + ~D (i)) -1, and KR is the racemization factor (RF) which is the reciprocal relaxation time of y to zero upon switching off of the AF (g = 0). The maximum chiral polarization ~max,which is attainable in systems of the evolutionary type, is given by the expression ~max = ( g / k R ) [
system (5), the dynamic equation for the chiral polarization of the monomeric takes the form
(7)
When the AF to RF ratio is large, the mirror symmetry breaking is strong (for (g/KR) o~ 10 2, Ymax = 1--10-2). Therefore, if there are no additional requirements, the problem concerning strong mirror symmetry breaking of the medium, in principle, may be discussed within the framework of processes of the evolutionary type. It is known that the AFs caused by different external asymmetric effects on chemical transformations reach values of g g 10 -2. Consequently, it cannot be excluded that, in a certain organic area, conditions of transformation of the mirror isomers may have arisen for which the AF to RF ratio was greater than 1 and, as result, strong mirror symmetry breaking of the medium occurred. However, we shall demonstrate that if such an event preceded the stage of polymeric takeover of the organic medium, it could not play an essential role in subsequent stages of prebiological evolution. Taking account of the asymmetric efflux of mirror isomers into the polymeric sub-
Suppose now, that the conditions of the first stage of prebiological evolution are fulfilled, i.e. for a certain AF the ratio (g - roKT)/KR o: 102, ~max 1--10 -2, and abiogenic synthesis (7 10 -2, K a r0 -1) of homochiral polymers of the length N ~ 100 creates a selective efflux of the isomers into the subsystem X. The next stage of evolution is the formation of stereospecific catalytic function. At this stage 7 - 7c ~1 - 1 0 -2 and K ~ K" > r0 -1. It is obvious, however, that for any abiogenic AF, condition (8) will be violated even before the critical stereoselectivity % is reached. Consequently, the formation of the stereospecific function will be blocked. It should be noted that since for all the known abiogenic AFs g << 1, the formation of polymer structures of the biological level of complexity in monomeric systems of evolutionary type proves to be not feasible. Now we shall consider systems of the bifurcation type. In such systems symmetry breaking is a nonlinear process, leading to instability of the symmetric (racemic) state when passing the critical values of the control parameters (bifurcation point) (Frank, 1953). For the given class of the processes of mirror symmetry breaking, (t) is defined by the system of dynamic equations of the form (Morozov, 1979; Morozov et al., 1984) ~
d~--E
=
- A ( O , X ) • na
dt dO__ = f(O,;~,~2) dt
+
B(O,),) •
147
where E) = XL + XDis the total concentration of mirror isomers in the system, ~ is a parameter, whose value may vary the concentration of the achiral reagent or the density of the flux of energy through the system, A (O,k) and B(O,~) are implicit time functions, whose form is specified by the kinetics of the transformations of the Land D-isomers. The value of chiral polarization n(~)in the stationary state (see Fig. 6) is found from the real solutions of the bifurcation equation of the form _~3
+ (1 -
(9)
(lip)) • y = 0
where p is the controlling parameter, dependent on ~. When 0 < p < 1, the only stable state ~s) = 0 exists to which there corresponds a racemic state of the system. In the given range of p values the symmetry breaking may occur only due to the AF. Therefore in the subcritical region the system of bifurcation type is similar to the system of evOlutionary type. However, at p > 1, equation (9) has th~ree real solutions, to one of which (~) -- 0) there corresponds an unsteady racemic state, and to the other two (y(~) = ± [1 - (l/p)] 1/2) there correspond steady states with broken mirror symmetry. Thus, upon passage of the critical value pc -- 1, there occurs spontaneous mirror symmetry breaking in the system.
(*)
0
Fig. 6. Bifurcation diagram for monomeric subsystem X in the absence of stereoselective pressure. Points correspond to strong mirror symmetr, t' breaking in X.
Note that the formation of the chirally pure state (~(8) ~- ~-1) is possible upon attaining large values of the controlling parameter (p >> 1). For obtaining 7/(8) ~ 1--10-2 (or ,1~) = - (1--10-2)) it is required that p a 100. In the absence of AF the probabilities for the appearance of both ~(~)and ~(s)states from the initial racemic one have the same value. If, however, AF is acting during the symmetry breaking, one of these two states becomes more probable. Note that this circumstances may determine the sign of handedness of the biosphere (the choice of L-isomers of amino acids and D-isomers of sugars). Especially intensive discussions of this problem have been connected with parity nonconservation in electroweak interactions (Mason and Tranter, 1985; Kondepudi and Nelson, 1985; Avetisov et al., 1987). However, this question is not essential for the analysis of stability of chirally pure states with regard to stereoselective efflux of mirror isomers from the monomeric subsystem X into the polymeric subsystem Q. Taking into account the processes described by (6), for p >> 1 the bifurcation equation (12) takes the form -r/a
+ (1 - ( l i p ' ) ) ' , /
- y'(1
- 7/2) = 0
(10)
where p' ¢¢ p (the bifurcation diagram is shown in Fig. 7). Let the conditions of polymeric takeover be fulfilled (the subsystem X is found on the branch ~ ) in the point S of Fig. 7), i.e. p'~ 10-2, y~) = 1--10-2. Then the subsystem Q is composed of homochiral L-polymers of the length N ¢c 100. We are interested in whether the solution ~(s) remains in the required neighborhood of the chirally pure state in the case of the same values p ~ N, if ~ - ~c ~- 1--AT- 1 (At p >> 1 the growth of K proves to be inessential.) An answer may be obtained by direct calculation of the roots of equation (10). For any values of ~ belonging to the range ~ < l - N - 1 , the solution ~js) exists, it is stable, and with an accuracy of up to corrections ¢¢ O(N-2), it has the form ~(s) _- (1 - /~N-1) + O(N-2), /3 ~ 1. Therefore, for all values ~ -- ~c the chiral polarization of the subsystem Q satisfies the condition (2) and the evolution of the polymeric sub-
148
t
s-T
!
J
0
-t Fig. 7. Bifurcation diagram for monomeric subsystem X, taking into account stereoselective pressure. Point S corresponds to the conditions of the stage of polymeric takeover.
spontaneous symmetry breaking, the formation of protoenzymes capable of enantio-differentiation is possible only in the latter case. Note that until now we have ignored the possibility of forming primary stereospecific protoenzymes on the basis of achiral polymers. Such a scenario, however, assumes the formation of some special achiral polymers in monomer medium. Similar to the case of the formation of heterochiral polymers with a certain regular alternation of the L- and D-isomers in their chains, the probability of this scenario is also exponentially small. The arguments set forth above, in our opinion, give grounds for asserting that spontaneous mirror symmetry breaking of the organic medium was just that specific event in the early history of the Earth, which initiated the prebiological evolution and led to the origin of self-replicating systems based on homochiral structures.
Acknowledgements system X in the direction of structures and functions of biochemical level of complexity proves to be possible. It should also be noted that as soon as ~ reaches values = 1--N -1, the stationary state of ~ ) loses stability and the subsystem Q tends to the mirror antipodal stationary state ,1(_8). These conclusions d e m o n s t a t e t h a t requirements necessary for the successful course of the two basic stages of prebiological evolution are satisfied only in chiral systems of the bifurcation type.
6. Conclusions In the present paper we have demonstrated that a strong evolutionary correlation exists between such important properties of biomacromolecules as homochirality and the ability for self-replication. We have shown that a chirally pure environment is necessary for the origin of homochiral macromolecules at the biochemical level of complexity. Although a chirally pure environment may be reached due to the asymmetric effect or due to
The authors would like to express their gratitude to Prof. L. Keszthelyi and Dr. V. Kuz'min for their valuable discussions of this problem. We would also like to thank unknown referees for valuable comments which have helped to improve the quality of our paper.
References Avetisov, V.A., Anikin, S.A., Goldanskii, V.I. and Kuz'min, V.V. 1985, The strong mirror symmetry breaking as the necessary condition for self-replication. Dokl. Biophys. 282, 115--119. Avetisov, V.A., Kuz'min, V.V. and Anikin, S.A., 1987, Sensitivity of chemical chiral systems to weak asymmetric factors. Chem. Phys. 112, 179--187. Barron, L.D., 1986, True and false chirality and absolute asymmetric synthesis. J. Am. Chem. Soc. 108, 5539--5542. Brack, A. and Spach, G., 1979, B-Structures of polypeptides with L-and D-residues. Part I and Part II. J. Mol. Evol. 13, 35--56. Brack, A. and Spach, G., 1980, B-Structures of polypeptides with L-and D-residues. Part III. J. Mol. Evol. 15, 231--238. Frank, F., 1953, On spontaneous asymmetric synthesis. Biochim. Biophys. Acta 11, 459--463. Goldanskii, V.I., Avetisov, V.A. and Kuz'min, V.V., 1986,
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Chiral purity of nucleotides as a necessary condition of complementarity. FEBS Lett. 207, 181--183. Goldanskii, V.I. and Kuz'min, V.V., 1989, Spontaneous breaking of mirror syrametry in nature and the origin of life. Soy. Phys. Usp. ~;2, 1--29. Grosberg, A.Yu. and Khokhlov, A.R., 1989, Statistical Physics of Makromolekules (Nauka, Moscow) pp. 286--339 (in Russian). Joyce, G.F., Visser, G.M., van Boeckel, C.A.A., van Boom, J.H., Orgel, L.E. and van Westrenen, J., 1984, Chiral selection in poly(C)-directed synthesis of oligo(G). Nature 310, 602--604. Kondepudi, D.K. and Nelson, G.W., 1985, Weak neutral currents and origin of biomolecular chirality. Nature 314, 438--441. Lundberg,R.D. and Doty, P., 1957, Polypeptides. XYII. A study of the kinetics of the primary amino-initiated
polymerization of N-carboxy-anhydrides with special reference to configurational and stereochemical effects. J. Am. Chem. Soc. 79, 3961--3972. Mason, S.F. and Tranter, G.E., 1985, The electroweak origin of biomolecular handedness. Proc. R. Soc. London Ser. A 397, 45--65. Morozov, L.L., 1979, Mirror symmetry breaking in biochemical evolution. Origins Life 9, 187--218. Morozov, L.L., Kuz'min, V.V. and Goldanskii, V.I., 1984, Mathematical grounds and general aspects of the mirror symmetry breaking in prebiological evolution, in Sov. Sci. Rev. ser. D Physicochem. Biol. 5, V.P. Skulachev (ed.) (Harwood, New York) pp. 357--405. Weber, A.L., 1989, Glyceraldehyde as a source of energy and matter for the origin of life, in: Proc. IX Int. Conf. of Origins of Life (ISSOL-89), Prague, Czechoslovakia, pp. 99-100.
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Elsevier Scientific Publishers Ireland Ltd.
Homochirality and stereospecific activity: evolutionary aspects V l a d i k V. A v e t i s o v a n d Vitalii I. G o l d a n s k i i N.N. Semenov Institute of Chemical Physics, Academy of Sciences of USSR, 117334Kossygin st.4, Moscow (USSR) (Received September 4th, 1990) (Accepted March 8th, 1991)
The problem discussed in this paper is the connection between the unique property of biopolymers (proteins, DNA and RNA), i.e. homochirality, and their main functionalproperty, i.e. self-replication. Our approach is based on an analysis of the conditions for the origination of the mechanism of self-replication of chiral polymers. It is demonstrated that self-replication could originate only on the basis of homochiral structures, possessing stereospecific (enzymatic) activity. It is also shown that complete breaking of the mirror symmetry of the organic medium is required both at the stage of polymeric takeover and at the stage of formation of sl;ructures possessing stereospecific activity. This requirement is satisfied only in the framework of the mechanism of spontaneous symmetry breaking i.e. the mechanism of non-equilibrium phase transition from the racemic state of the organic medium to the chiraily pure one. The results obtained suggest that homchirality is a necessary condition for the origination of biological specificity and plays a fundamental role in the formation of structures capable of self-replication.
Keywords: Biopolymer,% Homochirality; Self-replication; Stereospecific activity; Symmetry breaking; Evolution.
1. Introduction It is well known that the organic compounds (nucleotides and amino acid residues) which make up polymeric chain units are chiral (except for glycine); their' spatial structure does not have mirror symmetry and therefore they may exist in two mirror-isomeric L and D forms. However, these biopolymers consist of fragments of a defini~e stereoisomeric form only. For example, all enzymes contain only Lisomers of amino e~id residues, whereas nucleic acids contain only D-isomers of ribose or deoxyribose. The existence of the property mentioned above means that the scenario of prebiological evolution either should include the step of the formation of homochiral polymers or make it possible at some subsequent stage of evolution. Some arguments for the formation of homochiral polymers during prebiological evolution
are presented in Sections 2 and 3. In Sections 4 and 5 we discuss conditions necessary for this step while the last section contains our main conclusions. 2. Is homochirality a consequence of specific features of polymeric takeover of the medium? Let us consider the conditions for the assembly of a polymeric chain, for instance of L-type, in a medium with chiral polarization = (XL - XD)/(XL + XD) (XL and XDbeing the concentrations of L- and D-isomers from which the chain is assembled). The quantity ~ describes the relative enantiomeric excess. If the probability of addition of a unit to the end portion of the chain does not depend on its isomeric form, the relative probability l) of assembly of a homochiral portion of the chain of the length N is equal to fl -- ¢~N _- exp[N In ~1,
0303-2647/91/$08.50 (9 1991 Elsevier Scientific Publishers Ireland Ltd. Published and Printed in Ireland
142
where co = (1+ 7)/2 is the relative concentration of L-isomers in the medium. The value decreases with N and becomes exponentially small when - N In co < 1. For this reason, the formation of homochiral polymers of length N is possible only when - l n w < N - 1, and consequently, chiral polarization of the medium must satisfy the condition 7 > 1 - 2N-1. This is a very rigid condition. For instance, for the formation of a homochiral chain of length N oc 100, the medium must be practically chirally pure (7 > 1--10-2). In a racemic medium (7 = 0) the probability of random assembly of a homochiral portion of the same length (fl a 2-100) is vanishingly small even for time periods of the order of the age of the Universe (~ 1017 s). However, this result, assuming no stereoselectivity, is an idealization: it is necessary to take into account not only the isomeric composition of the medium, but also stereoselectivity `/of the interaction of mirror antipodes with an active portion of the growing chain. Let col and COd -- 1 - COLbe the relative probabilities of addition of L- and D-isomers to the end fragment of L-type in the racemic environment. It is convenient to specify the value `/in the form `/ = 1 - 2ooD. If the chain growth is nonselective, ~0L ---- COD = 1/2 and `/ = 0, as considered above. If the chain growth is absolutely stereoselective, then COD ---- 0 and `/ = 1. The relative probability of assembly of a homochiral portion of length N is now equal to
Figure 1 shows the dependence of 7c on `/for N 100 (the area of values 7 satisfying condition (2) is hatched). At sufficiently large N the dependence 7c (`/) has the character of abrupt turnover. For almost all values of `/in the large 0 to 1 except the narrow area `/ > 1--10 -2, corresponding to absolute stereoselective growth of the polymer chain, the values of 7c change slightly, remaining in the neighborhood of the chirally pure state (7c ~ 1--10-2). However, near `/= 1, in the area of-/ > 1--10 -2, 7c drops sharply down to zero. Thus, the polymeric takeover of the organic medium by homochiral structures is possible either (A) in a chirally pure medium (7 > 1--10 -2) or (B) in the case of absolute stereoselectivity in the polymer assembly (`/ > 1--10-2). In the scenarios of prebiological evolution based on situation (A), the stage of polymeric takeover must be preceded by strong symmetry breaking of the organic medium. Therefore, the origin of homochiral polymers and their evolution along the path to almost absolute stereoselection (i.e. the formation of structures possessing stereospecific activity) must take place in a chirally pure medium. Steady maintenance of the chirally pure state throughout the stage of formation of specifically active structures is also necessary.
----(CO * 00L)N ----expIN In(co • COL)}
/L0"2
I
and it is not exponentially small when -ln(~ • COL) <~ N -1, i.e. when (1 - ~) (1 -`/)
< N -1
(1)
0.5-
From (1) it is easy to derive the condition for formation of homochiral polymers of length N taking into account the stereoselectivity `/:
0
2(1 + ,!`/)
2a
7/ >,Ic = 1 - - - ,
N+~
wherea--
i+7
1-`/
(2)
i
/.=
Fig. 1. The plot of ~c(7) in the case of assembly of a homochiral polymer. The area of the ~ and V values satisfying the condition of assembly of a homochiral chain is hatched.
143
In the scenarios based on situation (B), the organic medium is racemic, i.e. it does not possess any nontrivial properties. But the appearance of homochiral polymers must of necessity have been preceded by a stage of formation of heterochiral structures possessing stereospecific activity. In this case the origination of homochiral self-replicating systems is the result of evolution of their heterochiral precursors. This dilemma may be solved if one shows that only homochiral protoenzymes might be formed during the prebiological evolution. 3. should heteroclMral protoenzymes exist? It should be stressed at once that complete understanding of the process of selforganization of biological macromolecules has not been reached so far. Nevertheless, it is clear already that their main feature is their hierarchic structures (Grosberg and Khohlov, 1989), i.e. primary, secondary and tertiary structures. The role of the stereoisomeric composition of the polymeric chain in the formation of its second'ary and tertiary structures is thus of special interest. This important problem was investigated in detail in a number of studies (Lundberg and Doty, 1957; Brack and Spach, 1979; Brack and Spach, 1980; Goldanskii et al., 1986), where it was shown that chiral defects hinder the formation of both the double helix in polynucleic acids and the a-helix and/3-sheets in polypeptides, i.e. they hinder the formation of the main motifs of the secondary structure of the biomacromolecules. In heterochiral polymers with random disposition of mirror isomers along the chain there arise such strong steric hindrances that formation of these secondary-structure motifs proves to be impossible. However, one cannot exclude that a certain regular alternation of the L- and D-isomers in the chain could alh)w the formation of secondary structure (such heterochiral polymeric structures were discussed, for example, by Weber, 1989). Could such macromolecules play an essential role in the prebiological evolution? An
answer to this question may be obtained from an analysis of the conditions of takeover of the organic medium by polymers with a certain definite sequence of the L- and D-isomers. Let the primary structure of the heterochiral polymer of length N be a certain ordered alternation of m fragments of L-type and n fragments of D-type (m = n). A chiral defect here will be simply a violation of the order of alternation of the isomers in any pair of the units (see Fig. 2). Suppose also that the mechanism of stereodifferentiation of mirror antipodes at the end portion of the chain ensures a certain advantage for the addition of a correct isomer and, consequently, the stereoselectivity of ~ ffi 1 - 2¢0def > 0 (~def being the relative probability of the appearance of a chiral defect in racemic environment). Then the probability ON of the assembly of a defect-free chain of the length N -- m + n is fiN = (1-o~Lef)m (1-¢0Def)n ffi
exp[m ln(i-o~dief) + n ln(1-~Def)/
where (1+,1) ( l - v ) 2(1 + 'r/)
o)Le f _-
and o~Def= (1-7) (1-7) 2(1 + 'I~)
are the relative probabilities of formation of chiral defects of L- and D-types, respectively. The value fin is not exponentially small when I n ( l - ~Lef) + n In(1 - o~dDef)} < 1
-/m
---
II
---
~'.
---
I
---
O
""
U
---
O
.--
chain
defect-free
C]
---
(3)
II
---
II
---
•
---
O
---
I chiral
defect
Fig. 2. Chiral defect in heterochiral chain: • and [] are conventional designations of mirror antipodes.
144
From (3) it is not difficult to obtain the condition of takeover of the organic medium by defectfree polymeric structures: N-or
N+~
o/-i
< Y <
(4)
cz+N
where, as in (2), a = (1 + 7)/(1 - 7). It should be noted that condition (4) is fulfilled only for a > N, i.e. when 7 > 1 - 2 N -1. The region of the values (~,7), satisfying condition (4), is demonstrated in Fig. 3. When N ~ 100, it is a narrow peak (having a width oc 10-2), confined near the value 7 = 1. Thus, in the absence of almost absolute stereoselectivity in a chain assembly, takeover of the organic medium by heterochiral polymers with any sequence of the L- and D-isomers specified in advance is exponentially suppressed at all values ,1 of the chiral polarization. As a result, we come to the conclusion that the formation of heterochiral protoenzymes is impossible either because of strong structural limitations (when the disposition of the L- and Disomers in the polymeric chain is random) or because of strong kinetic limitation of the process of polymeric takeover (by structures with any unique sequence of the chiral fragments).
4. Two main stages of prebiological evolution
From the above analysis it follows that only situation (A) provides a consistent scenario for prebiological evolution. Within this, the stages of prebiological evolution may be represented by the scheme in Fig. 4. This scheme reflects two distinctive features which are, in our opinion, important. First of all, strong breaking of the mirror symmetry of the organic medium preceded the stage of polymeric takeover and, thus, predetermined the formation of homochiral polymers. This conclusion was derived earlier (Avetisov et ai., 1985) from the assumption that at the stage of polymeric capture an essential role in the formation of homochiral polymers might be played by the process of matrix oligomerization (Joyce et ai., 1984). However, as shown above, this conclusion may also be derived from more general consideration. Another specific feature of the prebiological evolution is that the chiral purity of the medium was maintained not only at the stage of z synthesis o f organic compounds
i V racemic organic medium (~=0, ¥<10"21
strong breaking of mirror symmetry V chirally pure organic medium { ~ > 1 - 1 0 -2,
o5
~<10 -2 }
q V homochiral polymers ( ~ > 1 - 1 0 "2 , ~<<1)
#--.40o
,
0
~
formation of stereospecific enzymatic activity
V homochiral "chemical automata" ( ~ > 1 - 1 0 "2 ) II V
Fig. 3. The plot of ,c(7) in the case of assembly of a heteroehiral (L,D)-polymer. The area of the ~/and 7 values satisfying the condition of assembly of heteroehiral chains is hatched.
polymeric takeover of medium
(
f.... tion of selfreproducin~ systems
Fig. 4. Scheme of the main stages of prebiological evolution.
145
polymeric takeover, but also in the next important stage: the formation of structures and functions of the biochemical level of complexity. It was only after the appearance of the stereospecific mechanism of the synthesis of homochiral polymers that chiral purity of the medium was no longer necessary. Thus, the specilSc feature of prebiological evolution is not oni[y strong breaking of mirror symmetry, but also stability of the chirally pure state of the medium throughout the stage of formation of protoenzymes. The latter requirement is stronger than the requirement of mirror symmetry breaking itself. This is due to the fact that the efflux of mirror isomers of predominantly one kind (and their incorporation into polymeric structures) is an asymmetric process, which may lead to a reduction of the chiral purity of the monomer medium. Indeed, let us consider a simple kinetic diagram of an asymmetric withdrawal of L- and D-isomers from a monomeric subsystem X into a polymeric subsystem Q (Fig. 5): L
kL
--
Q, D
kD
--
Q
(5)
(k L and kD being the effective values of the polymerization rate constants of the L- and D-
isomers, respectively). The contribution of processes (5) to the dynamic equation for the chiral purity of the monomeric subsystem has the form d~ dt
K~(l_~2)
(6)
where K = (kL + kD)/2 and ~ -- (kL - kD)/(k L + kD) is the stereoselectivity of the formation of polymeric chains (for the sake of definiteness we assume that chiral defects correspond to the incorporation of D-isomers into the L-chain, i.e. ~>0). It is easy to see that equation (6) describes the process of diminution of ~ to zero. Consequently, in the formation of homochiral polymers, the monomeric medium experience an additional asymmetric effect of racemizing type. This asymmetric kinetic factor, brought about by the interaction of the polymeric and monomeric subsystems, is called by us the stereoselective pressure and denoted as a = KT. In the course of polymeric takeover of the chiral medium and formation of stereospecific catalytic functions, the value of a increases because of the growth of ~/ from ~/ ~ 10 -2 to ~ ¢¢ 1 - - 1 0 -2 Therefore, a viable mirror symmetry breaking process must also be able to maintain chiral purity despite the growth of stereoselective pressure.
5. Strong breaking of mirror symmetry: evolutionary accumulation of asymmetric action or non-equilibrium phase transition?
I//,
/: J/ / / / )
x"
Fig. 5. Model presentation of the stage of polymeric takeover. Asymmetric efflux of L- and D-isomers from monomeric subsystem X into polymeric subsystem Q creates stereoselective pressure.
Finally, let us consider which processes of mirror symmetry breaking satisfy these conditions. Strong mirror symmetry breaking in the prebiological evolution has been the subject of recent extensive discussions (see the review of Goldanskii and Kuz'min, 1989 and references therein). There are two basic classes of symmetry breaking mechanisms; evolutionary or the bifurcation type. For each of them we investigate changes of chiral purity during the growth of stereoselective pressure.
146 In systems of the evolutionary type, the symmetry breaking is brought about by the asymmetry of the constants of mirror-conjugated channels of the transformations of the L- and Disomers, arising as a result of a certain (external) asymmetric effect (for example, circularly polarized radiation, an asymmetric mineral catalyst, etc. (Barron, 1986)). The change of chiral polarization (t) with time has the form d__~ = g (l_y2) _ KRrt dr
i +
[1 + (g/KR) 2] 1/2 ]-1
d,, -"
fir
= (g - roK'l) (1-7/2) - KRr/
The value Ymaxin this case may by derived from (7) through the replacement g -- (g -- r0Ky). Therefore, the condition of strong mirror symmetry breaking has a similar form:
(8)
(g - roK~l)/K R >> 1
where g = (kL(i) - kD(i))/(kb (i) + kn (/)) is the advantage factor (AF) (kL(0, kD(i) being the rate constants of mirror-conjugated reactions of i-th type), , -- 7o-1" t is the dimensionless time related to the scale ~'o o¢ (kL(i) + ~D (i)) -1, and KR is the racemization factor (RF) which is the reciprocal relaxation time of y to zero upon switching off of the AF (g = 0). The maximum chiral polarization ~max,which is attainable in systems of the evolutionary type, is given by the expression ~max = ( g / k R ) [
system (5), the dynamic equation for the chiral polarization of the monomeric takes the form
(7)
When the AF to RF ratio is large, the mirror symmetry breaking is strong (for (g/KR) o~ 10 2, Ymax = 1--10-2). Therefore, if there are no additional requirements, the problem concerning strong mirror symmetry breaking of the medium, in principle, may be discussed within the framework of processes of the evolutionary type. It is known that the AFs caused by different external asymmetric effects on chemical transformations reach values of g g 10 -2. Consequently, it cannot be excluded that, in a certain organic area, conditions of transformation of the mirror isomers may have arisen for which the AF to RF ratio was greater than 1 and, as result, strong mirror symmetry breaking of the medium occurred. However, we shall demonstrate that if such an event preceded the stage of polymeric takeover of the organic medium, it could not play an essential role in subsequent stages of prebiological evolution. Taking account of the asymmetric efflux of mirror isomers into the polymeric sub-
Suppose now, that the conditions of the first stage of prebiological evolution are fulfilled, i.e. for a certain AF the ratio (g - roKT)/KR o: 102, ~max 1--10 -2, and abiogenic synthesis (7 10 -2, K a r0 -1) of homochiral polymers of the length N ~ 100 creates a selective efflux of the isomers into the subsystem X. The next stage of evolution is the formation of stereospecific catalytic function. At this stage 7 - 7c ~1 - 1 0 -2 and K ~ K" > r0 -1. It is obvious, however, that for any abiogenic AF, condition (8) will be violated even before the critical stereoselectivity % is reached. Consequently, the formation of the stereospecific function will be blocked. It should be noted that since for all the known abiogenic AFs g << 1, the formation of polymer structures of the biological level of complexity in monomeric systems of evolutionary type proves to be not feasible. Now we shall consider systems of the bifurcation type. In such systems symmetry breaking is a nonlinear process, leading to instability of the symmetric (racemic) state when passing the critical values of the control parameters (bifurcation point) (Frank, 1953). For the given class of the processes of mirror symmetry breaking, (t) is defined by the system of dynamic equations of the form (Morozov, 1979; Morozov et al., 1984) ~
d~--E
=
- A ( O , X ) • na
dt dO__ = f(O,;~,~2) dt
+
B(O,),) •
147
where E) = XL + XDis the total concentration of mirror isomers in the system, ~ is a parameter, whose value may vary the concentration of the achiral reagent or the density of the flux of energy through the system, A (O,k) and B(O,~) are implicit time functions, whose form is specified by the kinetics of the transformations of the Land D-isomers. The value of chiral polarization n(~)in the stationary state (see Fig. 6) is found from the real solutions of the bifurcation equation of the form _~3
+ (1 -
(9)
(lip)) • y = 0
where p is the controlling parameter, dependent on ~. When 0 < p < 1, the only stable state ~s) = 0 exists to which there corresponds a racemic state of the system. In the given range of p values the symmetry breaking may occur only due to the AF. Therefore in the subcritical region the system of bifurcation type is similar to the system of evOlutionary type. However, at p > 1, equation (9) has th~ree real solutions, to one of which (~) -- 0) there corresponds an unsteady racemic state, and to the other two (y(~) = ± [1 - (l/p)] 1/2) there correspond steady states with broken mirror symmetry. Thus, upon passage of the critical value pc -- 1, there occurs spontaneous mirror symmetry breaking in the system.
(*)
0
Fig. 6. Bifurcation diagram for monomeric subsystem X in the absence of stereoselective pressure. Points correspond to strong mirror symmetr, t' breaking in X.
Note that the formation of the chirally pure state (~(8) ~- ~-1) is possible upon attaining large values of the controlling parameter (p >> 1). For obtaining 7/(8) ~ 1--10-2 (or ,1~) = - (1--10-2)) it is required that p a 100. In the absence of AF the probabilities for the appearance of both ~(~)and ~(s)states from the initial racemic one have the same value. If, however, AF is acting during the symmetry breaking, one of these two states becomes more probable. Note that this circumstances may determine the sign of handedness of the biosphere (the choice of L-isomers of amino acids and D-isomers of sugars). Especially intensive discussions of this problem have been connected with parity nonconservation in electroweak interactions (Mason and Tranter, 1985; Kondepudi and Nelson, 1985; Avetisov et al., 1987). However, this question is not essential for the analysis of stability of chirally pure states with regard to stereoselective efflux of mirror isomers from the monomeric subsystem X into the polymeric subsystem Q. Taking into account the processes described by (6), for p >> 1 the bifurcation equation (12) takes the form -r/a
+ (1 - ( l i p ' ) ) ' , /
- y'(1
- 7/2) = 0
(10)
where p' ¢¢ p (the bifurcation diagram is shown in Fig. 7). Let the conditions of polymeric takeover be fulfilled (the subsystem X is found on the branch ~ ) in the point S of Fig. 7), i.e. p'~ 10-2, y~) = 1--10-2. Then the subsystem Q is composed of homochiral L-polymers of the length N ¢c 100. We are interested in whether the solution ~(s) remains in the required neighborhood of the chirally pure state in the case of the same values p ~ N, if ~ - ~c ~- 1--AT- 1 (At p >> 1 the growth of K proves to be inessential.) An answer may be obtained by direct calculation of the roots of equation (10). For any values of ~ belonging to the range ~ < l - N - 1 , the solution ~js) exists, it is stable, and with an accuracy of up to corrections ¢¢ O(N-2), it has the form ~(s) _- (1 - /~N-1) + O(N-2), /3 ~ 1. Therefore, for all values ~ -- ~c the chiral polarization of the subsystem Q satisfies the condition (2) and the evolution of the polymeric sub-
148
t
s-T
!
J
0
-t Fig. 7. Bifurcation diagram for monomeric subsystem X, taking into account stereoselective pressure. Point S corresponds to the conditions of the stage of polymeric takeover.
spontaneous symmetry breaking, the formation of protoenzymes capable of enantio-differentiation is possible only in the latter case. Note that until now we have ignored the possibility of forming primary stereospecific protoenzymes on the basis of achiral polymers. Such a scenario, however, assumes the formation of some special achiral polymers in monomer medium. Similar to the case of the formation of heterochiral polymers with a certain regular alternation of the L- and D-isomers in their chains, the probability of this scenario is also exponentially small. The arguments set forth above, in our opinion, give grounds for asserting that spontaneous mirror symmetry breaking of the organic medium was just that specific event in the early history of the Earth, which initiated the prebiological evolution and led to the origin of self-replicating systems based on homochiral structures.
Acknowledgements system X in the direction of structures and functions of biochemical level of complexity proves to be possible. It should also be noted that as soon as ~ reaches values = 1--N -1, the stationary state of ~ ) loses stability and the subsystem Q tends to the mirror antipodal stationary state ,1(_8). These conclusions d e m o n s t a t e t h a t requirements necessary for the successful course of the two basic stages of prebiological evolution are satisfied only in chiral systems of the bifurcation type.
6. Conclusions In the present paper we have demonstrated that a strong evolutionary correlation exists between such important properties of biomacromolecules as homochirality and the ability for self-replication. We have shown that a chirally pure environment is necessary for the origin of homochiral macromolecules at the biochemical level of complexity. Although a chirally pure environment may be reached due to the asymmetric effect or due to
The authors would like to express their gratitude to Prof. L. Keszthelyi and Dr. V. Kuz'min for their valuable discussions of this problem. We would also like to thank unknown referees for valuable comments which have helped to improve the quality of our paper.
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