Spontaneous chiral symmetry breaking in early molecular networks

Abstract

Background: An important facet of early biological evolution is the selection of chiral enantiomers for molecules such as amino acids and sugars. The origin of this symmetry breaking is a long-standing question in molecular evolution. Previous models addressing this question include particular kinetic properties such as autocatalysis or negative cross catalysis.

Results: We propose here a more general kinetic formalism for early enantioselection, based on our previously described Graded Autocatalysis Replication Domain (GARD) model for prebiotic evolution in molecular assemblies. This model is adapted here to the case of chiral molecules by applying symmetry constraints to mutual molecular recognition within the assembly. The ensuing dynamics shows spontaneous chiral symmetry breaking, with transitions towards stationary compositional states (composomes) enriched with one of the two enantiomers for some of the constituent molecule types. Furthermore, one or the other of the two antipodal compositional states of the assembly also shows time-dependent selection.

Conclusion: It follows that chiral selection may be an emergent consequence of early catalytic molecular networks rather than a prerequisite for the initiation of primeval life processes. Elaborations of this model could help explain the prevalent chiral homogeneity in present-day living cells.

Figure 1

The number of possible chiral (solid) and non-chiral (dashed) isomers as a function of the number of carbons in an Alkane. Red represents a case where one carbon is replaced by a hetero atom, and blue denotes a case of no hetero atom. Data is taken from [54]. This figure demonstrates that for sufficiently complex molecular structures it is a good approximation to assume that all molecules are chiral [51-55].

Figure 2

An illustration of a 2N_G × 2N_G β matrix and the value of α. Note that the two blocks along each diagonal have identical values of the affinities (β^LL = β^DD and β^LD = β^DL ).

Figure 3

A, Correlation diagram between pairs of time points during a C-GARD simulation, using Eq. 1. H = 1 and H = 0 (Eq. 2) are respectively marked by red and blue, and 0 <H< 1 is shown by intermediate rainbow colors. Parameter values used are: k_f = 5 × 10^-2, k_b = 5 × 10^-3, N_G = 100, N_max = 200, ρ = 10^-2 and σ_ε = 6; B, The time-dependent behavior of weak enantiomeric selection (W_w, Eq. 7) during this simulation; C, Composome assignments for the assemblies analyzed in B (see Methods). Note that each composome tends to have a distinct W_w value.

Figure 4

Time dependence of W_W for three simulations (σ_ε = 1 green, σ_ε = 3 red, σ_ε = 6 blue). Other parameter values are as in Figure 3. It is seen that the typical W_W increases with σ_ε, because higher enantiomeric discrimination (α) values are allowed. The saw-tooth patter arises from growth-fission cycles of the C-GARD assembly.

Figure 5

Two dimensional analysis of the dependence of average W_W on λ and σ_ε. Data are based on 60 simulations, each with 4000 time steps, with the same parameters as in Figure 3, except N_max = 300. Figure produced from ref[86].

Figure 6

Probability distribution of W_W at different values of σ_ε (colors as in Figure 4) based on 6000 simulations for each σ_ε value. Other parameter values are as in Figure 3, except k_f = 10^-2, k_b = 10^-3

Figure 7

A correlation diagram displaying the chiral compositional dynamics of C-GARD molecular assemblies with respect to both the similarity H (Eq.2) and the antipodicity M (Eq. 5). Three composomes (C1, C2 and C3) emerge in this simulation, with C2 and C3 being antipodes of each other. The 2-dimensional color scale is shown in the inset. Purple color indicates that at least one of the compositions is racemic, while off-diagonal blue shows appreciable antipodicity. Simulation parameters as the same as in Figure 6, except N_max = 300 and σ_ε = 0.8.

Figure 8

Compositional bar-chart for the composomes C2 and C3 (Figure 7). The molecule index is serial number representation of the different compounds (1...N_G), and D and L enantiomers are indicated by color and vertical direction. The Y axis is the count of a given molecule type within the composomal assembly.

Figure 9

C-GARD population dynamics emulating the competitive coexistence of composomes. The time dependent population sizes for the different composomes were reconstructed in an approximated fashion from single assembly simulations as described in the text. Simulation parameters are as in Figure 3.

Figure 10

A, the chiral relations among the composomes of Figure 9, with color scheme as in Figure 7; B, the compositional bar charts for all 9 composomes.

Figure 11

Distribution the values of α extracted from CHIRBASE [75] (circles) and a fit (solid line) as described in the Methods with σ_ε = 0.8 (Eq. 6 and ref. 69). CHIRBASE database holds experimentally obtained retention data (about 60,000 values at 2003) which were transformed into thermodynamic association constants according to published relationships derived for quantitative affinity chromatography [87-89]. The insert shows a double logarithmic transformation of the data over a larger range, with a limiting linear slope of -1.98 and R = 0.99, in line with a lognormal distribution tail.

Figure 12

Schematic illustrations of compositions giving rise to different values of W_W and W_S (Eqs. 6 and 7). In these illustrations N_max = 120 and N_G = 6. Figure details are as Figure 8.