Enantiomeric excess by magnetic circular dichroism in Archaean atmosphere

Evolution of homochirality requires an initial enantiomeric excess (EE) between right and left-handed biomolecules. We show that magnetic circular dichroism (MCD) of sun’s ultraviolet C light by oxygen in Archaean earth’s anoxic atmosphere followed by chirally selective damage of biomolecules due to circular dichroism (CD) can generate EE of correct handedness. Our calculation of EE uses published data for CD of biomolecules and accepted magnitude for Archaean earth’s magnetic field. Independent of atmospheric oxygen concentration calculated EE has the same sign for all pyrimidine nucleosides which is opposite to that for amino-acids. Purine nucleosides have smaller EE values with opposite sign to pyrimidines but are less susceptible to UV damage. Homochirality is explained by origin of prebiotic life in one hemisphere of earth and its evolution to EE ~ ± 1 before reversal of terrestrial magnetic field. Chirality of biomolecules is decided by the direction of magnetic field where prebiotic life originated on Archaean earth.

oxygen 12 that would support MIF-S is p(O 2 ) ~10 −2 PAL. As shown in this report the sign of EE of nucleosides and amino-acids is independent of oxygen concentration but depends significantly on the pressure of carbon-dioxide in Archaean atmosphere.

Results
Transmission of UVC in Archean atmosphere. For analysis in this report, carbon dioxide and oxygen are the two most important components of Archaean atmosphere when prebiotic life arose around 4 billion years ago. While CO 2 is primarily responsible for attenuating far UV sunlight in wavelength range of 200-300 nm 15 , O 2 is the only atmospheric component which is paramagnetic and capable of producing MCD of this UV light. Concentration of O 2 in atmosphere will determine the extent of MCD of UV light and the differential circular polarization (CP) intensity reaching earth's surface. Accepted models 16 for earth's atmosphere around 4,000 Mya require high CO 2 pressure (0.1-10 bar) to compensate for lower solar luminosity of young Sun. Figure 1 is a plot of calculated UVC flux reaching early Archaean earth's surface (p(CO 2 ) = 0.25, 1, 2 bar) and shows that wavelengths below 200 nm were strongly attenuated. In plotting these curves, accepted values are used for CO 2 absorption cross-sections, density-altitude profile and the spectral-intensity of sunlight reaching earth's upper atmosphere 4,000 Mya 15 . For wavelengths in 200-300 nm, molecular oxygen absorbs weakly by three forbidden transitions 17,18 , giving rise to the Herzberg continuum which originates in paramagnetic X 3 Σ − g ground state and is important for atmospheric physics. As seen in Fig. 1, total absorption cross section for these transitions in oxygen (X 3 Σ − g → A 3 Σ + u , X 3 Σ − g → c 1 Σ − u and X 3 Σ − g → A '3 Δ u ) rapidly decreases from 200 nm to 300 nm [17][18][19] . In laboratory, MCD of O 2 has been observed 20 within the Herzberg continuum by a matrix-isolation technique at low temperatures and high magnetic field. Attenuation by CO 2 and absorption cross-section for oxygen in Fig. 1 serves to explain why the effect of MCD by Archaean atmospheric oxygen is unimportant outside the spectral region of 200-300 nm.
Magnetic circular dichroism of UVC in Archean atmosphere. The dipolar geomagnetic field is as old 11 as the Earth itself with the dipole axis nearly but not exactly aligned with axis of earth's rotation. Paleomagnetism 11,21 evidence suggests that the magnitude of magnetic field has not changed significantly since 4,000 Mya. The magnetic poles have wandered by as much as 15-20° but for the purpose of this analysis we will assume that the axis of dipole coincides with the axis of earth's rotation (Fig. 2). We also assume the magnetic field intensity at the equator of 0.3 Gauss which is the present average value 22 for this latitude; and the tilt of earth's axis towards the ecliptic plane as θ T = 23.4° (current value). For MCD, the component (B S ) of geomagnetic field parallel to the direction of sunlight reaching earth at zenith (midday) varies with the latitude as well as the time of the year and is derived with reference to Fig. 2a. Close to the surface of Earth (radius R), the radial (B r ) component of the dipolar magnetic field and the component parallel (B || ) to earth's surface is given by 22 where B 0 is the magnetic field at the equator and θ L is the latitude of the position on earth. Average value of B 0 on the equator is 0.3 Gauss. For the geometry shown in Fig. 2a (northern solstice) when the North Pole is most tilted towards the sun, the component of earth's magnetic field in the direction of sunlight at zenith (midday) is: where θ T = 23.4° is the angle of tilt of the earth's axis towards the ecliptic plane. Similarly, for southern solstice when the North Pole is most tilted away from the sun, the component of earth's magnetic field in the direction of sunlight at zenith (midday) is: S r L T L T Both B r and B || vary 22 with radial distance (r) as (R/r) 3 which shows that for distances of up to 100 km above earth's surface B S varies by less than 3%. Atmosphere of this thickness accounts for 99% of all gaseous oxygen around earth 22 .
Magnetic field B S is shown in Fig. 2b for two different times of the year, i.e. for northern and southern solstices. For given latitude, B S varies over period of a year between the two extremes of solstices. As shown by the shaded (dark gray) region in Fig. 2b, only for a small range of latitudes (24°N to 58°N and 24°S to 58°S), B S remains significant (|B S | > 0.25 Gauss) throughout the year without changing sign. In the light-gray regions (close to equator and the poles) of Fig. 2b, B S changes sign in the course of a year. With these assumptions, 24°N to 58°N and 24°S to 58°S are the most important geographic regions where the effects of MCD are observed.
The significance of MCD-related transitions 20 in molecular oxygen which results in net circular polarization of UVC light is explained with Fig. 3. Of the three forbidden transitions, X 3 Σ − g → A 3 Σ + u is the strongest, accounting for most (86%) of the absorption 18 in Herzberg continuum. Zeeman splitting of states by the small (~0.25 Gauss) geomagnetic field and possible transitions with left circularly polarized (LCP, σ + ) and right circularly polarized (RCP, σ − ) light (propagating in the direction of magnetic field) are shown schematically. In the ground X 3 Σ − g state, Boltzmann distribution will result in a small excess of population in M S = −1 over M S = +1. As seen in this figure, for X 3 Σ − g → A 3 Σ + u and X 3 Σ − g → c 1 Σ − u transitions, M S = −1 in the ground state can only absorb σ + light while M S = +1 can only absorb σ − light. Population difference between M S = −1 and M S = +1 results in slightly greater absorption of σ + light over σ − . This is not possible with X 3 Σ − g → A ′ 3 Δ u transition (Fig. 3). Net (albeit very small) circular polarization of light reaching earth's surface is a result of 3 Σ → Σ transitions in molecular oxygen, i.e. UV light reaching earth will be net σ − when propagating in the direction of earth's magnetic field and net σ + when propagating against the direction of magnetic field. Differential (net) circular polarization (CP) intensity due to MCD by atmospheric O 2 is derived as follows: If I + (λ) and I − (λ) is the spectral intensity (W.m −2 . nm −1 ) of LCP (σ + ) and RCP (σ − ) circularly polarized solar UV radiation respectively, reaching the earth's surface after passing through the atmosphere, I 0 (λ) is the initial (above atmosphere) unpolarized intensity (equal components of RCP and LCP). Coefficients α + and αdescribe bulk of the atmospheric absorption 23 by CO 2 and relatively very weak differential absorption of circularly polarized light (MCD) by atmospheric O 2 .
The integration is over altitude (L) between 0 and 100 km of atmosphere which adequately 24 includes absorption by more than 99% of CO 2 and O 2 .
H is the energy difference between M S = −1 and M S = 1 Zeeman levels for magnetic field H; µ B is the Bohr magneton, g is the Lande factor, ΔM S = 2 for the two relevant sublevels of the ground state X 3 Σ − g and k is the Boltzmann constant. We assume, H ≡ B S = 0.25 Gauss, Lande g factor 25 ≈2 and T = 300 K giving, ΔE/kT = 2.24 × 10 −7 .
Due to three nearly degenerate magnetic sublevels of the ground state of O 2 , E H kT is the total number density of O 2 at altitude L. Spectral intensities I + (λ) and I − (λ) are calculated from above equations, published data for absorption cross-sections σ(CO 2 , λ) 15 and σ(O 2 , λ) [17][18][19] , and the density-altitude profile 15 for given surface pressure of CO 2 . We assume complete mixing of CO 2 and O 2 , i.e., N( . Energy levels for molecular absorption from the X 3 Σ − g ground state of paramagnetic molecular oxygen. X → A accounts for bulk of the absorption in the forbidden Herzberg band and is most important for MCD. Due to Boltzmann distribution in the ground state magnetic sublevels, σ + (LCP) light will be absorbed more than σ − (RCP) light and there will be a small relative excess of σ − light reaching earth's surface for magnetic field in the direction of light propagation.

Enantiomeric excess for biomolecules. Calculation of EE is made for biomolecules in aqueous medium
as is the case with most theories for origin of prebiotic life in marine/freshwater environment 26,27 . The products of Miller Urey type reactions with atmospheric gases collected over the large surface area of Archean oceans. Concentration of amino acids in Archean oceans is estimated to vary 27,28 from 4 × 10 −3 M to 10 −7 M. Concentration of five nucleobases in one Miller-Urey experiment 29 was measured to be between 1-100 ppm. While these numbers are small, there are several proposed mechanisms for amplifying the concentration of prebiotic molecules on ocean shorelines and drying freshwater ponds 30 . Additionally, enantiomeric excess depends on the ratio and not absolute values of enantiomeric concentrations. As shown in a recent report 31 , around 4000 Mya the pH of seawater was in the 6.5-7.0 range and not too different from freshwater. Data used in this report is for solutions of pH around 7. While asymmetric photolysis and enantiomeric enrichment of amino acids by circularly polarized light in liquid varies with the acidic pH in the range of 2-6, there is no effect of pH in the 6.5-7.0 range or higher 32,33 .
Chiral molecules like nucleic acid monomers and amino acids show circular dichroism 34,35 in the 200-300 nm region of UV light. Starting with a racemic population of these prebiotic building blocks of life, exposure to net circularly polarized UVC light will result in an enantiomeric excess that will be a seed for evolution to homochirality. Such an explanation has been proposed 4 for the observed enantiomeric excess of L-amino acids in chondritic meteorites and assumes that the UV damage/inactivation rates D R , D L of right-/left-handed biomolecules are proportional to light absorption rates. This is also seen from the observed similarity of absorption spectrum and action spectrum for direct photo-damage of nucleic acids by UVC radiation 36,37 . Using published CD parameter Δε(λ) 34,35 , extinction coefficient ε(λ) 35,38-40 and calculated differential CP intensity ΔI(λ) ≡ (I -(λ) − I + (λ)), the differential UV damage rate ΔD/D ≡ (D R − D L )/ (D R + D L ) for nucleosides and amino acids is derived below. As shown here, enantiomeric excess is related to ΔD/D.
Cross sections for absorption of UV by biomolecules (amino-acids/nucleosides) are listed below. .
. It is commonly assumed that the UV destruction/damage rate (D) for nucleic acids 36 Relative efficiency for photolysis has been studied only for a few amino acids and for some isolated wavelengths. As an example, photolysis of phenylalanine at 206 nm and 254 nm does not show any significant effect of wavelength 43 . Further, CD of amino acids is significant only over a band-width of 20-30 nm 34 . Above equation to calculate ΔD/D is used for nucleosides and amino acids.
In eqn. 11, Δε L (λ), Δε R (λ) is the molar CD parameter for L/R-handed enantiomer. Enantiomeric excess (N R − N L )/(N R + N L ) is the relative excess of right-handed molecular concentration (N R ) over left-handed (N L ) molecules. It is related to ΔD/D and the sign of EE is opposite to that of ΔD/D (if D R > D L , N R < N L ). In a simple model described below, for racemic production and UV damage of biomolecules enantiomeric excess, EE = −(ΔD/D).

Model for racemic production and UV damage of biomolecules. Correlation between EE and the parameter (ΔD/D) is explained with the help of a simple phenomenological model that describes the racemic production of prebiotic life-molecules and their destruction by Archaean UVC radiation. For number density N R and N L of right and left handed molecules,
The terms −D R N R, −D L N L describe destruction by UV light with rate constants D R and D L which could be different due to differential circular polarization intensity, ΔI(λ) ≡ I − (λ) − I + (λ). The racemic production rate P is same for both enantiomers. For time, t ≫ D R −1 , D L −1 the steady-state distribution (dN R,L /dt ≈ 0) results in an enantiomeric excess,  34,35 and extinction coefficient ε(λ) 35,[38][39][40] for R-nucleosides and L-amino-acids. A summary of reported 34,35 CD bands for these biomolecules is given in Table 1.

Discussion
UV damage rates D R,L depend on the action spectrum weighted, integrated UVC flux. For 200-300 nm and CO 2 pressure of 1 bar, total integrated UVC flux is 0.63 W/m 2 (Fig. 1) and is equivalent to 0.21 W/m 2 when weighted with the DNA action spectrum 37 . Several studies have measured wavelength specific damage rate constants for nucleic acids which is largely due to photo-damage of pyrimidine bases. From the measured nucleic acid damage rate constant of 0.061 cm 2 /mJ for wavelength of 260 nm 44 , D R,L has a value of 1.2 × 10 −3 s −1 . When subjected to Archean UVC flux, pyrimidine nucleosides will be damaged in a time of few minutes. The UV damage rate for purine nucleosides is much smaller than for pyrimidine nucleosides (D purine ≈ 0.01 D pyrimidine ) 45 and the corresponding damage time for purine nucleosides in the Archaean UV flux will be several hours. As seen from Equation 13a,b, for the estimated Archaean UVC flux, EE for pyrimidines will saturate to −ΔD/D in a time of few minutes but will take several hours for purines to do so. Compared to pyrimidines, the Archaean purine population density is racemic (EE ≈ 0).
Relatively fewer studies have measured wavelength specific UV photolysis rate constants for amino acids. Photolysis of amino acids for wavelengths shorter than 200 nm was investigated for space environment 46,47 outside of terrestrial atmosphere where UV light at these wavelengths is relatively abundant. Photolysis has also been investigated for wavelengths longer than 200 nm 48 and these are the only ones relevant to our investigation due to absence of vacuum UV light on Archean earth. In one investigation 43 Table 1. Summary of Circular Dichroism (CD) bands for L-amino-acids and R-nucleosides. Calculated values of EE for different pressures of atmospheric CO 2 and O 2 is given in Table 2 for nucleosides and five randomly selected amino-acids for a scenario where the intensity of σ − light reaching earth's surface is more than σ + intensity (ΔI(λ) ≡ I − (λ) − I + (λ) > 0).

P(CO 2 ) bar P(O 2 ) Bar
Enantiomeric is not possible to correlate these numbers with the Archaen UVC flux shown in Fig. 1. However, in the absence of any dramatic variation of photolysis rates with UVC wavelength, amino-acid half-life of a few hours is expected 43 .
The UV absorption coefficient of water varies from 7 m −1 for a wavelength of 200 nm to 0.7 m −1 for 300 nm and has a value of 1.7 m −1 for the central wavelength of 250 nm 49 . Thus UV light in this wavelength range easily penetrates around 0.5 meters of water. The products of Urey Miller type reactions will continue interacting with UV light till the molecules have sunk to depths greater than ~0.5 meters by diffusion. Diffusion coefficient (D) for molecules of the size of nucleosides and amino acids in water has a value 50 of ~1.5 × 10 −5 cm 2 /s. Time to diffuse 51 down by a distance (L) of 0.5 m is (T ≈ L 2 /4D) several months. This can be compared to a time of several minutes to a few hours required for photodamage of biomolecules in the Archean UV light flux, as explained above. Thus biomolecules in water get adequately illuminated for the photodamage processes described in this report with near-full UV flux from sun.
As seen from Table 1, Δε L is positive 34 for CD of L-amino-acids in 200-300 nm wavelength region. From equation 11b, ΔD/D is positive for ΔI(λ) > 0. Thus EE is negative (N L > N R ) for amino-acids and the sign of EE is independent of CO 2 pressure (Table 2). Unlike amino-acids, the CD spectra of nucleosides show both positive and negative bands 35 for Δε R (Table 1). Increasing atmospheric CO 2 shifts the UV pass-band (Fig. 1) and the differential circular polarization (Fig. 4) to longer wavelengths, resulting in a change of sign of ΔD/D (and EE) for pyrimidine nucleosides. As seen in Table 2, for pyrimidine nucleosides EE is positive (N R > N L ) above a threshold CO 2 pressure of around 1 bar. In these calculations, the pressure of atmospheric O 2 is kept at 0.002 bar (0.01 PAL). At low pressures of O 2 , calculated values of EE is approximately proportional to O 2 pressure. This is shown ( Table 2) for CO 2 pressure of 1.25 bar and lower O 2 pressure of 0.0002 bar. While magnitude of EE values reduce by a factor of 10, the sign of EE remains unchanged.
Interestingly, the magnitude of EE for both purine nucleosides is smaller and the sign is opposite to that for pyrimidines. However, as explained above (Eqn. 13), compared to pyrimidines EE will take much longer time to reach the saturation value of −ΔD/D and the population of purines is relatively racemic. Further, heterochiral nucleic acids involving pyrimidine and purine building blocks are significantly more unstable thermally 52,53 as compared to homochiral counterparts. It is conceivable that smaller EE values for purines and significant thermal stability of homochiral nucleic acids together with D purine ≈ 0.01(D pyrimidine ) 45 was a determining factor (not the sign of their enantiomeric excess) in the evolution of chirality of purines. Values of ΔD/D for aromatic amino-acids are lower by a factor of ~100 due to larger extinction coefficient ε(λ) 38 and relatively small circular dichroism Δε(λ) 34 . In all of these calculations we assume an ambient temperature (T) of 300 K and a magnetic field (B S ) of 0.25 Gauss. Varying conditions of atmospheric temperature and magnetic field can be accounted by the observation that differential circular polarization intensity ΔI(λ) and EE are proportional to B S /T (Fig. 4).

Conclusions
We have shown that magnetic circular dichroism of UVC by sparse oxygen in the anoxic Archaean atmosphere results in net circularly polarized light reaching earth's surface. This results in chirally selective damage of prebiotic molecules by circular dichroism and creates an EE which evolved to homochirality of R-nucleosides and L-amino-acids. Irrespective of the partial pressure of oxygen, the sign of enantiomeric excess of pyrimidine nucleosides and the amino-acids is predicted correctly when UVC light reaching earth has net σ − circular polarization (ΔI(λ) ≡ I − (λ) − I + (λ) > 0) and P(CO 2 ) > 1 bar. This is consistent with the requirement of large CO 2 pressure for greenhouse effect 16 to balance lower solar luminosity 4,000 Mya. It is also an indication that initial enantiomeric excess was generated by circularly polarized UV light and not by a stochastic event.
Since MCD depends on the direction of magnetic field with respect to the propagation of light, net σ − light in one hemisphere of earth would also result in net σ + light in the other hemisphere. Homochirality in life-molecules can be explained by assuming (i) prebiotic life originated either in the northern or the southern hemisphere of earth which had higher UVC flux of σ − over σ + (south magnetic hemisphere), (ii) evolution of homochirality was complete (EE ~ ±1) before the earth's magnetic field reversed. Recorded length of polarity intervals between reversals varies between 0.1 and several Million years 54 and (iii) no significant dispersal of prebiotic life molecules happened between hemispheres before the transition to homochirality was complete. For the terrestrial magnetic field in Fig. 2, the most important regions for effective MCD in atmospheric oxygen lie between latitudes of 24° and 58° in both hemispheres and any EE will be nullified by large-scale dispersal of enantiomers between these regions from south to north magnetic hemisphere.

Methods
Calculation of spectral flux I(λ) (W . m −2 . nm −1 ) of UVC light reaching earth's surface Calculation of differential circular polarization intensity ΔI(λ) (W.m −2 .nm −1 ) of UVC light reaching earth's surface. Equations   2b. Circular dichroism (milli.deg) for amino acids 34 is converted to Δε (mol−1 . cm−1) and is significant only for 200-240 nm Due to a small range of wavelengths for amino-acids, published data for Δε and ε values is taken in steps of 1 nm.
Following equation (11b)  Summation is done in steps of 2 nm. As seen from Figs 1 and 4, there is very little UV light intensity for wavelengths shorter than 220 nm and there is insignificant contribution to EE from this wavelength region. Likewise, differential circular polarization intensity (Fig. 4) is minimal for wavelength longer than 290 nm and again there is insignificant contribution from this long-wavelength region.