Ideas and perspectives: Same Carbon Different Elements- An Insight into Position-Specific Isotope Patterns Within a Single Compound

It is expected that information on the source, reaction pathway, and kinetics of an organic compound can be obtained from its position-specific isotope compositions or intramolecular isotope distribution (Intra-ID). To retrieve the information, 10 we could use its equilibrium Intra-ID as a reference for understanding the observed Intra-IDs. Historically, observed, apparently close-to-equilibrium carbon Intra-ID had prompted an open debate on the nature of biosystem and specifically the pervasiveness of reversible biochemical reactions. Much of the debates remain unresolved, and the discussion has not clearly distinguished two states of equilibrium: 1) the equilibrium among the bond-breaking/forming positions in reactant and product, and 2) the equilibrium among all carbon positions in a compound. For an organic molecule with multiple carbon positions, 15 equilibrium carbon Intra-ID can be attained only when a specific reaction is in equilibrium and the sources of each position are also in equilibrium with each other. An Intra-ID provides limited information if the sources and pathways are both unconstrained. Here, we elaborate on this insight using examples of the Intra-IDs of hydroxyl-bearing minerals, N2O, and acetic acid. Research effort aiming at calibrating position-specific equilibrium and kinetic isotope fractionation factors for defined processes will help to interpret Intra-IDs of a compound accurately and fully. 20

oxygen-bearing minerals have two or more position-specific oxygens. Their isotope composition difference was proposed as a potential single mineral geothermometer. For example, it had been proposed that water temperature could be reconstructed from intracrystalline oxygen isotope difference of single mineral copper sulfate pentahydrate (CuSO4· 5H2O) (Götz et al., 1975), kaolinite (Al2Si2O5(OH)4), illite (K0.65Al2.0(Al0.65Si3.35O10)(OH)2) (Bechtel and Hoernes, 1990), or alunite (KAl3(SO4)2(OH)6) (Arehart et al., 1992). To be a single-mineral geothermometer, different oxygen sites must have attained 85 equilibrium within the single mineral, which can be achieved when different positions in a compound have the same source or initially different sources are in equilibrium with each other.
Take alunite precipitation from a solution as an example. Alunite has sulfate and hydroxyl oxygen positions in its structure that precipitate from sulfate and hydroxyl ions in the solution (Fig. 1). Alunite with equilibrium Intra-ID can be produced from an equilibrium precipitation process, only if both the oxygen isotope compositions of sulfate and hydroxyl ions in the solution 90 equilibrated with the same ambient water oxygen at the same temperature. However, sulfate oxygen does not readily exchange with that of water; the isotope equilibration time for SO4 2and ambient water at Earth's surface condition is greater than 10 6 to in alunite can come different sources at different temperature, rendering alunite a flawed single-mineral geothermometer. The 95 same is true for gypsum (CaSO4· 2H2O) in which sulfate oxygen is not in equilibrium with formation water, and the crystallization water (· 2H2O) oxygen may be in equilibrium with a different type of water.

"Equilibrium-like" Intra-ID produced by a kinetic process
For a compound with two different positions of the same element, a simple way to describe its Intra-ID is to report the difference between the two isotope compositions, i.e. the SP value. The concept of SP originated from the study of nitrous 100 oxide ( β N α NO), which is defined as the nitrogen isotope composition difference between the center nitrogen (δ 15 N α ) and the terminal nitrogen (δ 15 N β ) (Yoshida and Toyoda, 2000). The predicted equilibrium SP value at room temperature in N2O is 45‰ (Yung and Miller, 1997;Wang et al., 2004;Cao and Liu, 2012). Although most observations fit the equilibrium prediction that 15 N preferentially enriches in the α N position by 30-40‰ (Yoshida and Toyoda, 2000;Toyoda et al., 2002;Sutka et al., 2006), negative SP values were observed nevertheless (Yamulki et al., 2001;Sutka et al., 2003). 105 The difference in SP values was explained by the difference in synthetic pathway associated with symmetrical or asymmetrical precursors (Schmidt et al., 2004;Toyoda et al., 2005;Sutka et al., 2006). If the precursor of N2O is symmetrical (e.g. -ONNO-, Fig. 2 left), the two nitrogens in the precursor are positionally equivalent; any prior isotope composition and fractionation difference would be erased by the symmetrical structures of the precursor. When producing N2O from a symmetrical precursor, the β N undergoes N-O bond cleavage and therefore has a primary isotope effect which is large, whereas the α N has only a 110 secondary isotope effect which is negligible (close to 1.000, Bigeleisen and Wolfsberg, 1958). Therefore, 15 N depletion is expected only on the β N or N2O produced from a symmetrical precursor is expected to have a positive SP value.
If the precursor is asymmetrical (e.g. -NH(OH)NO, Fig. 2 right), the two nitrogens in the precursor are not positionally equivalent. It is expected that the two nitrogens in the precursor were produced from different EIEs or KIEs because they went through different reaction pathways and may even have different nitrogen sources (Schmidt et al., 2004;Toyoda et al., 2005;115 Sutka et al., 2006). Therefore, during the formation of N2O from an asymmetrical precursor, the difference in the positionspecific δ 15 N values of the precursors and the difference in isotope fractionation during the formation processes will be recorded in the SP value of N2O. Such N2O can have either SP>0 or SP<0.
When we state that a compound displays an equilibrium Intra-ID, the underlying assumption is that there exists a mechanism for different positions to exchange isotopes intramolecularly. However, not all apparent equilibrium or equilibrium-like Intra-120 IDs are produced by an equilibrium process. For reactions like -ONNO-↔ N2O, two types of processes could produce SP>0.
First, the N2O formation reaction is fully reversible and attains an equilibrium. When fully reversible, the two nitrogens in N2O are scrambled when it forms the symmetrical precursor through the reverse reaction. At equilibrium, the terminal nitrogen in a weaker bond environment is expected to be depleted in heavier isotope than the central nitrogen by 45‰ at surface temperature. Second, the N2O formation reaction is uni-directional. When uni-directional, only the N-O bond-breaking position 125 ( β N) undergoes a KIE. Thus, the SP value is approximately equal to the KIE value. In this scenario, if the KIE < 1.000, the https://doi.org/10.5194/bg-2020-120 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.
terminal nitrogen is expected to be depleted in heavier isotope than the central nitrogen by the extent of KIE value. The Intra-ID would be similar to equilibrium Intra-ID in this case, but it is produced by isotope depletion on the bond-breaking process.
No intramolecular exchange involves. Therefore, even if the N2O produced by the uni-directional process has SP ≈ 45‰, it is not due to equilibrium or equilibrium-like SP. 130 Here we see that both fully reversible and uni-directional processes can result in a similar SP value, but the underlying mechanisms are entirely different. Furthermore, a positive SP value can also be achieved through a combination of nitrogen sources and isotope fractionations from an asymmetrical precursor. Thus, without knowing the underlying process, we cannot interpret an Intra-ID or SP value uniquely.

Position-specific isotope fractionations between reactant and product 135
As illustrated above, the Intra-ID of a compound can be used to gauge the degree of internal thermodynamic equilibrium only if we can determine the processes involved in isotope fractionation. It does not mean, however, that position-specific isotope composition is useless. Based on the predicted equilibrium Intra-ID, a predicted isotope fractionation factor of corresponding positions between reactant and product in a process can help to evaluate the thermodynamic state of a system and to decipher reaction pathways. In this section, we use a simple organic molecule, acetic acid (CH3COOH), and its measured Intra-IDs from 140 literature as examples to illustrate how position-specific isotope fractionation occurs between reactant and product.
The relative isotope enrichment between the carboxyl and methyl carbon in acetic acid is defined as ln 13 αcarb-met= ln( 13 Rcarb/ 13 Rmet) ×1000‰. 13 R (= 13 C/ 12 C) denotes the carbon isotope molar abundance ratio in a position. Our calculated equilibrium Intra-ID of acetic acid has the carboxyl carbon being 47.3 ‰ heavier than the methyl carbon at 25℃ (ln 13 αcarb-met (eq)= 47.3‰, He et al., 2020). The measured δ 13 Cmet values from literature can be lower, higher, or approximately equal to the 145 δ 13 Ccarb values for acetic acids from biological, artificial, or hydrous pyrolysis samples (Table 1). The position-specific δ 13 C values of biological, artificial, or hydrous pyrolysis produced acetic acid are largely overlapping on δ 13 Cmet-δ 13 Ccarb space. For the majority of biological acetic acids, the δ 13 Ccarb values are several per mil higher than the δ 13 Cmet values (Fig. 3 top, ln 13 αcarb-met=5.1±4.8‰, n=29), with two cases of ~18‰ higher and one case of -2.2‰ lower in δ 13 Ccarb values. It is expected that the metabolic and catabolic pathways and carbon sources are limited for most natural acetic acid. Therefore, the ln 13 αcarb-met value 150 of 5.1±4.8‰ could be characteristic but not necessarily exclusive for biologically produced acetic acid. Man-made acetic acids have a very large range of ln 13 αcarb-met values from -30.2‰ to 24.2‰ (Fig. 3 middle, 7.3±14.3‰, n=24). Biological and hydrous pyrolysis produced acetic acids do not have such negative ln 13 αcarb-met values. Except for the above-mentioned features, the production of man-made and biological acetic acid has too many unconstrained parameters. Thus, our discussion will focus on the acetic acid derived from hydrous pyrolysis of oil-prone source rocks. 155 The acetic acids produced from the hydrous pyrolysis of oil-prone source rocks have a ln 13 αcarb-met value of 18.3±7.7‰ (n=22, Fig. 3 bottom). ln 13 αcarb-met values of ~30‰ were produced at 310~350 ℃ from Mahogany Shale or Black Shale with a proposed mechanism of uni-directional pyrolysis of precursor acid forms (R-CH2COOH ↔ R + CH3COOH, Fig. 4, Dias et al., 2002b). https://doi.org/10.5194/bg-2020-120 Preprint. Discussion started: 2 June 2020 c Author(s) 2020. CC BY 4.0 License.
If we consider only the primary KIE between the methylene carbon in R-*CH2COOH and the methyl carbon in acetic acid (*CH3COOH), it is expected that a uni-directional process would lead to a 13 C depletion only on the methyl carbon position in 160 acetic acid. The Intra-ID of the produced acetic acid should equal to the δ 13 C value difference between the precursors minus the primary KIE. The primary KIE is expected to be more negative than the predicted equilibrium isotope fractionation factor, which is -14‰ (He et al., 2020). Thus, as long as the δ 13 C value difference between the methylene and carboxyl carbon in R-CH2COOH is greater than -14‰, the acetic acid produced from uni-directional pyrolysis of such precursor acid should have a carboxyl carbon with a higher δ 13 C value than that of the methyl carbon. If the carboxyl carbon in the precursor acid has a 165 higher δ 13 C than that of the methylene carbon, the pyrolysis process can easily produce acetic acid with a ln 13 αcarb-met value close to an apparent equilibrium Intra-ID. Such apparently "equilibrium-like" Intra-ID does not involve intramolecular exchange, but it is the product of uni-directional precursor acid pyrolysis.

Implications
Life sustains itself by feeding on negative entropy. Boltzmann first considered living organisms from a thermodynamic 170 perspective, and Schrodinger later applied equilibrium thermodynamics to living systems (Popovic, 2018). Those attempts were not pursued further, since, as we all know today, a living system is a dissipative system. The establishment of nonequilibrium thermodynamics by Prigogine and his coworkers has guided researchers to the theorem of minimum entropy production in biological systems (Prigogine and Wiame, 1946). Since then, efforts in applying nonequilibrium thermodynamics to living systems have been continued with mixed success (Stoward, 1962;Schneider and Kay, 1994;175 Hayflick, 2007;Demirel, 2010;Barbacci et al., 2015;Gerber et al., 2016).
The theorem on minimum entropy production applies only to linear thermodynamic systems. Therefore, it is necessary to demonstrate that the magnitude of reaction rate on the scale of interest in a living system is linearly dependent on the generalized force operating on the system. It is reasonable to view that a complex interacting and constantly involving nonlinear system is constructed by a series of synergistic reactions, and there should exist local linearity, local steady-state, even 180 local equilibrium (Galimov, 2006).
Local nonequilibrium of biochemical system is potentially significant for the increasing complexity and orderliness of life (Prigogine and Wiame, 1946;Galimov, 2006). Such a system should consist of a set of reversible but not necessarily equilibrium reactions conjugated with energy supplies that maintain in a steady-state not far from equilibrium. Such close-toequilibrium steady-state should be expressed as a tendency toward equilibrium inter-and intra-molecular stable isotope 185 distributions, i.e. a linear inter-and intra-molecular 13 β-δ 13 C correlation with a regression coefficient smaller than but close to 1 (Galimov, 2006). The observed correlations between position-specific δ 13 C and 13 β had been used to support the hypothesis that the theorem of minimum entropy production can be applied in biochemical systems (Galimov, 1985(Galimov, , 2004(Galimov, , 2006. In addition, such "equilibrium-like" Intra-ID in organic molecules was proposed as a "special feature of biological systems", which could be used as a criterion to identify biologically produced extraterrestrial organic molecules (Galimov, 2003). As we have illustrated above, observed Intra-ID in organic molecules is the product of a set of equilibrium or dis-equilibrium processes as well as their source isotope compositions. An Intra-ID itself cannot be used as conclusive evidence for the thermodynamic state of a system. Therefore, even if a compound does have a linear intramolecular 13 β-δ 13 C correlation with a slope of 1, it does not constitute supporting evidence for the existence of an equilibrium state among biochemical reactions in organisms. 195 A compound often consists of different elements, for instance, H and O in H2O (Dansgaard, 1964;Craig, 1961), N andO in NO3 -(Casciotti andMcIlvin, 2007;Wankel et al., 2009), S and O in SO4 2-(Antler et al., 2013), or C and H in organic compounds (Elsner, 2010Palau et al., 2017). The isotope fractionation relationship between these different elements, i.e. (αA-1)/(αB-1), lnαA/lnαB, or ΔδA/ΔδB, is often used to characterize a reaction pathway. The isotope composition difference of different elements is only useful if the isotope fractionation relationships are considered and their isotope compositions are 200 normalized, e.g. ∆(15,18)=(δ 15 N-δ 15 Nm)-( 15 α-1/ 18 α-1)×(δ 18 O-δ 18 Om), δ 15 Nm and δ 18 Om are the average isotope composition in a given profile (Sigman et al., 2005). The normalization procedure was necessary because the source isotope compositions can affect the values of the product. Similarly, if the same element at different positions have different sources, their source isotope composition difference must also be considered. In fact, the two or more oxygens in the same compound do not have a mechanism to exchange; these oxygens behave like different elements. A simple comparison of position-specific isotope 205 compositions in one sample, e.g. ln 13 αcarb-met values of one acetic acid sample, offer little information.

Conclusions
Organic compounds usually have an element, e.g. carbon, at different positions and therefore have Intra-IDs. The deviation of an Intra-ID from its equilibrium state has been used to evaluate the thermodynamic state of a system. Our analysis of oxygenbearing minerals, N2O, and acetic acids show that both isotope sources and all reaction processes need to be in equilibrium to 210 reach an intramolecular equilibrium state. However, such a condition is rarely satisfied. When different positions of the same element cannot exchange with each other, these different positions behave independently like different elements. Observed Intra-ID that is apparently similar to the equilibrium one can also be produced from a combination of different sources and uni-directional processes. Thus, an Intra-ID itself is not conclusive without adequate information on sources and reaction kinetics. Compared to position-specific isotope compositions, position-specific isotope fractionation of a defined process is 215 more informative to identifying bond-breaking/forming positions of a large molecule, to predicting its transition-state structure, to evaluating the reversibility of a biochemical process, and to determining and qualifying a process in a complex system. All in all, an understanding of a reaction process at molecular level will always be the first step required for later sound and wide application of stable isotope composition.