Introduction

Molecular oxygen (O2) is an important feature of the modern Earth’s atmosphere. However, why and how Earth evolved from the ancient O2-deficient environment to the modern O2-rich world remain mysterious. Geological and geochemical studies have revealed two rapid and irreversible transitions of Earth’s atmospheric oxygen levels (pO2) that occurred ~2.4–2.3 billion years ago (Ga) and 0.8–0.54 Ga, which are also known as the Great Oxidation Event (GOE) and Neoproterozoic Oxidation Event (NOE), respectively1,2. Oxygenation events remarkably altered geochemical characteristics such as the distribution, diversity, and abundance of minerals on Earth’s surface3,4. The information stored in sedimentary minerals therefore provides a window through which to investigate the evolution of the redox state of ancient Earth’s surface environment5,6. However, the causality in the reverse direction—whether and how mineral evolution contributed to the oxygenation events—remains understudied7.

Oxygen, a product of the three-billion-year-old biological invention of oxygenic photosynthesis, is consumed by aerobic respiration or oxidation of reducing compounds1,2. The existence of the redox couple of organic matter and O2, more generally known as the carbon cycle, implies that the supply of O2 in the environment is quantitatively related to detrital organic matter. A tiny leakage in the carbon cycle has been widely considered one major mechanism responsible for the accumulation of O2 in Earth’s atmosphere-ocean system: a small portion of organic matter produced by oxygenic photosynthesis is buried in sediments and loses the opportunity to react with O2, resulting in the rise of O2 levels8,9.

The long-term persistence of organic matter in natural environments is a consequence of its intrinsic recalcitrance, extrinsic environmental factors, or both10,11. Intrinsically recalcitrant organic matter is resistant to degradation due to its stable structures and strong chemical bonds12,13. For example, humified organic matter formed in soils and sediments consists of an intricate series of aliphatic/aromatic compounds and is persistent at the geologic timescale14,15. The other instance is graphitized petrogenic carbon, which is extremely resilient with repeated exposure to oxygenated environments and can survive multiple episodes of recycling12,13,16. Physical, chemical, and biological variables in surrounding environments significantly influence organic preservation as well10,11. For example, in the water column of lakes and oceans, microbial consumption can transform an organic matter system to a new ensemble in which the low concentrations of individual components prevent further uptake by microorganisms; this mechanism is also referred to as the “dilution hypothesis”17,18. Organic matter can also be associated with minerals in soils and sediments via ligand exchange, cation bridging, Van der Waals force, and hydrogen bonding19,20, which protects organic matter from the attacks of microorganisms and their digestive agents (e.g., carbon-degrading enzymes)11,20. This mechanism, also called “physical protection”, makes extensive contributions to the long-term preservation of organic matter11,21. Although these mechanisms responsible for the persistence of organic matter are observed in the modern environment, they are expected to have been the same or similar on the ancient Earth13,22.

In this study, I focus on the effects of physical protection on O2 accumulation and explore how the microscopic interactions between organic matter and minerals might have influenced the macroscopic evolution of Earth’s oxygen cycle in deep time. I first introduce a conceptual model to describe the system of organic matter and minerals and investigate the probabilistic properties of their interactions. I then show theoretically that adsorption/desorption of organic matter onto/off mineral surfaces are asymmetric and the former plays a dominant role. Analyses of the model predict that, under O2-limiting conditions, the negative feedback stabilizing the modern Earth’s oxygen cycle is unlikely to operate before the O2 level exceeds a threshold and mineral surface capacity is saturated. Based on these results, I speculate that mineral evolution in the ancient O2-deficient environment might have increased the capacity for organic matter adsorption and led Earth’s oxygen cycle to lose stability, facilitating the accumulation of O2. Finally, to test this speculation, I explore the possible contributions of iron(III) and clay minerals to the GOE and NOE, respectively, with the parameter values estimated from modern field observations as benchmarks. The results presented in this work provide a further step toward understanding the role of minerals in Earth’s oxidation.

Results and discussion

A conceptual model for organic matter-mineral systems

To investigate the effects of organic matter-mineral interactions on organic burial and O2 accumulation, I first consider the degradation of unprotected (y1) and protected (y2) organic matter in an aerobic environment. Figure 1 shows a conceptual model for the interactions of organic matter with mineral surfaces and its degradation paths. The y1 component is either directly oxidized to CO2 with rate constant k1 or transformed to the y2 component (i.e., associated with minerals) with rate constant kp, and the y2 component is oxidized to CO2 with rate constant k2. The degradation of the y2 component consists of two subprocesses (Fig. 1): (1) dissociation from mineral surfaces with rate constant kd and (2) oxidation to CO2 with rate constant k1. Since this study focuses on the influence of mineral protection on the degradation/preservation of organic matter, I assume that organic matter desorbed from mineral surfaces is rapidly oxidized to CO2 and the degradation rate of the y2 component is dominated by its desorption rate: k2 ≃ kd.

Fig. 1: Degradation paths of organic matter that is protected or unprotected by minerals.
figure 1

Unprotected organic matter is either directly oxidized to CO2 with constant k1 or adsorbed onto a mineral surface with rate constant kp. The physically protected organic matter needs to be dissociated from the mineral surface (with rate constant kd) before it can be degraded. The protected portion decays to CO2 with rate constant k2. The dashed arrow for k2 indicates that the transformation of protected organic matter to CO2 includes two steps: (1) dissociation from mineral surfaces with kd and (2) oxidation to CO2 with k1. The characteristic times of adsorption and desorption are denoted by tp and td, respectively.

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Conventionally, the degradation of organic matter and its adsorption/desorption on mineral surfaces are expressed in terms of the first-order kinetics23,24,25,26. Here, I write the rates of changes in the protected and unprotected components at time t as

$$\frac{d{y}_{1}}{dt}=-{k}_{1}{y}_{1}-{k}_{{{{{{{{\rm{p}}}}}}}}}{y}_{1}+{k}_{{{{{{{{\rm{d}}}}}}}}}{y}_{2}$$
(1)
$$\frac{d{y}_{2}}{dt}={k}_{{{{{{{{\rm{p}}}}}}}}}{y}_{1}-{k}_{{{{{{{{\rm{d}}}}}}}}}{y}_{2}.$$
(2)

I denote the total amount of organic carbon and the fraction of the y2 component at time t = 0 by y0 = y1(0) + y2(0) and f, respectively. The initial conditions then read y1(0) = y0(1 − f) and y2(0) = y0f. For the sake of simplicity, I introduce dimensionless rate constants κp = kp/k1, κ2 = k2/k1 and κd = kd/k1, and dimensionless time τ = k1t.

Under oxic conditions, degradation time t in Eqs. (1)–(2) is conventionally referred to as the oxygen-exposure time, which is the length of time during which organic matter is exposed to O210,27. I denote oxygen-exposure time and its dimensionless form as \({t}_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) and \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\), respectively. Oxygen-exposure time is positively correlated with the atmospheric O2 levels10,27: \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\propto p{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}\). The amount of physically protected organic matter after being exposed to O2 for \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) is then denoted as \({y}_{2}({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}})\). In the absence of O2, some types of organic compounds, especially unprotected components, can be degraded by microorganisms with weaker electron acceptors (e.g., nitrate and sulfate)10,28,29. However, the degradation of the protected portion, which requires more energy to overcome the activation barriers, becomes slow or even ceases when O2 is completely consumed or when organic matter is transported/sequestered into O2-free environments, where the energetic rewards of organic degradation to microorganisms are poor10,11,30. Here, I identify \({y}_{2}({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}})\) as the amount of organic matter protected by minerals in marine sediments, where most of the organic matter burial on Earth takes place11,13,27; this is also the portion contributing to O2 accumulation in the system of Eqs. (1)–(2). The initial fraction of the y2 component (i.e., f = y2(0)/y0) thus also represents the burial efficiency when \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}=0\). Table 1 summarizes the variables and parameters in this study.

Table 1 Symbols, physical meanings, dimensionless forms, and mathematical relations of variables.
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Probabilistic properties of organic matter-mineral interactions

To investigate organic matter-mineral interactions in natural environments, I consider an ensemble consisting of biopolymers with different compositions, lengths, and structures; these polymers are stochastically adsorbed onto or desorbed off mineral surfaces. Theoretical models31,32 and experimental observations33,34 have suggested that the (dimensionless) characteristic times for a polymer to be adsorbed onto and desorbed off a mineral surface can be expressed as \({\tau }_{{{{{{{{\rm{p}}}}}}}}}\propto \exp (-M \psi )\) and \({\tau }_{{{{{{{{\rm{d}}}}}}}}}\propto \exp (M \psi )\), respectively, where M is the molecular mass of the polymer and ψ is a parameter depending on other variables influencing the polymer-mineral interaction. Here, instead of following such a convention expressing molecular mass as a separate factor, I rewrite the two characteristic times as \({\tau }_{{{{{{{{\rm{p}}}}}}}}}\propto \exp (-\alpha )\) and \({\tau }_{{{{{{{{\rm{d}}}}}}}}}\propto \exp (\alpha )\), in which α is an overall factor characterizing the polymer-mineral interaction.

The interactions between biopolymers and mineral surfaces are affected by a variety of physical, chemical, and biological variables, such as temperature, pH, the mass and functional group(s) of a biopolymer, the area and charge capacity of a mineral surface, and microbial enzymes11,20,25. I denote individual factors corresponding to each of these variables by βi∈[0, N] and assume that βi’s are independent and identically distributed (i.i.d.). This assumption of i.i.d. is an idealization because some factors influencing the adsorption/desorption of biopolymers onto/off mineral surfaces may depend on each other and their distributions may vary across different types of biopolymers and minerals. The overall factor α is then rewritten as \(\alpha =\mathop{\sum }\nolimits_{i = 0}^{N}{\beta }_{i}\), where each βi characterizes the influence of one variable on adsorption/desorption times. Since κp = 1/τp and κd = 1/τd, I substitute this expression of α into the exponential relation between τj∈{p, d} and α introduced above and express these two rate constants by

$${\kappa }_{{{{{{{{\rm{p}}}}}}}}}\propto \exp \left(\mathop{\sum }\limits_{i=0}^{N}{\beta }_{i}\right)\quad \,{{\mbox{and}}}\,\quad {\kappa }_{{{{{{{{\rm{d}}}}}}}}}\propto \exp \left(-\mathop{\sum }\limits_{i=0}^{N}{\beta }_{i}\right).$$
(3)

Organic matter is highly heterogeneous; so, too, is the environment in which it interacts with minerals11,20,24,35. To obtain the average κp and κd for an organic matter-mineral system, I first calculate the probability distribution of κp and κd. To do so, I take the logarithm of both sides of Eq. (3) and obtain \(\log ({\kappa }_{{{{{{{{\rm{p}}}}}}}}})\propto \mathop{\sum }\nolimits_{i = 0}^{N}{\beta }_{i}\) and \(\log ({\kappa }_{{{{{{{{\rm{d}}}}}}}}})\propto -\mathop{\sum }\nolimits_{i = 0}^{N}{\beta }_{i}\). For a sufficiently large N, the Central Limit Theorem implies that the variable \(\log ({\kappa }_{j})\) satisfies

$$P\left(\log ({\kappa }_{j})\right)\to \exp \left[-\frac{{(\log ({\kappa }_{j})-{\mu }_{j})}^{2}}{2{\sigma }_{j}^{2}}\right],\quad j\in \{{{{{{{{\rm{p}}}}}}}},{{{{{{{\rm{d}}}}}}}}\}$$
(4)

in which μj and \({\sigma }_{j}^{2}\) represent the mean and variance, respectively, of the probability distribution. Mathematically, \({\mu }_{{{{{{{{\rm{p}}}}}}}}}\propto \mathop{\sum }\nolimits_{i = 0}^{N}\langle {\beta }_{i}\rangle\), \({\mu }_{{{{{{{{\rm{d}}}}}}}}}\propto -\mathop{\sum }\nolimits_{i = 0}^{N}\langle {\beta }_{i}\rangle\), and \({\sigma }_{{{{{{{{\rm{p}}}}}}}}}^{2}={\sigma }_{{{{{{{{\rm{d}}}}}}}}}^{2}\propto \mathop{\sum }\nolimits_{i = 0}^{N}\,{{\mbox{Var}}}\left({\beta }_{i}\right)\), where 〈 ⋅ 〉 and Var( ⋅ ) represent the expectation and variance of a quantity, respectively. To calculate the probability distribution of κj, I change \(P(\log ({\kappa }_{{{{{{{{\rm{p}}}}}}}}}))\) to \(P({\kappa }_{{{{{{{{\rm{p}}}}}}}}})\) via the Jacobian transformation: \(P({\kappa }_{j})=\frac{d\log \left({\kappa }_{j}\right)}{d{\kappa }_{j}}P(\log ({\kappa }_{j})) \sim (1/ \kappa_{j})\exp \left[-2{\left(\frac{\log ({\kappa }_{j})-{\mu }_{j}}{2{\sigma }_{j}}\right)}^{2}\right]\). Away from the two tails of the distribution (i.e., \(| \log ({\kappa }_{j})-{\mu }_{j}| \ll 2{\sigma }_{j}\)), the value of the exponential function approximates 1 and therefore the probability distribution of κj is

$$P({\kappa }_{j}) \sim \frac{1}{{\kappa }_{j}},\quad j\in \{{{{{{{{\rm{p}}}}}}}},{{{{{{{\rm{d}}}}}}}}\}.$$
(5)

The P(X) ~ 1/X distribution in Eq. (5) appears in many physical and biological systems36,37. However, to my knowledge, this study suggests for the first time that this distribution likely exists in organic matter-mineral interactions (i.e., adsorption and desorption) as well. Moreover, the P(X) ~ 1/X distribution is a common property of relaxation processes such as the aging of molecular and electron glasses38,39, variation of protein states40,41, and evolution of frictional strength42,43. These processes generally exhibit logarithmic-time decay (i.e., relaxation processes decay with the logarithm of time)36,37. The relaxation (e.g., conformational changes and reorientations) of biopolymers occurring in organic matter-mineral interactions11,20 and the logarithmic-time degradation of organic matter in natural ecosystems11,35 both support the P(κj) ~ 1/κj distribution predicted in this study.

With the probability distribution of κj (Eq. (5)), I calculate its average, 〈κj〉, over \([{\kappa }_{j,\min }, {\kappa }_{j,\max }]\). I first normalize the probability distribution of \({\kappa }_{j}\) and obtain its density function: \(p({\kappa }_{j})=(1/{\kappa }_{j})\big/[\int\nolimits_{{\kappa }_{j,\min }}^{{\kappa }_{j,\max }}(1/{\kappa }_{j})d{\kappa }_{j}]=(1/{\kappa }_{j})\big/\log ({\kappa }_{j,\max }/{\kappa }_{j,\min })\). The denominator, \(\log ({\kappa }_{j,\max }/{\kappa }_{j,\min })\), is a normalization factor that guarantees the summation of p(κj) between \({\kappa }_{j,\min }\) and \({\kappa }_{j,\max }\) to be 1. The expectation of κj, i.e., \(\langle {\kappa }_{j}\rangle =\int\nolimits_{{\kappa }_{j,\min }}^{{\kappa }_{j,\max }}{\kappa }_{j}p({\kappa }_{j})d{\kappa }_{j}\), then is

$$\langle {\kappa }_{j}\rangle =\frac{{\kappa }_{j,\max }-{\kappa }_{j,\min }}{\log ({\kappa }_{j,\max }/{\kappa }_{j,\min })},\quad j\in \{{{{{{{{\rm{p}}}}}}}},{{{{{{{\rm{d}}}}}}}}\}.$$
(6)

Dominance of adsorption processes

To explore the relation between 〈κp〉 and 〈κd〉, both of which depend on the overall factor α, I denote the range of α as \([{\alpha }_{\min },{\alpha }_{\max }]\). Correspondingly, the lower and upper limits of κp are \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\min }\simeq \exp ({\alpha }_{\min })\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\simeq \exp ({\alpha }_{\max })\), respectively; the lower and upper limits of κd are \({\kappa }_{{{{{{{{\rm{d}}}}}}}},\min }\simeq \exp (-{\alpha }_{\max })\) and \({\kappa }_{{{{{{{{\rm{d}}}}}}}},\max }\simeq \exp (-{\alpha }_{\min })\), respectively. I substitute \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\min },{\kappa }_{{{{{{{{\rm{p}}}}}}}},\max },{\kappa }_{{{{{{{{\rm{d}}}}}}}},\min }\), and \({\kappa }_{{{{{{{{\rm{d}}}}}}}},\max }\) into Eq. (6) and obtain \(\langle {\kappa }_{{{{{{{{\rm{p}}}}}}}}}\rangle \simeq \left[\exp ({\alpha }_{\max })-\exp ({\alpha }_{\min })\right]/({\alpha }_{\max }-{\alpha }_{\min })\) and \(\langle {\kappa }_{{{{{{{{\rm{d}}}}}}}}}\rangle \simeq [\exp (-{\alpha }_{\min })-\exp (-{\alpha }_{\max })]/({\alpha }_{\max }-{\alpha }_{\min })\). The ratio between these two average rate constants is \(\langle {\kappa }_{{{{{{{{\rm{p}}}}}}}}}\rangle \big/ \langle {\kappa }_{{{{{{{{\rm{d}}}}}}}}}\rangle \simeq \left[\exp ({\alpha }_{\max })-\exp ({\alpha }_{\min })\right] / \left[\exp (-{\alpha }_{\min })-\exp (-{\alpha }_{\max })\right]\). Since organic matter-mineral systems and the physical, chemical, and biological conditions of their surrounding environments are highly heterogeneous11,20,24, I assume that the overall factor α, which characterizes the influence of these factors on organic matter-mineral interactions, has a wide range: \({\alpha }_{\min }\ll {\alpha }_{\max }\), implying that \(\exp ({\alpha }_{\min })\ll \exp ({\alpha }_{\max })\) and \(\exp (-{\alpha }_{\max })\ll \exp (-{\alpha }_{\min })\). With these two inequalities, I rewrite the above expression of the ratio between 〈κp〉 and 〈κd〉 as \(\langle {\kappa }_{{{{{{{{\rm{p}}}}}}}}}\rangle /\langle {\kappa }_{{{{{{{{\rm{d}}}}}}}}}\rangle \simeq \exp ({\alpha }_{\max })/\exp (-{\alpha }_{\min })=\exp ({\alpha }_{\max }+{\alpha }_{\min })\). Again, since \({\alpha }_{\min }\ll {\alpha }_{\max }\), I obtain

$$\frac{\langle {\kappa }_{{{{{{{{\rm{p}}}}}}}}}\rangle }{\langle {\kappa }_{{{{{{{{\rm{d}}}}}}}}}\rangle }\simeq {\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }.$$
(7)

This relation suggests that the ratio of the average adsorption rate constant to the average desorption rate constant is predominantly determined by the maximum adsorption rate constant, \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\).

The dominance of the adsorption rate constant shown in Eq. (7) is a consequence of the asymmetry between the adsorption and desorption of organic matter onto and off mineral surfaces. The association of biopolymers with minerals is generally accompanied by the alteration of three-dimensional structures (i.e., conformational changes), formation of new ionic and covalent bonds, and variations in vibrational modes, resulting in irreversible adsorption11,44,45. For example, conformational changes can unfold/uncoil biopolymers and align them along mineral surfaces, suppressing their rotational dynamics and limiting their access to microbial enzymes11,45. These processes significantly increase the waiting time for biopolymers to be desorbed from mineral surfaces (i.e., τd↑ and κd↓) and even lead biopolymers’ adsorption to be irreversible (i.e., τd → ∞ and κd → 0). In order words, due to the asymmetry between adsorption and desorption processes, the net amount of protected organic matter formed in unit time primarily depends on adsorption rates. However, how are adsorption rates related to the variation of O2 levels? I explore this next.

Stability and instability of Earth’s oxygen cycle

As discussed above, I identify the physically protected component y2 as buried organic matter, which is responsible for the accumulation of O2 in Earth’s atmosphere. In the ancient environments, the atmospheric pO2 was low1,2 and \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) was short10,27. By definition, oxygen-exposure time \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) is the length of time t that organic matter stays and decays in the presence of O2; in other words, \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}=t\) in oxic environments. When O2 levels are sufficiently low (i.e., \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\to 0\)), I have y1 = (1 − f)y0 and y2 = fy0; in this case, Eq. (2) implies that \({[d\langle {y}_{2}\rangle /d{\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}]}_{{\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\to 0}=\left[\langle {\kappa }_{{{{{{{{\rm{p}}}}}}}}}\rangle (1-f)-\langle {\kappa }_{{{{{{{{\rm{d}}}}}}}}}\rangle f\right]{y}_{0}\). To investigate how 〈y2〉 changes with \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) under such O2-limiting conditions, I set \({[d\langle {y}_{2}\rangle /d{\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}]}_{{\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\to 0}=0\) and obtain a critical condition: \( \langle {{\kappa }_{{{\rm{p}}}}} \rangle / \langle {{\kappa }_{{{\rm{d}}}}} \rangle = f/(1-f)\). This equality indicates that, in O2-deficient environments, if \( \langle {{\kappa }_{{{\rm{p}}}}} \rangle / \langle {{\kappa }_{{{\rm{d}}}}} \rangle\, < \, f/(1-f)\), then 〈y2〉 decreases as \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) increases; if \( \langle {{\kappa }_{{{\rm{p}}}}} \rangle / \langle {{\kappa }_{{{\rm{d}}}}} \rangle\, > \, f/(1-f)\), then 〈y2〉 rises with an increase in \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\). I substitute Eq. (7) into the critical condition and rewrite the latter as \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }=f/(1-f)\). Henceforth, I denote the ratio \(f/(1-f)\) by \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\), which represents a critical value for \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\).

Figure 2 illustrates how the burial efficiency of organic matter (i.e., \( \langle {y}_{2} \rangle /{y}_{0}\)) changes with \({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\) and therefore pO2 in the two regimes divided by \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) (blue curve in Fig. 2b). When \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max } \, < \,{\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) (purple curve in Fig. 2a and purple region in Fig. 2b), burial efficiency monotonically decreases with pO2. However, when \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max } \, > \,{\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) (green curve in Fig. 2a and green region in Fig. 2b), burial efficiency increases with pO2 in the region of low pO2 and then declines as pO2 further increases after passing a tipping point. In other words, whether burial efficiency and therefore the net O2 production increase or decrease with pO2 in the regime of low pO2 depends on how much organic matter has been protected by minerals when it is initially deposited in sediments (i.e., f) and how large adsorption rates can be (i.e., \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\)).

Fig. 2: Stability and instability of Earth’s oxygen cycle in the parameter space of \(({{\kappa }}_{{{{{{{{\rm{p}}}}}}}},\max },f)\).
figure 2

a Burial efficiency (\( \langle {y}_{2} \rangle /{y}_{0}\)) versus oxygen exposure time (\({\tau }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\propto p{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}\)) when \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max } \, < \,{\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max } \, > \,{\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\). If \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max } \, < \,{\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) (purple curve), burial efficiency is high at low pO2 and monotonically decreases as pO2 increases. In this case, Earth’s oxygen cycle is stabilized by a negative feedback loop. If \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max } \, > \,{\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) (green curve), burial efficiency first increases with pO2 in the regime of low pO2 and then declines as pO2 further increases after passing a tipping point. In this case, negative feedback is absent at low pO2, permitting the rise of O2. Estimations based on the compiled datasets in Fig. 3 suggest that \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\in (0.05,2)\) and f ≃ 0.7 in the modern O2-rich environment (refer to the following sections). The purple curve is generated with \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }=0.5\) and f = 0.7 (i.e., \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) ≃ 2). Under the deep-time O2-limiting conditions, \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) is expected to have been larger than its modern value while f is expected to have been smaller than its modern value (refer to the following sections). The green curve is generated with \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }=3\) and f = 0.1 (i.e., \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) ≃ 0.1). b Parameter space of \(({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max },f)\) for stable and unstable regimes of Earth’s oxygen cycle. The borderline (blue) for the stable (purple) and unstable (green) regions is determined by \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }=f/(1-f)\). The horizontal red line represents parameter values estimated from field observations in modern environments (i.e., \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\in (0.05,2)\) and f ≃ 0.7). The domain under the horizontal red line and left of the blue curve represents the region of \(({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max },f)\) for the stable states in deep time (refer to the following sections). When mineral evolution causes a shift of Earth’s oxygen cycle from the stable to the unstable region, Earth’s oxygen cycle loses its stability, facilitating the accumulation of O2.

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When the initial fraction of protected organic matter is sufficiently high (i.e., a large f value), the capacity of mineral surfaces for further adsorption would be limited. Studies have shown that a larger initial coverage of organic matter on mineral surfaces would lead to higher repulsive barriers and therefore slower adsorption rates (i.e., a small \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) value)25,46,47. In this case (i.e., a large f and a small \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\)), O2 starts to inhibit the burial of organic matter when it is deposited in sediments; the amount of buried organic matter and therefore the net production of O2 monotonically decline as pO2 increases (purple curve in Fig. 2a and purple region in Fig. 2b). This relation is analogous to the negative feedback stabilizing the modern atmospheric O2 levels11,27. However, when the fraction of protected organic matter at the initial time point is low, mineral surfaces would have large capacities for further adsorption; in the meantime, the adsorption rates would be high due to the low repulsive barriers. Under such a condition (i.e., a small f and a large \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\)), unprotected organic matter continues to be adsorbed onto mineral surfaces and O2 does not immediately limit the burial of organic matter when it deposits in sediments. In this case, there exists an unstable regime in which negative feedback is absent, permitting O2 to continuously accumulate (green curve in Fig. 2a and green region in Fig. 2b). When the maximum adsorption capacity is reached, no more organic matter can be adsorbed onto mineral surfaces; negative feedback again starts to operate, and the amount of buried organic matter declines with a further increase in O2 (green curve in Fig. 2a).

Did mineral evolution facilitate Earth’s oxidation? – Investigation via Fermi estimation

The theoretical analyses above explore the influence of organic matter-mineral interactions on the stability/instability of Earth’s oxygen cycle; whether and how mineral evolution might have contributed to oxygenation events require investigation under the ancient circumstances. The values of parameters characterizing organic matter-mineral interactions in paleoenvironments, however, are currently unavailable. Here, I employ Fermi estimation48,49 to explore the influence of mineral evolution on the oxygen cycle in deep time with modern parameter values as benchmarks50. Fermi estimation refers to the technique of studying complex problems, the exact solutions to which require extensive theoretical analysis or experimental investigation, via systematically dividing them into multiple parts and solving them with basic arithmetic48,49. To do so, I break down the problem—the influence of mineral evolution on Earth’s oxidation—into three subproblems and investigate each one in the following sections. First, I estimate \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) in the modern environment, denoted as \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}}^{\star }\), using data compiled from field observations. Second, I suggest that \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\) can be used as references to test whether mineral evolution destabilized the oxygen cycle and facilitated O2 accumulation in deep time. Finally, with \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\) as benchmarks, I propose that the evolution of iron and clay minerals might have contributed to the rise in O2 levels during the Archean-Proterozoic and Proterozoic-Phanerozoic transitions, respectively.

Parameters \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) in the modern environment

To estimate the modern values of \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\), I first compile the data on burial efficiency versus oxygen exposure time (i.e., \({y}_{2} /{y}_{0}\) versus \({t }_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}\)) from field observations27,51,52,53,54. These data are presented in Fig. 3, which shows that burial efficiency declines logarithmically with oxygen exposure time; such a pattern has been shown to appear in the degradation of mineral-associated organic matter in sediments11,55. The value of burial efficiency (\({y}_{2} /{y}_{0}\)) at the left time boundary (i.e., 10−3 year) in Fig. 3 is set as the initial burial efficiency (\({y}_{2}(0) /{y}_{0}=f\)). I apply least-square regression to analyze the compiled dataset (Fig. 3) and obtain f ≃ 0.7 on average, which implies \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }=f/(1-f)\simeq 2\) in the modern environment.

Fig. 3: The relation between the buried fraction of organic matter and oxygen exposure time in modern sediments.
figure 3

Data are compiled from the studies by Hartnett et al.27 (yellow circles), Sobek et al.51,52,53 (green circles), and Zhang et al.54 (blue circles). The mathematical expression of the least-square regression (black dashed line) for the data is “buried fraction = \(-9.90\times {\log }_{10}({t}_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}})+38.43\)”. The buried fraction at the left boundary, \({t}_{{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}}}=1{0}^{-3}\) year, is around 70%.

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The longest timescale of the observations presented in Fig. 3 is 103 years; geological research, however, has suggested that organic matter can persist for millions of years in sediments11,56. Therefore, the timescale for organic matter degradation should range from 10−3 to 106 years. Since the unprotected component y1 rapidly decays to CO2, I take the rate constant corresponding to the shortest timescale as the characteristic degradation rate constant of the unprotected component, i.e., k1 ≃ 1/(10−3 year). The degradation of the protected component y2 is slower and depends on its interactions with minerals; I assume that its characteristic degradation rate constant k2 falls between 1/(106 year) and k1. Thus, 1/(106 year) ≲ k2 < k1 ≃ 1/(10−3 year). Again, I convert k1 and k2 to dimensionless quantities and obtain κ1 = 1 and κ2 ∈ (10−9, 1). As previously discussed, κd ≃ κ2; therefore, substituting \({\kappa }_{2,\min }=1{0}^{-9}\) and \({\kappa }_{2,\max }=1\) into Eq. (6) gives the average desorption rate constant: 〈κd〉 ≃ 〈κ2〉 ≃ 0.05. On the other hand, 〈κd〉 should be no greater than 〈κp〉; otherwise, all of the protected component y2 would eventually decay to CO2 and no protected organic matter would exist in the modern environment. This implies that \(0.05\simeq \langle {\kappa}_{{{{{{{{\rm{d}}}}}}}}}\rangle \le \langle {\kappa}_{{{{{{{{\rm{p}}}}}}}}}\rangle \, < \, {\kappa}_{{{{{{{{\rm{p}}}}}}}},\max }\). The modern Earth’s oxygen cycle is maintained at a stable state by some negative feedback mechanisms1,27, implying that \({\kappa}_{{{{{{{{\rm{p}}}}}}}},\max }\) should be less than \({\kappa}_{{{{{{{{\rm{p}}}}}}}}}^{\star }=2\) (Fig. 2). Therefore, \({\kappa}_{{{{{{{{\rm{p}}}}}}}},\max }\) should fall between 0.05 and 2 in the modern environment.

The red horizontal line in Fig. 2b represents the estimated parameter ranges under Earth’s modern conditions: \(0.05 \, < \, {\kappa}_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\, < \,2\) and fModern ≃ 0.7. The ranges of \({\kappa}_{{{{{{{{\rm{p}}}}}}}},\max}\) and f in deep time, nevertheless, remain unknown, preventing the direct determination of their exact positions in the parameter space (Fig. 2b). In the next section, I suggest that \({\kappa}_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and fModern can be used as references for deep time, providing an alternative approach to test whether mineral evolution contributed to oxygenation events on the ancient Earth.

Modern \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) as benchmarks for deep time

The diversity of minerals on Earth’s surface increased over geologic time as new mineral-generating processes, such as crust-mantle reworking and biological activities, came into play3,4. The abundance of terrestrial and riverine minerals, including those contributing to the physical protection of organic matter (e.g., iron(III) and clay minerals11,57,58), in deep time should have been lower than that in the modern environment3,59. Geological and biological evolution altered the residence times of organic matter on land as well. The growth of the land fraction on Earth’s surface during the Archean-Proterozoic transition60,61 might have remarkably elevated the length of time that organic matter stayed on the continents. Moreover, the Phanerozoic evolution of plant life significantly enhanced riverbank cohesion and reduced migration rates of meandering rivers62,63, leading to longer residence times of organic matter in floodplains64,65. The lower abundances of terrestrial and riverine minerals and shorter residence times of organic matter on land in the Archean and Proterozoic likely resulted in less pre-formed association of organic matter with minerals (before being deposited in marine sediments) than in the modern, implying that fArchean and fProterozoic are less than fModern ≃ 0.7 and therefore \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Archean}}}}}\,}^{\star } \,{{\mbox{ and }}}\,{\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Proterozoic}}}}}\,}^{\star } \) are less than \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\simeq 2\). On the other hand, a larger initial coverage of organic matter on mineral surfaces would lead to higher repulsive barriers and thus slower adsorption kinetics25,46,47; the relation between \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) and f is expressed as \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\propto \exp (-f)\)25,26, which implies that \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Archean}}}}}} \;{{\mbox{and}}}\; {\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Proterozoic}}}}}}\) are larger than \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}} \, > \,0.05\). These estimations suggest that the deep-time stable regime in the parameter space is the domain under the horizontal red line and left of the blue curve in Fig. 2b.

I denote the ratio of \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) to \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) by \(R={\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }/{\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\), which measures the change in \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) required to cross the boundary curve \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) and switch from the stable to the unstable regime (Fig. 2b). The analyses above suggest that RArchean and RProterozoic  are less than RModern, which means that a larger increase in \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) is required to destabilize Earth’s oxygen cycle in the modern (the horizontal red line in Fig. 2b) than in the Archean and Proterozoic (i.e., the region under the horizontal red line and left of the blue curve in Fig. 2b). In other words, if a growth in \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) is able to instigate Earth’s oxygenation under the modern conditions, then so, too, it should have been in the Archean and Proterozoic environments. The relation \(0.05 \, < \,{\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}} \, < \,{\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\simeq 2\) implies RModern ≤ 40, which suggests that, if the Archean or Proterozoic mineral evolution resulted in a 40-fold or higher increase in \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max )}\), then Earth’s oxygen cycle would have shifted into an unstable regime, facilitating the rise of O2. In the following, I use \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\) as benchmarks to investigate whether and how the evolution of iron and clay minerals contributed to the GOE and NOE, respectively.

Iron mineral evolution and the GOE

Iron(III) minerals play a significant role in preserving organic matter in the modern environment11,57,66. Amorphous ferrihydrite and crystalline iron(III) oxides promote the persistence of organic matter in natural ecosystems via different mechanisms such as co-precipitation, direct chelation, and inner-sphere interactions57,66. However, its reduced state, iron(II), which is commonly soluble in natural aquatic systems, has a much weaker affinity to organic matter67,68; as a result, the contribution of iron(II) to the protection of organic matter is generally negligible69,70. In the Neoarchean O2-deficient world, the majority of iron existed in the form of dissolved iron(II)8,71; the availability of iron(III) minerals was limited8,71. In such an environment, the transformation of dissolved iron(II) to iron(III) minerals, either through the direct iron-oxidation in photoferrotrophy72,73 or via the reaction with O2 produced by oxygenic photosynthesis72,74, probably promoted the protection of organic matter, elevating O2 levels on Earth’s surface. Here, I explore this possibility by investigating the variations in the parameter space presented in Fig. 2b.

To justify whether the Neoarchean evolution of iron minerals contributed to the GOE, I first consider the molar ratios of the protected organic matter to iron(II) and to iron(III), which are henceforth denoted as OM:Fe(II) and OM:Fe(III), respectively. As mentioned above, the association of organic matter with iron(II) is basically negligible66,68, implying that OM:Fe(II) ≪ 1. On the other hand, global-scale observations in modern marine sediments have suggested that organic matter is associated with iron(III) (via co-precipitation/chelation) with OM:Fe(III) ≥ 457,67,75. Therefore, the Neoarchean transformation of iron(II) to iron(III) likely resulted in a ≫ 4 times increase in the capacity for organic matter-mineral associations. Since \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) is an e-folding function of capacity25,26, a ≫ 4-fold growth in capacity implies a ≫ e4 times rise in \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\). A ≫ e4-fold change appears very large; experimental research, however, has shown that the rate constants of organic matter-mineral associations can vary across several orders of magnitude76. With \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\) as benchmarks, this ≫ e4-fold growth in \({\kappa }_{p,\max }\) suggests that the Neoarchean evolution of iron minerals might have contributed to the GOE because such an increase is greater than the estimated threshold of 40-fold growth required to destabilize the oxygen cycle and facilitate the rise of O2 (Fig. 4).

Fig. 4: Influence of iron and clay mineral evolution on Earth’s oxygen cycle in deep time.
figure 4

Theoretical analyses in this study suggest that the Neoarchean transformation of dissolved iron(II) to ferrihydrite/iron(III) oxides and the Neoproterozoic production of weathering-derived clay minerals likely induced a ≫ e4-fold and ~ e4-fold growth in \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max )}\), respectively. These increases are greater than the estimated 40-fold rise in \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max )}\) required to cross the critical value \({\kappa }_{{{{{{{{\rm{p}}}}}}}}}^{\star }\) (Fig. 2b), suggesting that the Neoarchean evolution of iron minerals and Neoproterozoic evolution of clay minerals might have destabilized Earth’s oxygen cycle and facilitated O2 accumulation.

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The most prominent geological observation that appears to depart from the theory here is the scarcity of organic matter in iron formations, which were widely deposited during the Neoarchean and contain iron(III) oxides such as magnetite and hematite72,77. The deficiency of organic matter in iron formations has been attributed to its desorption during the aging of reactive ferrihydrite in diagenetic processes78,79. However, a large fraction (~23−27%) of the total organic matter remains bound to iron(III) in mature sediments on the modern Earth57, and the fate of desorbed organic matter in the Neoarchean environment remains poorly understood. Although a substantial portion of the organic matter released during the diagenesis might have been remineralized with O2 as the final electron acceptor80,81, the rest was probably consumed in the temperature/pressure diagenesis (in the absence of O2)82 or sequestered/immobilized in deep sediments13,22. Moreover, experimental studies have suggested that ferrihydrite aging may instead enhance the stabilization of organic matter under certain natural conditions83,84,85, which adds another layer of complexity to predicting the fate of organic matter associated with reactive iron(III) phases. Future field and laboratory investigations of organic matter bound to ferrihydrite/iron(III) oxides in diagenetic processes under conditions analogous to the Archean environment would offer validation of these speculations.

Clay mineral evolution and the NOE

Clays are the other major type of minerals contributing to the long-term preservation of organic matter on the modern Earth11,58. However, not all types of clay minerals were created equal in terms of their surface areas and therefore adsorption capacities over geologic time; whether and how clay mineral evolution contributed to the NOE remain debated7,59,86. The “clay mineral factory” hypothesis7 proposed that the enhanced production of pedogenic phyllosilicates (e.g., smectites and kaolinites), which are weathering-derived and have high absorption capacity47,58, during the Neoproterozoic might have promoted the burial of organic matter and therefore the accumulation of O2. Nevertheless, other studies suggested that pedogenic phyllosilicates had developed well prior to the Proterozoic-Phanerozoic boundary59 and the clay minerals formed during the Neoproterozoic were likely dominated by micas and tectosilicates/feldspars86, which are inherited largely from parent rocks and possess low absorption capacities47,58. Here, instead of investigating the predominance of inherited versus pedogenic clays on the Neoproterozoic Earth’s surface, I explore whether and how clay mineral evolution might have led to a shift from the stable to the unstable regime in the parameter space (Fig. 2b).

Earth’s geosphere and biosphere underwent significant evolution in the Phanerozoic; the Neoproterozoic production of clay minerals therefore was likely to have differed significantly from that in the modern3,59. The intensity of oxidative weathering, which remarkably influences clay formation59,87 and is positively correlated with the atmospheric O2 level13,88, should have been lower during the Neoproterozoic than in the present. The production flux of terrigenous minerals deriving from oxidative weathering, Fow, is generally expressed as a function of atmospheric O2 levels88,89: \({F}_{{{{{{{{\rm{ow}}}}}}}}}\propto {(p{{{{{{{{\rm{O}}}}}}}}}_{{{{{{{{\rm{2}}}}}}}}})}^{1/2}\). The pO2, as suggested by geological and geochemical studies74,90,91, increased by about 10 − 100 times during the Late Neoproterozoic, implying a 3- to 10-fold rise in the production flux of weathering-derived clays and therefore in the surface capacity for organic matter association. This range is basically consistent with the estimated 4-fold growth in the surface capacity caused by the enhanced production of pedogenic phyllosilicate during the Neoproterozoic-Cambrian transition7. Here, I take this 4-fold rise7 for the analysis. As discussed in the last section, such a 4 times increase in adsorption capacity corresponds to an e4-fold rise in \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\). Again, with \({\kappa }_{({{{{{{{\rm{p}}}}}}}},\max ),{{{{\mbox{Modern}}}}}}\) and \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\,{{{{\mbox{Modern}}}}}\,}^{\star }\) as benchmarks, this growth induced by the evolution of clay minerals is higher than the estimated threshold of 40-fold elevation required to destabilize the oxygen cycle and promote the rise of O2 (Fig. 4).

The theoretical analysis so far has explored the possible role of clay minerals in the NOE; the specific sources of weathering-derived clays in the Neoproterozoic are not well known. In addition to the inherited and pedogenic clays discussed in previous studies7,86, other possible sources of clays remain understudied. The highly weatherable mafic and ultramafic rocks in large igneous provinces92,93 and ophiolites94,95 may serve as the sources of a variety of clay minerals with high absorption capacity, especially the smectite group. The emplacement and weathering of continental flood basalts and ophiolites in the Neoproterozoic96,97 might have produced substantial clay minerals possessing large surface areas and enhanced the burial of organic matter. Moreover, the Neoproterozoic distribution, abundance, and evolution of authigenic iron(III)-bearing clays such as vermiculite, nontronite, chamosite, and glauconite deserve more investigation. The increased availability of ferric iron3 and elevated intensity of reverse weathering98 during the Neoproterozoic probably promoted the production of authigenic iron(III)-bearing clays59,99, facilitating organic matter preservation and therefore O2 accumulation.

Implications and limitations

The results presented here suggest several approaches for further exploring the role that minerals played in Earth’s oxidation. In addition to ferrihydrite/iron(III) oxides and clays, other types of minerals such as calcites and biogenic opals11,20 probably contributed to the accumulation of O2 in deep time as well. Future studies on the evolutionary history of these minerals and their absorptive abilities in the paleoenvironment would support or falsify this speculation. Furthermore, this study uses parameter values estimated from observations in the modern environment (Fig. 3) as references to explore deep-time variations. Laboratory investigations of organic matter-mineral interactions under conditions analogous to Earth’s ancient, especially the Neoarchean and Neoproterozoic, environments may offer precise parameter values and provide validation for the theory presented here. Besides, geochemical studies of the changes of mineral-associated organic matter abundance in sedimentary records over geologic time, especially during the periods of Earth’s oxygenation events, possibly using ramped pyrolysis/oxidation21,100, would offer direct support for the mechanisms proposed in this work.

The physical interactions and chemical reactions in the system of organic matter, minerals, and O2 are interwoven and complex; the theoretical results obtained from the mathematical model (Eqs. (1) and (2)), such as the probability distribution of adsorption/desorption rate constants (Eq. (5)) and the stable/unstable regimes of Earth’s oxygen cycle (Fig. 2), are based on simplified and idealized assumptions. The 40-fold growth of \({\kappa }_{{{{{{{{\rm{p}}}}}}}},\max }\) required to destabilize the oxygen cycle (Fig. 4) is therefore a rough estimation; high-dimensional models with more general assumptions may offer more realistic predictions. Moreover, this study investigates how mineral evolution might have influenced O2 levels via affecting organic matter-mineral interactions (Fig. 1); variables directly characterizing the evolution of minerals are not explicitly included in the minimalistic model (Eqs. (1) and (2)). Parameterizing these variables in the present theoretical framework would provide deeper insights into the contribution of mineral evolution to Earth’s oxygenation. In addition, the geochemically-based model in this study does not consider biological processes, which can significantly influence the production/consumption of organic matter and O2 and the physical/chemical proterites of minerals11,24. Integrating biological factors into the model presented here may provide a more comprehensive understanding of how the changes in biosphere might have influenced O2 levels on Earth’s surface via inducing mineral evolution.

In summary, this work explores whether and how organic matter-mineral interactions might have contributed to Earth’s oxidation in deep time. Although the theoretical results and proposed mechanisms require further experimental and field justification, this study links for the first time the microscopic interactions between organic matter and minerals to the macroscopic dynamics (i.e., stability/instability) of Earth’s oxygen cycle. These results may provide a step toward a quantitative understanding of how mineral evolution has shaped the surface environments of Earth and exoplanets.