Microkinetic characterization of ROS-driven methane production through quantum and classical simulations

Abstract

Methane is ubiquitous in natural and engineered settings, but the mechanisms of reactive oxygen species (ROS)-driven methane production in living organisms remain unclear. Unraveling the interactions and microkinetics among ROS, iron species, and organic methyl groups (MET) is crucial for reducing emissions and optimizing energy recovery. In this study, the quantum Harrow–Hassidim–Lloyd (HHL) algorithm and classical Levenberg–Marquardt (LM) algorithm were employed to: (1) investigate the primary pathway of Fe³⁺ and ascorbic acid (ASC) reactions, (2) determine the kinetic parameters for the reaction between [Fe^IV=O]²⁺ and MET, and (3) simulate the ROS-driven methane production pathway under specific abiotic conditions. The results revealed that Fe³⁺ and ASC are primarily responsible for the redox reaction, with a kinetic rate constant of 1.83 × 10⁻⁴ M⁻¹ s⁻¹ for the reaction between [Fe^IV=O]²⁺ and MET, and a ∼10% conversion rate of MET to methane. Our study establishes a theoretical framework for ROS-driven methane production. While identifying a feasible pathway for engineered and natural systems, further investigation and validation are needed to quantify its specific contribution in complex environments. Furthermore, this work demonstrates the potential of hybrid quantum-classical simulations for microkinetic analysis.

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Environmental significance

Methane is a double-edged molecule—an important renewable energy source yet a potent greenhouse gas. This study elucidates a previously unclear abiotic and biotic mechanism of reactive oxygen species (ROS)-driven methane formation, revealing how cellular redox reactions involving Fe³⁺, ascorbic acid, and methylated compounds can generate methane even in oxygenated environments. By integrating quantum (Harrow–Hassidim–Lloyd) and classical (Levenberg–Marquardt) microkinetic simulations, we quantify key rate constants and demonstrate that ferryl ion reactions, rather than hydroxyl radicals, dominate ROS-mediated methane production. These insights advance understanding of methane cycling in both engineered and natural systems, offering new directions for optimising micro-aerated anaerobic digestion and predicting methane emissions from oxygen-exposed ecosystems under changing redox and oxygen conditions.

1. Introduction

As global warming intensifies, it is of great significance to develop clean energy that can replace fossil fuel energy.¹ Methane is a renewable, clean energy source, albeit also a potent greenhouse gas. Harnessing methane production and collection for energy purposes presents a promising approach to mitigate greenhouse gas emissions. Methane production through anaerobic digestion (AD) can be enhanced by 10–30% using micro-aeration (2.63–37.5 mL O₂/L_R d, where L_R is the reactor working volume), which improves hydrolysis and generates reactive oxygen species (ROS) (0.27–0.29 mM H₂O₂ per cycle.^2–8 Contrary to popular belief that methane can only be produced under anaerobic conditions, enhanced methane formation has been observed in natural systems in the presence of oxygen, including oxygen-rich wetlands and oceans, where the addition of oxygen increased methane emissions by 4–10 fold.^9,10 The ability to produce methane appears to be deeply rooted in evolution and present in all living organisms. Through coupling oxygen-generated ROS with methane production as part of an organism’s innate oxidative stress mechanism, this mitigates ROS-induced oxidative damage. For example, Bacillus subtilis and Escherichia coli showed a 1.2–3.2 times methane yield increases in the presence of ROS as compared to that of non-ROS condition.³ Leveraging on these emerging insights can provide new avenues for mitigating emissions and improving renewable energy harvesting. However, the precise mechanisms and micro-kinetics underlying the role of ROS in facilitating methane production remain poorly understood.

ROS-driven methane production has been linked to the presence of methyl group-containing organosulfur compounds, ROS, Fe²⁺and reducing agent ascorbic acid (ASC) (Fig. 1a).^3,11 Fe²⁺ and H₂O₂ (a form of ROS) can undergo Fenton reaction to generate Fe³⁺, hydroxyl radicals (˙OH) and ferryl ions ([Fe(IV)=O]²⁺). [Fe(IV)=O]²⁺ and ˙OH can react with methyl-containing organosulfur compounds to form methane.¹¹ The Fe³⁺ produced can be reduced by ASC to regenerate Fe²⁺, sustaining the Fenton reaction. It is expected that these chemical species are present in natural and AD-engineered systems. Iron, an active metal predominantly coordinated in heme groups and iron-sulfur clusters that drive electron transport chains and participates in redox reactions, is widely present in living organisms including microorganisms.¹² Exposure of microbes to oxygen often produces ROS, which damage cellular structures and impair metabolisms.¹³ ASC may play a crucial role in cellular protective mechanisms from ROS damage by facilitating iron and ROS redox reactions, thereby producing methane as a byproduct. However, there is a discrepancy in the proposed mechanisms for the interaction between ASC and iron species (Fig. 1b). Here, two competing mechanisms are possible: a catalytic mechanism proposed by Buettner (eqn (1)) and a redox mechanism proposed by Buettner and Jurkiewicz (eqn (2)),^14,15 as shown below:

ASC + Fe³⁺ + O₂ = Fe³⁺ + DHA + H₂O₂ (1)

where DHA is dehydroascorbic acid

ASC + Fe³⁺ = Fe²⁺ + A^˙− + 2H⁺ (2)

where A˙⁻ is the ascorbate radical.

Fig. 1 Proposed reaction pathways of the ROS-driven methane production loop: (a) the chemical processes involved in the biological Fenton reaction; (b) the catalyst and redox reactions between ASC and Fe³⁺; (c) the two possible reaction loops: ROS regeneration loop and ROS-driven methane production loop.

Models proposed by Shen et al. showed that the catalysis degree of the reaction was 4 to 6-fold greater than that of the redox reaction.¹⁶ However, experimental data from Elmagirbi et al. indicated that 76% of Fe³⁺ was converted to Fe²⁺ in the presence of ASC, suggesting that only 24% of Fe³⁺ may participate in the catalyst reaction.¹⁷ Currently, it is unclear which pathway, whether redox or catalysis, plays a more significant role in promoting ROS-activated microkinetics. If the redox reaction between ASC and Fe³⁺ dominates, it can produce Fe²⁺ which promotes the ROS-driven methane production pathway to mitigate oxidative cell damage. In contrast, if the catalytic reaction is dominant, it will produce additional H₂O₂, which can cause cell damage and inhibit the methane production pathway.

Overall, the interaction between ASC and iron species drives two competing loops (Fig. 1c). The catalytic pathway (blue loop) regenerates H₂O₂, potentially leading to ROS accumulation. In contrast, the redox pathway (orange loop) reduces Fe³⁺ to Fe²⁺, driving the Fenton reaction to generate [Fe(IV)=O]²⁺ and hydroxyl radicals. These intermediates subsequently oxidize methyl-containing organosulfur compounds to produce methane while regenerating Fe³⁺ for the next cycle. Consequently, determining the dominant microkinetic pathway is essential to distinguish between the ROS regeneration and the methane production loop. Based on this, we hypothesize that methane production proceeds via ferryl ions and methyl group-containing organosulfur compounds such as methionine (MET), through the pathway described in eqn (9) (Table 2).

The ROS regeneration loop may produce H₂O₂ continuously and cause cell damage, however, the generation of ˙OH and [Fe(IV)=O]²⁺ as intermediates in the Fenton-driven methane production loop may contribute to methane production. Addressing the counteracting effects of the ROS regeneration loop and the Fenton-driven methane production loop would require the preferred reaction for ROS-driven methane production microkinetics to be established. To this end, microkinetic simulation was used to determine which reaction cycle (the orange, or blue), or both reaction cycles shown in Fig. 1c is more favorable.

Microkinetic simulation can be conducted using both quantum and classical computing algorithms, each offering its own set of advantages. Most recently, the Harrow Hassidim and Lloyd (HHL) quantum algorithm has been successfully applied in solving linear microkinetic matrices.^18,19 The Levenberg–Marquardt (LM) classical algorithm has already been used to determine the microkinetic parameters with nonlinear matrices.^20–22 These studies have demonstrated the versatility of microkinetic simulation and its potential to couple both quantum and classical computing approaches.

In the context of ROS-driven methane production microkinetics, the mass balance of the reaction between ASC and Fe³⁺ can be formulated as a system of linear equations, whereas that of the associated reactions between ferryl ion and MET can be modelled non-linearly. This study, thus, aims to achieve three objectives: (1) determine the microkinetic model between ASC and Fe³⁺ using the quantum HHL algorithm, (2) employ the classical LM algorithm to calculate the microkinetics between ferryl ion and MET, and (3) simulate the ROS-driven methane-forming microkinetics using the HHL algorithm. The quantum HHL simulation results were benchmarked against classical computations, with further validation conducted against existing experimental data from relevant studies. Additionally, the microkinetics of ROS scavenging, ASC, oxygen, and iron species for ROS-driven methane production will be discussed. The findings of this study will advance our understanding of ROS-driven methane production in natural and engineered systems. Moreover, the insights for future research studies associated with applying quantum and classical computing simulations in microkinetic models are addressed.

2. Methodology

2.1 Simulation parameters and assumptions

To develop our microkinetic simulation, we utilized experimental data from Althoff et al., who investigated abiotic methane formation from organosulfur compounds (MET) in the presence of iron, ascorbate, and H₂O₂.^11,23 We adopted their reported reactant concentrations and environmental conditions to define the initial settings for our computational model (Table 1).

Table 1 Reactants and reaction conditions used in the analysis^11,23

Reactant	Concentration (mmol L^−1)
ASC	50
Ferric ion	40
MET	0.5
Hydrogen peroxide	100
Dissolved oxygen	160

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Condition	Value
pH value	3
Temperature	25 °C
Reaction time	30 h
Reaction volume	1 mL

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In this simulation, a pH of 3 was selected for the following reasons: (1) previous research indicated a maximum ROS-driven methane production at pH = 3 based on experiments conducted in the pH range of 1–9.¹¹ (2) In our case, ROS-driven methane production in E. coli likely occurs in the E. coli periplasmic cell envelope, where its pH is in the range of pH = 1–3.²⁴ Since such a pathway is applicable to all organisms, it is plausible to have it in the E. coli periplasm.³ Moreover, ASC formation by E. coli has been reported previously, indicating its capability to survive in acidic conditions.²⁵ Furthermore, E. coli, possesses regulatory hydrogenase that can effectively ensure its survival under lower pH conditions (pH ≥ 2).²⁶ (3) Some archaeal species can still be active even at pH = 1–2.²⁷ (4) The cytoplasmic proteins of acetogens remain stable under extremely acidic conditions.²⁸ Therefore, ROS-driven methane production pathways may occur in organisms at low pH.

Table 2 provides a summary of the stoichiometry, reaction kinetics, and thermodynamic constants used for the microkinetic simulations. Here, eqn (1)–(7) were used to describe the interactions between different reactants. The chemical reactions eqn (1)–(4) represent the catalytic and redox reactions between ASC and Fe³⁺, as well as the interactions between the corresponding products. Eqn (5) and (6) reflect the products of the two Fenton reactions, namely ˙OH and [Fe(IV)=O]²⁺. Finally, eqn (7) reflects the role of ASC in scavenging ˙OH.

Table 2 Reactions used in this analysis and their standard Gibbs free energies and reaction rate constants at 25 °C^e

	Reaction	Kinetic parameter (k) (M^−1 s^−1)	Reference	Gibbs free energy (ΔG0) (kcal mol^−1)	Reference
a The ΔG0–1 was calculated using the relationship ΔG0 = −nF Ecell, where n = 2 and F is the Faraday constant. Ecell is the change of total reaction reduction potential, which was obtained between E(O2/H2O2) = +0.28V and E(dehydroascorbate/ascorbate) = +0.06V.^32,33b The ΔG value was calculated based on the standard Gibbs free energies of formation ΔGf for the individual chemical species.^35,42,43c Calculated using the equilibrium constant (K) estimated from the MATLAB kinetic simulation.d Refer to Section 2.1 and SI Table 1.e Enzymatic scavengers (SOD, Catalase) are excluded in this study. Their presence in vivo regulates ROS levels but does not alter the fundamental role of Ferryl iron in driving methane formation.
(1)	ASC + Fe^3+ + O2 = DHA + Fe^3+ + H2O2	k1 = 4.0 × 10^5	31	ΔG0–1 = −10.2	32 and 33 ^a
(2)	ASC + Fe^3+ = Fe^2+ + 2H^+ + A^˙−	k2 = 4.5 × 10^3	34	ΔG0–2 = 1.1	35
(3)	Fe^2+ + O2 = Fe^3+ + O2^˙−	k3 = 1.0 × 10^−5	36	ΔG0–3 = −91.6	37
(4)	A^˙− + O2^˙− + H2O = DHA + HO2^˙− + OH^−	k4 = 2.6 × 10^8	38	ΔG0–4 = 38.4	39
(5)	Fe^2+ + H2O2 = Fe^3+ + ˙OH + OH^−	k5 = 5.7 × 10^2	40	ΔG5 = 28.7	^b
(6)	Fe^2+ + H2O2 = [Fe^IV=O]^2+ + H2O	k6 = 1.0 × 10^6	41	ΔG6 = −14.9	^c
(7)	ASC + ˙OH = A^˙− + H2O + H^+	k7 = 7.9 × 10^9	16	ΔG7 = −30.4	^b
(8)	ASC + O2 = 2H^+ + O2^˙− + A^˙−	—	^d	—	^d
(9)	2[Fe^IV=O]^2+ + MET + H2O2 + 2H^+ = 2Fe^3+ + HCyA + CH4 + H2O	—	^d	—	^d
(10)	ASC + Fe^2+ + H2O2 = Fe^3+ + A^˙− + 2H2O	—	^d	—	^d

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To establish the microkinetic model, several assumptions were made: (1) the molar concentration of DHA in eqn (1) and (4) shown in Table 2 was taken to be the same as the concentration of HO₂˙⁻ and H₂O₂, according to the stoichiometric ratio of 1 : 1; (2) the concentration of DHA has a linear relationship with Fe³⁺;²⁹ (3) the concentration of O₂^˙− is 3.9 mM, using a conversion rate of 1.5% for [O₂] to [O₂^˙−] according to previous literature;³⁰ (4) eqn (2) and (3) can be combined as eqn (8) in Table 2, and since eqn (3) is the rate limiting reaction, the kinetic reaction rate constant can be taken as k₃, (5) the interaction pathway between [Fe^IV=O]²⁺ and MET, as proposed by Althoff et al., can be summarized as eqn (9) in Table 2.¹¹ (6) Reactions eqn (5) and (7) can be combined as eqn (10) in Table 2, and the kinetic reaction rate constant can be taken as k₅ (rate limiting).

2.2 Kinetic estimation using HHL algorithm

In this study, the HHL algorithm was used to simulate microkinetic models to determine the mechanism behind ASC, Fe³⁺, and the ROS-driven methane production (redox and/or catalysis pathway). We constructed the model according to the chemical equilibrium principle that the rates of forward reaction and reverse reaction are equivalent. The forward reaction rate constant (k) and Gibbs free energy (ΔG₀) used are shown in Table 2 and in the SI Table 1. Detailed calculations are shown in the SI Note 1.

To investigate the mechanism for ROS-driven methane production microkinetics in non-methanogenic microbes at the conditions listed in Table 1, the following system of linear equations was built.

A·x = b (11)

where A and b are known matrices while x is the unknown matrix to be determined.

The HHL algorithm requires matrix A to be Hermitian, necessitating the transformation of A into matrix A^H.

where A^† denotes the complex conjugate transpose of A.

After the conversion of matrix (A) of eqn (11) into the Hermitian matrix (A^H) in eqn (12), the unknown term x was calculated using eqn (13) in the HHL algorithm:

x = b × A^H−1 (13)

Hence, to investigate whether the redox and/or catalysis pathway drives the reaction between ASC and Fe³⁺, a microkinetic linear matrix model (eqn (14)) was constructed based on eqn (1), (4) and (8) at steady state. The procedure for establishing eqn (14) is shown in the SI Note 2.

To investigate the ROS-driven methane production pathway, a microkinetic linear matrix (eqn (15)) was built initially to simulate the probability of the Fenton reaction forming [Fe^(IV)=O]²⁺ to participate in the ROS-driven methane production pathway. Eqn (15) was constructed based on reactions eqn (2), (6) and (10) at steady state. The process for establishing eqn (15) is given in the SI Note 3.

To investigate the methane production of MET oxidated [Fe^(IV)=O]²⁺ in the ROS-driven methane production pathway, a microkinetic linear matrix model (eqn (16)) was constructed based on the eqn (9) reaction at steady state. According to the stoichiometric ratio in the eqn (9) reaction, the production of HCyA represents methane production. The process for establishing eqn (16) is shown in the SI Note 3.

2.3 Kinetic estimation using LM algorithm

The reaction rate constant between MET and [Fe^(IV)=O]²⁺ was determined using mass balances derived from reaction eqn (2), (5), (6), (7) and (9). The resulting non-linear matrix (eqn (17)) was solved using MATLAB with a LM algorithm. Further information about the matrix development is given in SI Note 4.where V denotes the reaction volume, and t refers to the reaction time.

3. Results

3.1 Mechanistic determination analysis

Table 3 summarizes the simulated concentrations of the reaction products, [HO₂^˙−], [A^˙−] and [H₂O₂] associated with ASC and Fe³⁺ participation in redox and catalytic reactions, respectively. The results obtained using the quantum HHL algorithm showed good agreement with the classical MATLAB simulation. Notably, regarding the catalytic product [HO₂^˙−], the classical simulation yielded a value of ∼10⁻²⁰ mol L⁻¹. It is important to clarify that this non-zero value represents a numerical artifact (asymptotic residue) inherent to classical ODE solvers using floating-point arithmetic, rather than a physical concentration. In contrast, the quantum simulation reported a concentration of 0.00 mol L⁻¹, correctly identifying the absence of this species within the algorithmic resolution.

Table 3 Summary of the simulation results^a

Unknown parameter	Estimated values (quantum)	Estimated values (classical)	Remarks	Error
a Classical results include a numerical artifact from ODE solvers. The residual values (∼10^−7) for trace species are negligible in representing physical concentrations.b Products of catalytic/redox reaction indicated in eqn (14).c k9 is the kinetic parameter for eqn (11).d The proportion of iron ions involved in Fenton reaction.e Methane production.f Simulated conversion rate (η) of MET to methane in Google Quantum AI.g Experimentally measured conversion rate (η) of MET to methane conducted by Althoff et al.^11
Mechanistic determination by Google Quantum AI & Classical MATLAB
[ASC]	0.00 (mol L^−1)	0.00 (mol L^−1)	—	1.56 × 10^−20
[HO2^˙−]	0.00 (mol L^−1)	1.56 × 10^−20 (mol L^−1)	Redox reaction^b
[H2O2]	0.00 (mol L^−1)	0.00 (mol L^−1)	Catalytic reaction^b
[A^˙−]	5.00 × 10^−2 (mol L^−1)	5.00 × 10^−2 (mol L^−1)	Redox reaction^b
Kinetic reaction rate constant determination by Classical MATLAB
k9^c	—	1.83 × 10^−4 (M^−1 s^−1)	—	—
Microkinetic simulation by Google Quantum AI & Classical MATLAB
[Fe^3+]	0.00 (mol L^−1)	2.93 × 10^−7 (mol L^−1)	0^d	4.14 × 10^−7
[Fe^2+]	0.00 (mol L^−1)	1.20 × 10^−11 (mol L^−1)	0^d
[Fe^IV=O^2+]	4.00 × 10^−2 (mol L^−1)	4.00 × 10^−2 (mol L^−1)	100%^d
[MET]	4.71 × 10^−4 (mol L^−1)	4.71 × 10^−4 (mol L^−1)	—	1.23 × 10^−12
NMethane^e	4.71 × 10^−8 mol	4.71 × 10^−8 mol	—
Conversion rate^f	9.42%		This work	—
Conversion rate^g	10.00%		Althoff et al.^11	—

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Consequently, both simulations confirmed that nearly 100% of the reaction proceeded via the redox pathway. This result was consistent with the fact that the Gibbs free energy for eqn (8) (ΔG = −90.5 kcal mol⁻¹) is significantly more negative than that for eqn (1) (ΔG = −10.2 kcal mol⁻¹), indicating a strong thermodynamic preference for the redox pathway. In the presence of oxygen, ASC, and Fe³⁺, A^˙− generation by eqn (8) is more favorable. Eqn (8) is dependent on the redox reaction between ASC and Fe³⁺ occurring, rather than the catalytic reaction. These findings aligned well with the results of the studies conducted by Timoshnikov et al. and Buettner & Jurkiewicz, which showed the high degree of Fe³⁺ reduction by ASC under aerobic conditions and at a pH of 3.^15,44 The simulation results showed that ASC is beneficial for promoting methane production in the Fenton-driven methane production loop. Thus, the redox reaction between ASC and Fe³⁺ plays a decisive role in tilting the microkinetics towards the ROS-driven methane production pathway.

3.2 Kinetic reaction rate constant determination

The kinetic rate constant k₉ in the matrix (eqn (17)) was derived as 1.83 × 10⁻⁴ M⁻¹ s⁻¹ (Table 3) by implementing the LM algorithm in MATLAB. Comparing the reactions represented by eqn (6) and (9), the reaction rate constant (k₉) between [Fe^(IV)=O]²⁺ and MET is approximately ten orders of magnitude lower than the reaction rate constant (k₆) of the Fenton reaction to produce [Fe^(IV)=O]²⁺, implying that the reaction of [Fe^(IV)=O]²⁺ and MET is the rate-determining step in the ROS-driven methane production pathway. SI Table 2 provides a summary of the MATLAB output results.

3.3 Microkinetic simulation

The results derived from the execution of eqn (15) matrix on Google Quantum AI platform were consistent with classical MATLAB computations (Table 3). It is evident that through the Fenton reaction, iron is prone towards ferryl ion formation (4.00 × 10⁻² (mol L⁻¹), with near 100% conversion rate from iron to ferryl ion. This result matched the findings of Deguillaume et al., which showed that at a low pH of 3.5, the concentration of ferryl ion produced by the reaction of Fe²⁺ and H₂O₂ was 10⁴ times greater than the concentration of ˙OH produced.⁴⁵ From the microkinetics perspective, the kinetic reaction rate constant between Fe³⁺ and H₂O₂ to produce ferryl ion (k₆) is 10⁴ times greater than that of ˙OH formation (k₅) in the ROS-driven methane production process. Fe³⁺ (k₂) and ˙OH (k₇) exhibit a greater susceptibility to reduction by ASC as compared to k₅. As a result, the ferryl ion serves as a primary reactant with MET to produce methane.

According to the stoichiometric ratio in eqn (9), the product concentration of HCyA is directly proportional to the methane produced. Therefore, methane production can be estimated using eqn (16) through the HHL algorithm. In addition, the conversion rate (η) of MET to methane can be calculated. The quantum-simulated conversion rate (η) was 9.42% (Table 3), showing strong agreement with the classical calculation (10.00%) and the experimental value reported by Althoff et al.¹¹ The detailed calculations are shown in SI Note 5.

4. Discussion

4.1 Effect of radical kinetics and oxygen levels for methane production

An investigation of the ˙OH concentration in cells is of paramount importance. In the ROS-driven methane production pathway studied in this work (conditions presented in Table 1), ˙OH produced by the Fenton reaction (Fig. 1c), can either react with methyl compounds to form methane or be scavenged by ASC. ASC reportedly has a strong affinity for ˙OH with a high reaction rate of 7 × 10⁹ M⁻¹ s⁻¹.⁴⁶ Meanwhile, the reaction rate constant of ˙OH attacking intracellular DNA is 3 × 10⁸ M⁻¹ s⁻¹.⁴⁷ This difference in the order of magnitude indicates that the scavenging effect of ASC occurs at a higher rate than ˙OH-induced cellular damage. As a result, it is proposed that ROS in the methane production pathway does not cause significant damage to cells. Furthermore, the reaction rate constant of methyl-containing compounds and ˙OH is 1.5 × 10⁷ M⁻¹ s⁻¹, which is notably lower than the scavenging rate of ˙OH by ASC (7 × 10⁹ M⁻¹ s⁻¹).⁴⁸ Therefore, the contribution of ˙OH may not be as significant as that of ferryl ions in the ROS-driven methane production pathway (Fig. 2).

Fig. 2 Schematic indicating that ˙OH (the product of the Fenton reaction) does not participate in the ROS-driven CH₄ production loop and damages intracellular DNA. k_a is the reaction rate constant between ASC and ˙OH;⁴⁶ k_b is the reaction rate constant between DNA and ˙OH;⁴⁷ k_c is the reaction rate constant between methyl-containing compounds and ˙OH.⁴⁸

Our findings mechanistically demonstrate the feasibility of a ROS-driven methane production pathway under the specific abiotic conditions modeled. This pathway offers a theoretical framework to interpret methane enhancement phenomena not only in micro-aeration anaerobic digestion (MAAD), but also in natural systems, such as wetlands.^6,49 While these systems can synthesize H₂O₂ under oxygen (∼21 µM in wetlands vs. 270–290µM in MAAD), which reacts with Fe²⁺ to promote the generation of ferryl ions and facilitates the conversion of MET to methane.^8,50,51 Extrapolating these microkinetic results to complex environmental matrices introduces inherent uncertainties. Factors such as pH variations, organic ligand complexation, and microbial interactions in natural ecosystems may significantly alter the reaction kinetics compared to our simplified model. Recent studies suggest that ROS can promote Fenton reaction in bacteria and archaea, generating ferryl ions that oxidize methyl-containing donors.³ These biological observations align with our mechanistic findings; however, distinguishing the specific contribution of this ROS-driven pathway from canonical enzymatic processes in diverse oxygen environments requires further in situ validation to bridge the gap between idealized modeling and ecosystem complexity.

However, excessively high oxygen levels may negatively impact the overall methane production in these systems. For instance, in cyanobacteria, the conversion rate of organic MET is affected when the oxygen concentration is close to that of air-saturated water.^23,50 Higher intracellular oxygen levels have been shown to lower the conversion rates for both MET (about 10%) and [Fe^IV=O]²⁺.¹¹ In addition, Althoff et al. reported a lack of CH₄ formation in an oxygen-saturated environment, most likely due to oxygen’s adverse effects on ROS-driven methane production.²³ This might be attributed to the reaction between the methyl radical (˙CH₃), the methane precursor, and O₂, forming methylperoxyl (CH₃OO˙) with a significantly high reaction rate constant of 3.7 × 10⁹ M⁻¹ s⁻¹.⁵¹ The formation of methylperoxyl reduces the production of methane. This rate constant for the reaction between ˙CH₃ and O₂ is notably larger than the calculated rate constant for the methane production reaction of [Fe^IV=O]²⁺ with MET (1.83 × 10⁻⁴ M⁻¹ s⁻¹) investigated in this study. Aside from ROS-driven methane production, oxygen overload also affects methanogenesis by creating an unfavorable environment for methanogens’ survival, lowering the overall methane production rate.² Hence, ascertaining the oxygen concentration threshold required for striking a balance between ROS-induced and methanogen-based methane production would be advantageous for engineered systems such as MAAD seeking enhanced methane production as well as the control and mitigation of methane emission from natural ecosystems. Future work must bridge the gap between this idealized microkinetic model and in situ environmental conditions to validate these broader implications.

4.2 Perspectives and limitations of microkinetic using quantum computing

Quantum computing incorporates the superposition and entanglement properties of quantum mechanics and can surpasses classical computation in analyzing and quantifying information under certain conditions. Notably, it can efficiently simulate the energy consumption of the Haber–Bosch process (1–2% of global energy consumption), an energy-intensive process, by analyzing the underlying chemical reaction mechanisms.⁵² Specifically, the HHL algorithm enables the implementation of chemical microkinetic models on quantum computers, for processes such as CO oxidation, aiding in the resolution of chemical kinetics-related issues.^19,53 Furthermore, Becerra et al. used the same quantum algorithm to quantify the uncertainties in Rh(III)-catalyzed CO oxidation pathways, which classical computation struggles to calculate. This emerging trend suggests that quantum computing may be a promising technique for simulating chemical reaction mechanisms and microkinetic models.^18,54 It foreshadows the potential mainstream adoption of quantum simulation for predicting molecular properties, activation energies, and reaction rate constants.^55,56

While classical solvers remain efficient for these small-scale systems, this study establishes a prospective algorithmic advantage. By replacing classical polynomial scaling (e.g., O(N³) for matrix inversion), the HHL algorithm offers an exponential speedup with logarithmic scaling (O(log N)).⁵⁷ To illustrate this, for a hypothetical large-scale network with N = 10⁶ species, classical computational cost would surge to 10¹⁸ operations, whereas the quantum complexity grows only to the order of log(10⁶) (approx. 20). Nevertheless, this scaling analysis indicates that quantum solvers will be indispensable for future large-scale biochemical reaction network simulations, where high dimensionality renders classical approaches computationally prohibitive. This capability will enable the study of more complex environments for further investigation and related systems in the future.

Variations in the oxygen content of organisms may have an impact on ROS concentration, thereby influencing variations in the methane content.⁹ Consequently, this study investigated the impact of oxygen concentration in the range of 0–1000 mM in the models. The concentration of O₂^˙− in the initial model is influenced by the oxygen content, consequently affecting the relative importance of the redox and catalysis reactions. However, the results have shown that the redox reaction dominated within this oxygen concentration range, as detailed in SI Fig. 1. For the microkinetic simulation of ROS-induced methane production modelling, alterations in oxygen concentration ought to influence H₂O₂. However, the model’s foundation is based on the chemical experimental data presented by Althoff et al.^11,23 Hence, the H₂O₂ concentration remained constant throughout this study. Furthermore, the proportional relationship between the conversion of oxygen to H₂O₂ within living organisms remains unclear and it is not known how much oxygen can be converted into H₂O₂ within a cell. A comprehensive investigation into the influence of oxygen concentration on methane production in methanogenic pathways driven by ROS is thus unattainable. Moreover, the simulation of this work was largely based on the experimental data of Althoff et al., obtained through the reactions of pure chemicals at pH 3.¹¹ There is a lack of research on ROS-driven methane production in organisms at higher biological pH. In nature and environmental systems such as anaerobic digesters, which operate at circumneutral pH (6.5–8.0), iron speciation differs significantly, often involving precipitation or complexation with organic ligands.⁵⁸ These structural changes alter reaction energy barriers and kinetic rate constants (k). To extend our algorithmic framework to these conditions, we propose a hybrid computational strategy: theoretical methods like Density Functional Theory (DFT) or the Variational Quantum Eigensolver (VQE) can be employed to calculate the specific activation energies and rate constants for iron-ligand complexes at neutral pH.^59,60 Additionally, experimental techniques such as Electron Paramagnetic Resonance (EPR) spectroscopy could be integrated in future studies to directly detect the transient ferryl iron intermediates predicted by our model.⁶¹ These derived parameters can then serve as updated inputs for the HHL solver, ensuring the model’s applicability across diverse biochemical settings.

From a biological perspective, fermentative bacteria, which are known for their ability to survive and function well in a wide pH range (4–8), could serve as better candidates to study this phenomenon.⁶² The intracellular pH is generally lower than the extracellular pH, reaching 3.5 to 4.5.⁶³ Methods to study methane production in vivo such as microbial electro-methanogenesis, may be used to explore ROS-driven methane production at pH 3.5 to 7.5 in future investigations.⁶⁴

5. Conclusion

This study employed a hybrid quantum-classical computational framework to investigate the microkinetics of ROS-driven methane production. The results indicate that the redox reaction between ASC and Fe³⁺ is favored over the catalytic pathway, thereby supporting continued Fenton-driven methane production through Fe²⁺ regeneration. The reaction between [Fe(IV)=O]²⁺ and MET was identified as the rate-determining step, and the quantum simulated MET to methane conversion rate showed good agreement with current experimental observations, supporting the proposed mechanistic pathway.

These findings identify a feasible abiotic pathway for ROS-driven methane production and provide a theoretical framework for interpreting methane enhancement phenomena in micro-aeration anaerobic digestion and potentially in natural systems such as wetlands. More broadly, this work demonstrates the potential of the HHL quantum algorithm for microkinetic modelling, particularly in larger biochemical reaction networks where classical computation may become challenging. Further experimental validation under more complex biological conditions will be important for extending the applicability of this framework.

Author contributions

Ronghan Zhang and Zexuan Wang: conceptualization, methodology, software, formal analysis, investigation, writing – original draft, writing – review & editing. Kin Tung Michael Ho: conceptualization, writing – review & editing. Nigel J. D. Graham: writing – review & editing. Giin-Yu Amy Tan: writing – review & editing. Po-Heng Lee: supervision, conceptualization, writing – review & editing.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The source code and the detailed model-building procedure are available in the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d5va00420a.

Acknowledgements

The authors gratefully acknowledge Prof. Aleksandra Szczuka from the Department of Civil and Environmental Engineering, University of Michigan, Ann Habour, for her valuable input in modelling and reviewing the paper.

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