Authors: James A. Imlay (Department of Microbiology, University of Illinois, Urbana, Illinois, USA)
Categories: Perspective, hydrogen peroxide, obligate anaerobiosis, oxidative stress, superoxide
Source: Molecular Microbiology
Doi: 10.1111/mmi.15353
Authors: James A. Imlay
Molecular oxygen, superoxide, and hydrogen peroxide are related oxidants that can each impair the growth of microorganisms. Strikingly, these species exhibit large differences in their abilities to cross biological membranes. This Perspective explains the basis of those differences, and it describes natural situations in which the permeability of membranes to oxidants determines the amount of stress that a bacterium experiences.
Molecular oxygen (O2), superoxide (O2
^−^), and hydrogen peroxide (H2O2) each have the capacity to disable enzymes, and when they do, they can block key metabolic pathways and suppress bacterial growth (Imlay 2013). Virtually all bacteria encounter these oxidants in some circumstances. Oxygen is present at various levels in natural environments, and even committed anaerobes confront it during transit to new habitats. Superoxide and H2O2 are routinely formed inside oxygen‐exposed cells when O2 adventitiously oxidizes redox enzymes, and these species can also be generated outside the cell by both biotic and abiotic processes. But to understand how these oxidants affect bacteria, it is essential to consider how easily each of these species can cross membranes. Important questions hang in the balance. Can cellular respiration shield cytoplasmic enzymes from oxygen? Will superoxide made by phagosomes penetrate into target bacteria? Does catalase protect the local community, or only those cells that contain it? Early thoughts about these questions were often incorrect, and they have been reconsidered in light of information about the barrier properties of biological membranes.
This report reviews the permeability of lipid bilayers to O2, O2
^−^, and H2O2. It describes how permeability was measured and how these values were validated in living cells. It explains why this property determines how cells experience oxidative stress and how they defend themselves against it.
Many bacteria respire oxygen at very high rates. A well‐fed
E. coli
cell consumes 3.3 mM cytoplasmic O2/s—which is a lot, given that 37°C air‐saturated water contains only 0.2 mM O2. Effectively, the cell consumes the equivalent of its total intracellular O2 every 60 ms. In hypoxic environments, where the level of dissolved O2 might be 20‐fold lower, fewer than 5 ms would be required to exhaust the cellular oxygen content. It seems intuitively obvious, then, that respiration must lower the intracellular O2 concentration below what is outside the cell.
But intuition lies. Molecular oxygen is extremely small—diatomic!—and utterly nonpolar. It slides fluidly through membranes. In fact, its solubility in membranes exceeds that in water, and the experience of an O2 molecule as it approaches a lipid bilayer would be to suddenly whisk forward as the resistance of its solvent diminishes when O2 enters the membrane. Lipid bilayers are not a diffusion barrier to oxygen.
Membrane permeability coefficients effectively describe the likelihood that a solute will enter and cross a membrane rather than bounce off. The membrane permeability coefficient of molecular oxygen has been determined to be 40–120 cm/s^−1^, depending upon the lipid bilayer composition and protein content (Ligeza et al. 1998; Subczynski et al. 1989; Moller et al. 2019). The low end of the range coincides with elevated protein content. This value is very high. Using it, plus measurements of oxygen consumption by well‐fed E. coli , one can calculate the difference in oxygen concentration between the external and internal environments (Appendix A1). The upshot is that the intracellular level is virtually equivalent to that outside the cell (Figure 1A). Molecular oxygen equilibrates across the membrane orders of magnitude more quickly than the respiratory chain consumes it.

This result has been demonstrated experimentally. Becker et al. monitored the dose of oxygen that was needed to inactivate
E. coli
Fnr, a transcription factor whose iron–sulfur cluster reacts directly with O2. They observed that the inactivation threshold was not lowered by mutations that abolished respiration—proving that respiration had no impact on the cytoplasmic level of oxygen (Becker et al. 1996).
In a different study, the respiration rate of intact cells was observed to be half‐maximal when external oxygen was 2 μM—the same value as the apparent KM of the respiratory chain in inverted vesicles, with outward‐facing cytochrome oxidase. The implication was that even at low oxygen levels, the intracellular and extracellular concentrations are the same (Imlay and Fridovich 1991).
Due to its high membrane permeability, oxygen need not be actively transported into cells, avoiding what would otherwise be a substantial energetic cost. On the other hand, the absence of active transport means that, unlike other growth substrates, oxygen cannot be concentrated inside cells. This situation poses a particular challenge for microbes that live in low‐oxygen environments and requires that oxygen‐using enzymes evolve an extraordinarily high affinity for their substrate.
E. coli
, for example, employs as its primary respiratory ubiquinol oxidase a cytochrome bo enzyme with a KM for oxygen of 6 μM. When oxygen levels fall lower still, the bacterium induces a bd oxidase with a KM of 0.3 μM (Mason et al. 2009). Enzymes typically struggle to tightly bind substrates that lack shape, polarity, and charge, but they succeed with oxygen by using the half‐filled d‐orbitals of iron and copper to pair with the O2 di‐radical (Naqui and Chance 1986). The same tactic is also used by other oxygen‐requiring proteins, from non‐heme iron oxygenases and hemoglobins to oxygen‐sensing transcription factors like Fnr and FixL. Such high binding constants—rare among other metabolic enzymes—also enable O2 to outcompete competitive inhibitors like hydrogen sulfide and nitric oxide, which are commonly produced in low‐oxygen environments by the metabolic schemes of neighboring anaerobes. Consequently, one ramification of O2 membrane permeability is that respiring organisms depend upon access to environmental iron and copper.
Aerobic respiration, of course, is a boon to bacterial energetics. However, the dark side of oxygen is that it and its partially reduced species can damage enzymes and poison metabolism. Molecular oxygen is especially toxic to select enzymes that play critical roles in anaerobic metabolism. Because oxygen itself is a di‐radical, it directly adducts glycyl‐radical enzymes that use radical chemistry to conduct specialized reactions; formate lyase (PFL) and NrdD‐type ribonucleotide reductase are prominent examples (Knappe et al. 1984; Sun et al. 1996). Molecular oxygen is also a sufficiently strong univalent oxidant that it can inactivate enzymes with low‐potential redox clusters, such as ferredoxin oxidoreductase (PFOR) and nitrogenase. Consequently, these enzymes can function only in hypoxic or anoxic cells. Organisms that evolved to dwell in oxic environments did so by replacing PFL and PFOR with pyruvate dehydrogenase, which has no oxygen‐sensitive features, and NrdD with oxygen‐resistant ribonucleotide reductases.
The especially interesting case is that of nitrogenase, an enzyme whose function—the assimilation of nitrogen atoms from N2—would in principle be as valuable to oxic cells as to anoxic ones. The aerobic bacterium Anabaena solved this problem. Its secret? Every tenth or so bacterium in a cell chain is differentiated into a heterocyst, a specialized nitrogenase‐containing cell. Each heterocyst is bounded by a thickened, waxy glycolipid layer that suppresses oxygen penetration (Walsby 2007). The heterocyst receives nutrients from adjacent cells in the chain, and with minimal oxygen influx, an active cytochrome bd oxidase drives the O2 concentration to sub‐micromolar levels. These concentrations are low enough to keep nitrogenase active. Heterocysts, then, are the exception that proves the normal lipid membranes are not barriers to oxygen.
Of course, the suggestion that respiration can create a protected, anoxic region is still true in the sense that the collective action of many respiring bacteria can lower the oxygen concentration within a shielded microhabitat into which oxygen has limited influx. This process enables facultative anaerobes to create local environments that permit obligate anaerobes to thrive in soil and gut (Espey 2013), and it may even be facilitated by the oxygen oxidoreductases or cytochrome bd oxidases that many of those obligate anaerobes carry (Forte et al. 2017). These niches require a size on the scale of many microns, and they are particularly enabled by biofilms, which block convective microcurrents. Diffusion is then the sole route of oxygen entry from nearby oxic regions. Diffusion times rise in accordance with the second power of distance; therefore, whereas diffusion across a membrane (10 nm) is virtually instantaneous, penetration into a hypoxic microhabitat (> 10 μm) is extremely slow (Espey 2013).
On a practical level, experimental protocols must accommodate the fact that laboratory cultures make themselves hypoxic if the cell density is high and oxygenation is slow. This effect has been nicely quantified with
E. coli
chemostat cultures (Alexeeva et al. 2002). In the author's laboratory, the phenotypes of oxidative stress are studied in cells that are vigorously shaken in flasks filled to occupy no more than 20% of the flask volume, at cell densities no higher than 0.1 OD600 (ca. 3 × 10^7^ cfu/mL). Growth studies begin at 0.005 OD600 so that cell behavior can be observed over several generations while cultures are air‐saturated. Oxygen saturation can be achieved at higher densities if air is directly bubbled through cultures. Phenotypes on agar plates are less We suppose that the liquid layer on the surface of plates is air‐saturated, but as microcolonies grow, that local oxygen concentration is expected to diminish. Using a lacZ transcriptional fusion to the tdc operon of
Salmonella typhimurium
, Charles Miller observed that these anoxically expressed genes were strongly induced only in the center of colonies (personal communication).
The oxygen‐producing reaction center of photosystem II arose in a world that was anoxic, and it is interesting to consider why this world‐changing evolutionary step was possible. The anaerobic metabolism of that era relied upon enzymes such as PFL, PFOR, and NrdD, which are acutely oxygen‐sensitive; would not the production of oxygen immediately poison the cell that first generated it? Actually, calculations show that even if molecular oxygen were generated in that novel bacterium at the same rate as in its contemporary cyanobacterial descendants, rapid efflux across the membrane would have kept cytoplasmic oxygen at such vanishingly low concentrations [ca. 25 nM (Kihara et al. 2014)] that glycyl‐radical enzymes would have remained fully functional (Appendix A2). It was only much later, after oxygen had accumulated in the environment, that evolution was tasked with developing defensive strategies. As detailed by Mrnjavac et al. (Mrnjavac et al. 2024), the first adaptation was not the appearance of cytochrome oxidases—which would have failed to shield planktonic cells—but the evolution of oxygen‐resistant isozymes or pathways.
In most aerobic organisms, the primary threat of oxygen is not that it will directly damage enzymes but that it will generate O2
^−^ and H2O2, reduced forms of oxygen that are more potent oxidants than O2 itself. These reactive oxygen species (ROS) are created when oxygen collides with the reduced flavins and metal centers of redox enzymes, precipitating electron transfer. Such reactions are adventitious and therefore occur in proportion to collision frequency—hence, in proportion to oxygen concentration. Most cells have evolved sufficient defenses that they can withstand the rate of ROS production that occurs in their native habitats, and they are poisoned when they are exposed to higher concentrations of oxygen. Conversely, microaerophiles are organisms that escape this threat by confining themselves to low‐oxygen niches. Interestingly, this term also fits human cells, which are exposed to lower concentrations of oxygen in situ due to the oxygen‐buffering effect of hemoglobin. Accordingly, primary cultures of mammalian cell lines often exhibit physiological defects and hypermutagenesis if they are grown outside of reduced‐oxygen incubators.
Lynch and Fridovich first noted that superoxide (O2
^−^) cannot penetrate membranes (Lynch and Fridovich 1978). The pKa of the species is 4.8, which means that at a cytoplasmic pH of 7.2, the species is protonated only 0.4% of the time; the remainder of the time, its charge precludes entry into the lipid bilayer. The permeability coefficient of the protonated form—HO2—was evaluated by testing the ability of external superoxide to reduce cytochrome c that was enclosed inside liposomes (Korshunov and Imlay 2002). The resultant value, 0.9 × 10^−3^ cm‐s^−1^, is close to that of H2O (3 × 10^−3^ cm‐s^−1^ (Fettiplace 1978)), which is of similar polarity and size. Notably, these values are 10,000‐fold lower than that of O2. The coefficient of the O2
^−^ anion was too low to measure (< 10^−7^ cm‐s^−1^ Figure 1B).
Superoxide stress then is effectively compartmentalized. Superoxide is routinely formed inside the oxic bacterial cytoplasm when oxygen oxidizes redox enzymes. This superoxide threatens other cytoplasmic enzymes that use solvent‐exposed [4Fe‐4S] clusters or Fe(II) moieties as prosthetic cofactors (Imlay 2013). Therefore, some superoxide dismutases must be located in the cytoplasm. A second group of superoxide dismutases, encoded by sodC, is found in the periplasms of many Gram‐negative bacteria. These enzymes scavenge superoxide that leaks from the outer face of the respiratory chain or superoxide that is made by environmental sources and that enters the periplasm through porins (Korshunov and Imlay 2006). Because superoxide cannot equilibrate across membranes, the presence of periplasmic SODs cannot compensate for the absence of cytoplasmic ones, and vice versa. Therefore, the existence of periplasmic SOD implies that there must be periplasmic or cell‐surface molecules that superoxide can attack. This is an intriguing The periplasm lacks iron‐cofactored enzymes of the types that superoxide is known to inactivate in the cytoplasm, meaning that a novel target of oxidation has thus far escaped detection.
E. coli
and Salmonella mutants lacking periplasmic SOD do not exhibit any obvious growth defects under routine culture conditions (Gort et al. 1999; Uzzau et al. 2002). However, the virulence of several bacteria, including the model pathogen
Salmonella typhimurium
, is diminished in sodC mutants that lack periplasmic SOD (De‐Groote et al. 1997). Salmonella shares with
E. coli
a housekeeping SodCII that is primarily expressed in the stationary phase, but it also has an auxiliary SodCI that is induced during infection. Data support the inference that SodCI is specialized to defend the bacterium against superoxide that is released by the macrophage NADPH oxidase (Golubeva and Slauch 2006). This oxidase sprays superoxide into the interior of the phagosome, the compartment in which engulfed bacteria are trapped. The projected concentration of superoxide is orders of magnitude higher than in the bacterial cytoplasm (Appendix A5.1). The phagosomal program also includes a drop in pH that can approach the pKa of superoxide—which raised the possibility that protonated HO2 might penetrate the bacterium and disable its cytoplasmic enzymes. However, kinetic modeling suggested that the rate of entry would be moderate (Korshunov and Imlay 2002), and subsequent genetic studies confirmed that the absence of SodC did not create disabling cytoplasmic stress during infection (Craig and Slauch 2009). Therefore, it seems more likely that phagosomal HO2 acts by directly damaging periplasmic biomolecules (Slauch 2011). Because HO2 is uncharged, it should be able to abstract electrons from periplasmic biomolecules with which O2
^−^, already an anion, cannot react. It has proven difficult to test this notion. Experimental systems have not yet produced superoxide in the quantity and duration that would replicate the dose to which bacteria are exposed in the phagosome. Consequently, the target of phagosomal superoxide remains one of the important mysteries in the fields of oxidative stress and cell‐based immunity.
A second route by which superoxide is weaponized is through the excretion of redox‐cycling antibiotics (Inbaraj and Chignell 2004; Turner and Messenger 1986). Walnut trees, for example, lace their leaves and seeds with juglone, a soluble quinone. When these leaves are dropped, juglone acts as an herbicide that kills undergrowth, helping seeds to find bare ground. Similarly, the lung pathogen
Pseudomonas aeruginosa
excretes pyocyanin, a redox‐active phenazine that may be involved in supporting respiration but that also can suppress the growth of competitors. In both cases, the antibiotic enters the interior of target cells and serves as a bridge that rapidly transfers electrons from redox enzymes to molecular oxygen. Internal O2
^−^ production can rise > 20‐fold above normal levels, overwhelming defenses and inactivating metabolic enzymes (Hassan and Fridovich 1979). Bacteria that produce such antibiotics are protected by dedicated drug‐export systems (Dietrich et al. 2008), and because superoxide cannot cross membranes, the superoxide that is generated in nearby target cells will never rebound to harm the drug producer.
Hydrogen peroxide has perhaps the most interesting membrane‐permeability behavior of the reactive oxygen species—and this feature has a substantial impact upon the biology of oxidative stress. Early work tended to assume that H2O2 flows “freely” across membranes, implying that intracellular and extracellular concentrations were equilibrated, as with O2. Indeed, one study of
E. coli
asserted that cytoplasmic catalase did not lower H2O2 levels inside the cell below that of the surrounding environment (Ma and Eaton 1992). The authors suggested that catalase serves a communal purpose in clearing H2O2 from the local habitat rather than from the specific cell.
This inference turned out to be wrong. The membrane permeability coefficient of hydrogen peroxide was determined by measuring the rate at which intracellular scavenging enzymes can clear H2O2 from cell medium, a situation in which H2O2 entry into the cell is the rate‐limiting step (Seaver and Imlay 2001b; Winterbourn et al. 2006). The value of 1.6 × 10^−3^ cm‐s^−1^ is similar to that of H2O and that of protonated superoxide (HO2). It is orders of magnitude lower than that of molecular oxygen, in keeping with the polarity of H2O2.
At the same time, the scavenging activity of cytoplasmic peroxidases such as AhpCF was found to be quite high (Seaver and Imlay 2001b; Parsonage et al. 2005). The upshot is that scavenging activity outstrips the rate of H2O2 flow into cells, so that an outside‐to‐inside gradient arises (Figure 1C). Using data from
E. coli
, one calculates that in an environment containing micromolar H2O2, the steady‐state H2O2 concentration in the cytoplasm may be 10‐fold lower (Imlay 2013) (Appendix A3). This effect was overlooked in the earlier studies because they had employed unnaturally high (millimolar) concentrations of H2O2 that inactivated the peroxidase system.
This conclusion has been verified in several ways. Notably, a scavenging‐proficient cell fails to protect a peroxidase/catalase mutant when they are cocultured (Seaver and Imlay 2001b). Were H2O2 to equilibrate between intracellular and extracellular environments, both cells would experience the same degree of internal H2O2 stress.
Extracellular hydrogen peroxide is generated in microbial habitats by a number of photochemistry, chemical reactions at anoxic interfaces, the metabolism of lactic acid bacteria, and the oxidative burst of phagocytes (Imlay 2018). Most microbes possess transcription factors in their cytoplasms, such as OxyR and PerR, whose role is to detect and respond to this H2O2 when it flows into the cell (Zheng et al. 1998; Sen and Imlay 2021). Experiments with
E. coli
indicate that 100–200 nM intracellular H2O2 is sufficient to activate its OxyR system (Aslund et al. 1999; Seaver and Imlay 2001b). This level of cytoplasmic H2O2 is reached when 3 micromolar H2O2 is provided in the growth medium (Li and Imlay 2018)—which is consistent with the idea that the combination of high scavenger activity and sluggish H2O2 movement across the membrane creates a > 10‐fold gradient of H2O2. The 3 micromolar value is near the upper range of H2O2 levels that have been observed in such diverse environments as streams, open waters, and the bloodstream (Forman et al. 2016; Morris et al. 2022). Microfluidic studies have shown that similar concentrations elicit stress responses in other bacteria as well (Padron et al. 2023).
Single‐cell experiments with microfluidics have nicely demonstrated that induced scavenging enzymes generate a strong transmembrane concentration gradient. When
E. coli
was exposed to a constant flow of 100 micromolar H2O2, genes controlled by OxyR were quickly and strongly induced—and then their expression subsided to a lower constant level (Lagage et al. 2022). As intracellular scavenging enzymes became abundant, the activity of OxyR diminished, despite the persistence of the extracellular dose.
Among the genes that are induced by OxyR are the scavenging enzymes AhpCF and catalase, as well as enzymes that protect iron and DNA (Sen and Imlay 2021). As AhpCF and catalase titers rise, the outside‐to‐inside gradient will become even steeper. Indeed, even though 0.3 μM intracellular H2O2 can be enough to poison biosynthetic pathways (Sobota et al. 2014),
E. coli
can continue to grow in minimal medium when the extracellular H2O2 rises as high as 10 micromolar (Li and Imlay 2018). In bacteria with higher activities of scavenging enzymes, the gradient—and tolerated levels of environmental H2O2—may be even greater.
This startling tolerance of the bacterium for H2O2 is underscored by the fact that OxyR even induces a cytochrome c peroxidase (Ccp) (Khademian and Imlay 2017) that exploits H2O2 as a growth substrate. Ccp is a membrane‐bound protein that catalyzes electron transfer from reduced respiratory quinones to H2O2, and it thereby allows the cell to employ H2O2 as a terminal electron acceptor for respiration. The Ccp active site is located on the periplasmic face of the membrane; this arrangement allows the internal scavenging enzymes to keep cytoplasmic H2O2 below bacteriostatic levels, while Ccp still has access to the higher H2O2 concentration in the periplasm. The KM for H2O2 of Ccp—5 micromolar—nicely fits the environmental H2O2 concentration that is needed to activate its inducer. Therefore, the barrier property of the membrane allows
E. coli
not only to tolerate H2O2 but also to thrive in it.
Is Unlikely to Kill Captive Bacteria
From this perspective, it is instructive to consider whether a bacterium is affected by the H2O2 that is formed in phagosomes during the oxidative burst. The dismutation of superoxide generates the H2O2. In macrophages, the H2O2 will rise to a steady‐state level that is limited by the fact that the H2O2 will steadily flow across membranes—not only into the captive bacterium but also out of the phagosome. In neutrophils, H2O2 production is faster, but the H2O2 is simultaneously consumed by myeloperoxidase. Labs have projected that the H2O2 levels rise no higher than 1–4 micromolar in macrophage phagosomes (Imlay 2009; Appendix A5.2) and 2 micromolar in neutrophil phagosomes (Winterbourn et al. 2006), which are well within the range that
E. coli
can tolerate. Higher concentrations would be achieved only if H2O2 were to accumulate in the regional tissue, as might be the case during chronic inflammation—a situation that would be suppressed if host cells scavenged the local H2O2. Hydrogen peroxide itself, then, seems unlikely to be a main bacteriocide in phagocytes. Its precursor superoxide and downstream product hypochlorous acid in neutrophils (Sultana and Dahl 2023) seem more likely to be the agents that kill bacteria.
Stress Primarily Stems From Media
Aerobic cells continuously generate internal H2O2 at a substantial ca. 15 μM/s in the model organism
E. coli
(Seaver and Imlay 2001b). Against this backdrop, one might wonder whether H2O2 influx from the environment comprises a significant additional threat. In fact, calculations (Appendix A4) show that 0.2 μM external H2O2 creates an influx equivalent to the pace of internal H2O2 production. Therefore, if cells enter an environment containing, say, 2 μM H2O2, the total H2O2 within the cell interior immediately rises tenfold. This situation is very pertinent to laboratory experiments because most sterile media contain at least this much H2O2, which is generated either by photochemistry under lab lights or by the chemical oxidation of sugars (Li and Imlay 2018). The stress is substantial enough that isolated colonies of *
E. coli oxyR* mutants cannot form when the cells are deposited on standard LB or glucose plates (Ezraty et al. 2014; Li and Imlay 2018). It turns out that every time workers streak wild‐type
E. coli
upon plates, the cells survive only because they induce this stress response. A similar effect has been documented when sterile LB is delivered to
Pseudomonas aeruginosa
in microfluidic chambers (Padron et al. 2023). In fact, the inability of some environmental bacteria to grow in lab media apparently derives from their inability to contend with the H2O2 that those media contain (Martin et al. 1976; Tanaka et al. 2014; Dione et al. 2016).
I close this article with the hydroxyl radical. It warrants mention because it is the most powerful of reactive oxygen species, reacting readily with virtually all biomolecules (Davies 2005). It is the oxygen species that can oxidize DNA and potentially kill cells, rather than merely inhibit their growth. Hydroxyl radicals are formed in biological systems by the Fenton reaction, in which cytoplasmic Fe(II) atoms transfer an electron to H2O2. The hydroxyl radical is tiny and uncharged, and in principle, it might be expected to cross membranes relatively freely. However, its reactivity—with nucleic acids, proteins, lipids, or anything else—is so great that it is believed to oxidize nearby biomolecules almost immediately at its site of formation (Chevion 1988; Imlay et al. 1988). Therefore, the destructive effects of hydroxyl radicals are focused upon iron‐rich compartments, and in particular upon biomolecules that bind iron. In most natural habitats, the environmental concentration of loose iron is low (Wandersman and Delepelaire 2004), and it seems doubtful that cell‐surface oxidation by hydroxyl radicals is a common event.
The membrane permeability of reactive oxygen species has a large imprint upon how cells cope with oxidative environments. Molecular oxygen equilibrates across membranes, superoxide barely crosses them at all, and hydrogen peroxide is somewhere in the middle. These distinctions have guided how cells defend themselves against them. Respiration does not make a cell hypoxic relative to its immediate environment, and so oxygen‐sensitive cells must protect themselves by seeking hypoxic habitats. Superoxide is an especially toxic compound that does not cross membranes, and so cells need to implant a superoxide dismutase or reductase in each cellular compartment in which it is formed. Hydrogen peroxide crosses membranes at a moderate pace. Cells can therefore be threatened by external H2O2—but they also can defend themselves by degrading it as quickly as it enters.
James A. Imlay: conceptualization, formal analysis, writing – original draft, writing – review and editing.