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the Creative Commons Attribution 4.0 License.
| 15 Jul 2024
An elucidatory model of oxygen’s partial pressure inside substomatal cavities
Abstract. A parsimonious model based on Dalton’s law reveals substomatal cavities to be dilute in oxygen (O2), despite photosynthetic O2 production. Transpiration elevates the partial pressure of water vapour but counteractively depresses those of dry air’s components – proportionally including O2 – preserving cavity pressurization that is negligible as regards air composition. Suppression of O2 by humidification overwhelms photosynthetic enrichment, reducing the O2 molar fraction inside cool/warm leaves by hundreds/thousands of ppm. This elucidates the mechanisms that realize O2 transport: diffusion cannot account for up-gradient conveyance of O2 from dilute cavities, through stomata to the more aerobic atmosphere. Rather, leaf O2 emissions depend on non-diffusive transport via mass flow in the form of “stomatal jets” forced by cavity pressurization, which is not negligible in the context of driving viscous flow. Jet expulsion overcomes massive inward O2 diffusion to force net O2 emission. At very high leaf temperatures, jets also influence transport of water vapour and carbon dioxide, physically decoupling their exchanges and reducing water-use efficiency, independent of stomatal regulation.
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RC1: 'Comment on egusphere-2024-1966', Anonymous Referee #1, 08 Sep 2024
This manuscript presents a theoretical, physically based model to explain the possible occurrence of non-diffusive exchange of gases between plant leaves and the atmosphere. The approach is founded in fluid dynamics and makes some simple assumptions in arguing that plant physiologists have been incorrect in their treatment of gas exchange processes. The article is really more like an opinion piece in the way it’s written, starting from the first sentence of the introduction. If the author wants to develop a dialog, a more moderate tone might help.
The paper could be improved by starting with a clear statement of the evidence that there is a potential mistake in the conceptual framework underpinning leaf gas exchange, specifically the assumption that stomatal fluxes are always diffusive. The broad context of the “decoupling” of photosynthesis and transpiration is a widely observed phenomenon especially in response to heat waves. The author has developed a possible physical explanation for this observation. The paper could also be improved by clarifying a number of issues as described below.
Specific comments
L9. “preserving cavity pressurization that is negligible as regards air composition.” This part of the sentence could be a separate sentence because the total cavity pressure is an important and separate consideration from the partial pressures. Indeed, cavity pressurization caused by transpiration appears to be the main mechanism for O2 emissions, according to the theory.
L10. Change “suppression” to “dilution”
L 59, It is confusing to say that cavity pressurization can be neglected, because in the abstract it is implied that cavity pressurization is not negligible.
L 90, here we see that pressurization is negligible but non non-zero…
L 108-110, I am not convinced that the substomatal cavity is dilute in O2. Inward diffusion will offset the vapor effects. It would be nice to see some evidence for this theory, such as in the isotopic composition of O2 or CO2 that might be altered in the process of biosphere-atmosphere exchange.
L 134-135, It is hard to understand this sentence “If these increases in water vapour transport rates seem modest, versus what can be achieved by diffusion alone, they grow in importance when considered in combination with jet suppression 135 of photosynthesis.”? Until one reads L 137-139. This is another example of how the paper could be improved by putting the problem statement before the solution, instead of vice-versa.
L 144-145, It seems unnecessary to “cast doubt on the very meaning of stomatal conductance.” Certainly the concept is useful, as is the concept of hydraulic conductance as it pertains to water flow through porous media, where both diffusion and mass flow occur.
Citation: https://doi.org/10.5194/egusphere-2024-1966-RC1 -
AC1: 'Reply on RC1', Andrew Kowalski, 13 Sep 2024
I thank the anonymous referee for this constructive assessment of the manuscript, since several of the comments have enabled me to propose revisions that should improve clarity. The comments are repeated below in italicized font, followed by my replies in normal font.
This manuscript presents a theoretical, physically based model to explain the possible occurrence of nondiffusive exchange of gases between plant leaves and the atmosphere. The approach is founded in fluid dynamics and makes some simple assumptions in arguing that plant physiologists have been incorrect in their treatment of gas exchange processes. The article is really more like an opinion piece in the way it’s written, starting from the first sentence of the introduction. If the author wants to develop a dialog, a more moderate tone might help.
For decades now, reviewers have admonished me regarding the "tone" of my writing. Clearly it is a defect, and one that I have worked to improve, but apparently without great success. I am very much open to any specific suggestions that would improve the tone without changing the scientific meaning.
The paper could be improved by starting with a clear statement of the evidence that there is a potential mistake in the conceptual framework underpinning leaf gas exchange, specifically the assumption that stomatal fluxes are always diffusive. The broad context of the “decoupling” of photosynthesis and transpiration is a widely observed phenomenon especially in response to heat waves. The author has developed a possible physical explanation for this observation. The paper could also be improved by clarifying a number of issues as described below.
The introduction section, a lone paragraph of just four sentences, is intented as "a clear statement of the evidence that there is a potential mistake in the conceptual framework underpinning leaf gas exchange, specifically the assumption that stomatal fluxes are always diffusive." I have no doubt that other authors could state it more clearly, but have done my best in this regard.
Specific comments
L9. “preserving cavity pressurization that is negligible as regards air composition.” This part of the sentence could be a separate sentence because the total cavity pressure is an important and separate consideration from the partial pressures. Indeed, cavity pressurization caused by transpiration appears to be the main mechanism for oxygen emissions, according to the theory.Total cavity pressure is not separate consideration from the partial pressures, but rather directly linked via Dalton's law. This is the very basis of my analysis as reflected by the fact that it is mentioned in the first sentence of the manuscript.
L10. Change “suppression” to “dilution”
There are two processes that lead to depression of oxygen. Dilution is certainly one, but the other is displacement. Perhaps an examination of a stomatal cavity in light of the Ideal Gas Law will clarify this.
Consider a cavity of constant volume, and for simplicity at constant temperature, with an initial pressure (p1) and containing n1 moles of air. If transpiration adds a single water vapour molecule to the cavity, then some other molecule (very probably nitrogen) must exit, since n2>n1 implies pressurization (p2>p1) via the Ideal Gas Law, driving outward flow until pressurization is exhausted. Ultimately, the cavity is both enriched in water vapour and depleted in nitrogen, which will then tend to diffuse back inward while water vapour diffuses outward.
Now if we repeat this experiment five times, statistically we can expect expulsion of four nitrogen and one oxygen molecules. Oxygen is both diluted and displaced by transpiration. Note that in steady-state conditions, nitrogen is displaced outward but diffuses inward, and the two transport mechanisms cancel out such that there is no net transport of nitrogen (except, perhaps, for legumes or other nitrogen-fixing plants; I am no expert on nitrogen uptake). The same argument could be made regarding oxygen, but then we must take into account photosynthetic enrichment.
If we repeat the experiment a million times, then things get interesting for the vital gases. Of the million displaced molecules:
- about 780,000 will be nitrogen;
- nearly 210,000 will be oxygen, far exceeding what photosynthesis can add;
- thousands will be water vapour, whose departures represent non-diffusive vapor transport because they were pushed out;
- hundreds will be carbon dioxide, whose depletion (and subsequent diffusion) are not due to photosynthesis.To me, it is clear that dilution is not the only process that reduces substomatal oxygen. Displacement also does so, implying non-diffusive transport. This is the point of the manuscript, and therefore I prefer not to change "suppression" to "dilution".
L 59, It is confusing to say that cavity pressurization can be neglected, because in the abstract it is implied that cavity pressurization is not negligible.
Context is very important. Clearly the same phenomenon can be negligible in one regard but not in another. For example, at 2 ppm methane plays a negligible role in determining the specific heat of air, but not in absorbing infrared ratiation.
The abstract says that cavity pressurization is "negligible as regards air composition" (line 11), but "not negligible in the context of driving viscous flow" (line 18; bold emphasis added in each case). To reduce confusion, I propose to modify the sentence mentioned at L 59 begins to specifically state that the context in which pressurization can be neglected is that of air composition, because it is about to be used in Eq. (7) to model the partial pressure of oxygen.
L 90, here we see that pressurization is negligible but non nonzero…
This is because the context of Table 1 is that of air composition, not dynamics. Again, to make this more clear, I propose to change the Table caption so that it begins with "Consequences of negligible stomatal-cavity pressurization regarding air composition."
L 108110, I am not convinced that the substomatal cavity is dilute in oxygen. Inward diffusion will offset the vapor effects. It would be nice to see some evidence for this theory, such as in the isotopic composition of oxygen or carbon dioxide that might be altered in the process of biosphereatmosphere exchange.
Substomatal cavities are dilute in oxygen because leaf gas emissions are dilute in oxygen. As I have written elsewhere in Copernicus open discussions (https://doi.org/10.5194/bg-2023-30-CC1), even with a modest evaporation rate and robust photosynthesis, less than 2% of the molecules emitted within substomatal cavities are oxygen (versus 21% in the atmosphere). (More than 98% are water vapour.) Thus, the combination of transpiration and photosynthesis results in dilution of stomatal cavities, driving inward oxygen diffusion.
Evidence of this in the isotopic composition of oxygen has long existed and is known as the "Dole effect", with tropospheric air richer in heavy oxygen than seawater (Dole, 1935). The massive inward diffusion of oxygen results in fractionation, with only the lightest oxygen molecules able to diffuse upstream against the jet and so be consumed by respiration within the stomatal cavity, leaving the atmopshere enriched in heavy oxygen. I did not include this in the paper because it seems likely to cause even more controversy.
Dole, M., 1935, The relative atomic weight of oxygen in water and in air, J. Chem. Phys., 4(4), 268-275.
L 134135, It is hard to understand this sentence “If these increases in water vapour transport rates seem modest, versus what can be achieved by diffusion alone, they grow in importance when considered in combination with jet suppression 135 of photosynthesis.”? Until one reads L 137139. This is another example of how the paper could be improved by putting the problem statement before the solution, instead of viceversa.
I generally appreciate suggestions to improve the structure of my writing, but in this case cannot understand the referee's meaning.
This section of the paper addresses the influence of jets on transport of carbon dioxide and water vapour. It has three paragraphs whose themes appear in the first sentence of each: the first (L 116) addresses carbon dioxide, the second water vapour (L 129), and the third their relative behaviour (L 137) including water-use efficiency and decoupling. The sentence cited by the referee, as the last in the paragraph about water vapour, is intended guide the flow of the text to the following paragraph.
Perhaps if the referee could clarify what is meant by "problem statement" and "solution", I could understand how to improve this section of the paper.
L 144145, It seems unnecessary to “cast doubt on the very meaning of stomatal conductance.” Certainly the concept is useful, as is the concept of hydraulic conductance as it pertains to water flow through porous media, where both diffusion and mass flow occur.
I disagree. Stomatal conductance describes diffusive fluxes as a function of concentration gradients, while hydraulic conductance describes non-diffusive fluxes as a function of pressurization. Physically, they are very dissimilar.
Physiologists often interpret stomatal conductance as meaning the degree to which stomata are open (e.g., Urban et al., 2017). Strictly speaking, however, it is a ratio of flux to concentration difference. In the diffusion-only paradigm, stomatal conductance for water vapour and carbon dioxide are coupled (via Graham's law), and covary with the degree of stomatal aperture. But non-diffusive transport, when not negligible, makes this not so. Within a stomatal aperture of fixed dimensions, a temperature increase to extreme values invalidates the paradigm, enhancing water vapour egress but inhibiting carbon dioxide ingress. This is best illustrated by the case of boiling (where the vapour pressure equals the total pressure, yielding a specific humidity of 100%). Gas exchange through the spout of a boiling tea kettle has nothing to do with diffusion:
- water vapour is the only gas present, and so cannot diffuse with no concentration gradient but has a large flux (infinite stomatal conductance) that is non-diffusive in nature (i.e., a jet);
- carbon dioxide cannot enter the kettle despite an enormous concentration gradient (zero stomatal conductance) because the jet is so strong that it cannot diffuse upstream.(Recall that boiling can be achieved, either by raising the temperature at constant pressure, or by lowering the pressure at constant temperature.)
When state conditions tend towards boiling, stomatal conductance for water vapour increases but this does not mean that the aperture has expanded, and stomatal conductance for carbon dioxide decreases but this does not imply that the aperture has contracted. I believe, therefore, that jet transport casts doubt on the meaning of stomatal conductance.
Urban, J., et al., 2017, Increase in leaf temperature opens stomata and decouples net photosynthesis from stomatal conductance in pinus taeda and populus deltoides nigra, J. Exp. Bot., 68, 1757-1767.
Citation: https://doi.org/10.5194/egusphere-2024-1966-AC1
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AC1: 'Reply on RC1', Andrew Kowalski, 13 Sep 2024
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RC2: 'Comment on egusphere-2024-1966', Anonymous Referee #2, 21 Sep 2024
I agree that the model of stomatal flux as exclusively diffusive is oversimplified; at times I’ve said that one person’s diffusion is another’s advection, and applying advective flux principles to stomata is likely to lead to new insights.
The parentheses aren’t needed in equations 1-3, and ‘mere trace’ should perhaps be quantified more explicitly, perhaps as greater than 0.9% (argon) or 0.4% (water, on average), because many peoples’ research careers depend on these key trace gases including CO2!
In equation 4, the delta implies a surplus or a deficit depending on direction (the text only states surplus)
54: This value still seems quite fast, even as an upper bound, but could be justified in more detail by explaining a bit more the contents of Kowalski 2017 as it applies to the present study
I’m having trouble fully following the paragraph on line 57. The difference is about 1 Pa, which isn’t much. Is the argument that, even with extreme parameter values there is little reason to believe that delta_p is approximately zero such that positive delta_e implies negative delta_p of the other gases?
I still find the evidence to be by omission: if O2 can’t leave stomatal cavities by diffusion, it must be ‘jets’. But what do these jets look like, how do they ‘burst’ and do other mechanisms like Bernoulli pumping cause the transport in practice? To me the major weakness is a lack of description of how the jets work, for lack of a better word, in practice and if fluid mechanical simulations, conceptual models, or studies of ‘bursting’ when stomata open (or the ‘thermostat’ model that Joe Berry described) would be most fruitful for better understanding stomatal dynamics going forward.
Citation: https://doi.org/10.5194/egusphere-2024-1966-RC2 - AC2: 'Reply on RC2', Andrew Kowalski, 25 Sep 2024
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