Hello Hadi:
I have seen another interpretation of the model of Farquhar et al, that is:
The steep part of the response of assimilation rate to p(CO2) follows the RuBP saturated kinetics of Rubisco, but the flat part is RuBP limited.
What is your opinion?
Thanks

The comments of the last year (7 July 04 to 7july 05) are removed to be condensed and posted at a later date. Brad has opened another line of interpretation of the model of Farquhar et al that may be more in line with the understanding of the model users. I would welcome more questions and comments on this direction and comparative analysis of the two models.
If interested in the comments before they are condensed and posted, please send your request to hadi@farazdaghi.com

PS. Due to some remarks from the viewers, the comments are included without change in a separate section on the site.

Hello Brad,
Thank you for your good question. This is a very short, simple, appealing, and dual-purpose description that can be used for both the single enzyme and the two-process models, and confusing in that respect. This description can be interpreted as carboxylation is limited by CO2 at low CO2, by RuBP supply at high CO2 and by Rubisco when both CO2 and RuBP are saturating, which is the definition of single enzyme models. This description does not expose the differences between the single enzyme, (for example Farazdaghi&Edwards 1988) and the two-limitation or two-process models of Farquhar et al. Von Caemmerer & Farquhar (1981) write:
“CO2 assimilation rate is governed by different processes at low and high intercellular p(CO2)….
Brad, the description given by you clearly indicates that Rubisco is involved in the steep part of the curve. Does it mean that the plateau of the curve is independent of Rubisco? If it is independent how does it gain the identity of photosynthesis. The two-process model writes:
A = min{We, Wc}
It means that assimilation is equal to the lesser of the two values, We, that is an empirical function of electron transport with a maximum of Jmax, and Wc, that is an enzymatic function of Rubisco reaction with CO2 and has a maximum of Vcmax. Surely, “Wc” and “We” must both be of the same nature, and necessarily photosynthesis, in order to choose between the two. In order for any entity in the C3-plant internal or external environment to become photosynthesis, it requires the possibility to pass through Rubisco. I would like to know how does “We” become photosynthesis without loosing its independence to Rubisco.
Let us face it Brad. There is no reflection of the two-process theory and model in this short, simple, and appealing description. Isn’t it confusing?
Farazdaghi & Edwards (1992) showed that consideration of two separate/independent processes with two unrelated single-factor equations is not valid for describing the two-substrate ordered reaction under a single enzyme, that is Rubisco. Similarly, Wullschlegger (1993) examined photosynthesis data of 109 C3-plant species and rejected the independence of Vcmax and Jmax that represent the two processes proposed by Farquhar et al. Leuning (1997) re-examined the data of Wullschlegger (1993) and introduced correction factors, for differences in temperature to the data. He confirmed the conclusions of Wullschlegger with a higher correlation coefficient. He noted that Jmax and Vcmax were strongly correlated, rejecting the independence of the two processes, which were the foundation of Farquhar et al model. The modelers did not acknowledge the problem, but later Ruuska et al (Ruuska, S.A., T.J. Andrews, M.R. Badger, G.S. Hudson, A. Laisk, G.D. Price, and S. von Caemmerer (1998). Functional Plant Biology, 25(6)867 column 2 ) wrote:
“Both (Vcmax and Jmax) can be calculated from steady-state photosynthesis measurements, and lately Wullschlegger (1993) and Leuning (1997) have studied these parameters extensively. J(…) can be calculated … Vcmax can be calculated from the transient CO2 assimilation values (…).”
To be continued.

Brad cont…
The above quote is from a small paragraph of Ruuska et al’s article.
It is a unique paragraph with two conflicting statements for the calculation of Vcmax, from “steady state” or “transitional” values, and a confusing statement in the middle. I try to be as conservative as possible, mainly because some of my colleagues consider that my criticisms of the “widely used model” may be offending to some users.

So, with my apologies to all, there is one question here. It is not clear, at least to me, which measurement is right for the calculation of Vcmax? Steady-state or transitional? Why should this question be raised at all? The authors have been presenting experimental evidence in support of the findings of Laisk 1985, that Michaelis-Menten applies only to the initial velocity of the reaction and the reaction is transitional. The experimental evidence clearly invalidates that the Rubisco-limited component of Farquhar et al model that uses Michaelis-Menten equation for steady state photosynthesis is invalid. Indeed Michaelis-Menten equation is invalid for steady-state reaction of any enzyme, no matter single or two-substrate. Why there is no mention of such conflicts of the theory and model of Farquhar et al with the experimental data of the authors? Why even von Caemmerer (2000) doesn’t mention the invalidation of this only “Mechanistic” component of the model? and…
Next, what is the message of the authors in mentioning the extensive studies of Wullschlegger and Leuning? Does it mean that their findings were in support of the Two-Process Theory or against it? Did their extensive studies yield to anything worthy of mentioning at all? Did the modelers do something with the results? If their results were irrelevant, then what was the reason for referring to them? Was it just an assurance to those who had not read the articles that there is no need to read them? Is this the right way of presenting scholarly work? Has this been peer-reviewed? Isn’t it confusing and misleading?..

Let us look at the assumption of the Two-Process model again. Collatz, Berry, Farquhar & Pierce (1990) write:
“Jc=min{We,Wc},…. We is proportional to I, and Wc (a function of the concentration of CO2 and the Vm of Rubisco) is independent of I.”

Unlike the previous case, or the simplistic but misleading definition that we discussed earlier, the description of Collatz et al is clear and differentiates between the two-process and the single-enzyme theory.
Let us examine the independence of Wc from I, first experimentally. Quick et al (Quick, WP, K. Fichtner, E.D.Schulze, R.Wendler, R.C.Leegood, H.Mooney, S.R.Rodermel, L.Rogorad, M.Stitt. Planta(1992):188:522-531 Fig3A-C) demonstrate that consistent with single-enzyme theory, the rates of CO2 fixation for any Rubisco content Changes with irradiance, I. This is a clear evidence that variations in Wc is dependent on I, and the basic assumption of the theory of Farquhar et al for the existence of two independent processes is invalid.
To be continued.

Brad cont.
Quick et al (1992) showed clearly that “the rate of CO2 fixation was affected by short term changes in irradiance”. These results are in CONTRAST with the description of Collatz et al that: “Wc (a function of the concentration of CO2 and the Vm of Rubisco) is independent of I.”
In their description of the two-process theory, Farquhar, von Caemmerer & Berry (1980) state that the equation of Vc=min{Wc, We} “will emerge as a limiting case of perfect coupling of photochemical cycle with the other two” (PCR and PCO cycles). Again, if the reaction of Rubisco with photochemical cycle for RuBP regeneration can be defined by two independent processes with “perfect coupling”, then there must be a “perfect fit” of the experimental data of “multiple I and CO2” curves, as defined by the authors.

An examination of the model (see Fig.3 of the text), with multiple datasets of Ogren &Evans (1993) demonstrated that a systematic departure (underestimation) of modeled curve from experimental data occurs as the level of photosynthesis increases. The results can hardly meet the expectation of a “perfect coupling” given by Farquhar et al (1980). However, they are in line with the observations made from the data of Quick et al (1992).
In order to verify the above findings further, an examination was made of the original validation documents of von Caemmerer & Farquhar (1981). The physical data and their modeled curve were located in two different graphs (Fig.1a and 1b of the authors), which made their visual comparison difficult. The figure contains two sets of photosynthesis data for different CO2 concentrations, at two high radiation levels (950 and 1400 µmol quanta/m2/s). The data were extracted from the graph and compared with a simulation of the model based on the instruction of the authors. Dr. von Caemmerer provided the information for CO2 compensation concentration due to photorespiration (personal communication). The results were in line with previous findings, i.e. underestimation at higher CO2 and radiation levels. Such differences may not easily catch the eye, when placed in separate figures.
To verify that the problem is a systematic one, an examination was made of another set of data given by von Caemmerer (2000). This one provided the responses to CO2 at 3 radiation levels. Here again, the experimental data and the simulated curves are placed in two different figures (p54, Fig.2.18 &p.55, Fig.2.19) and drawn in different scales. This time, as an alternative method, the two figures were scanned, brought to the same scale and superimposed, all electronically.
The results confirmed that the two-process model could not provide reasonable estimates of integrated photosynthesis, and produces a systematic underestimation at higher CO2 and radiation. We observe that there is no “perfect coupling” of the two processes and no perfect fit. A perfect fit does not need any curvature or convexity factor.
To date, I have not seen an “Integrated Dataset” that can be supported by the two-process model.
To be continued.

Brad Cont.
This has become a long comment on a short, appealing, but incomplete and thus misleading description.

The description is based on the incorrect assumption of the validity of Michaelis-Menten model for RuBP saturated steady-state rate reaction of Rubisco.

This assumption is incorrect theoretically, at least because of the order of reactions and the irreversibility of the carboxylation step; and experimentally, as shown by several experiments by Laisk and his colleagues, and Ruuska et al (1998), which include Dr. von Caemmerer among the authors. We also provided both theoretical and experimental evidence (Farazdaghi & Edwards 1992) that the steady state maximum rate of carboxylation, Vmax (in-vivo), cannot exceed ˝ of its transitional (in-vitro) Vcmax. This was a significant evidence for invalidity of Farquhar et al model.

Yet, despite the theoretical and experimental evidence against Rubisco-limited theory, the modelers have insisted in providing indirect evidences for the validity of their theory, including Contradicting Interpretations from experiments with transgenic plants.
So, let us summarize the arguments for and against the two-process model again.

The Two-Process Theory of Farquhar et al:
• FvC&B abandoned “approaches based on the kinetics of a single enzyme.” (Collatz et al 1990),
• FvC&B considered that “CO2 assimilation rate is governed by different processes at low and high intercellular p(CO2)…
• (A) Assimilation rate is limited by the RuP2 saturated rate of RuP2 carboxylase-oxygenase at low intercellular p(CO2) and
• (B) By the rate allowed by RuP2 regeneration capacity at high intercellular p(CO2).” von Caemmerer & Farquhar (1981).

Why the Theory of Farquhar et al is Flawed:
• The Liebig Law of Minimum, and its expansion as Blackman law Require that:
• 1) Under any given condition only one factor can be limiting, thus either
a): RuBP-saturated Rubisco, or
b): CO2.
• 2) When a factor is limiting the rate of reaction does not increase unless by increasing the supply of that factor.
• If RuBP-saturated Rubisco is limiting at CO2=G*, Assimilation Rate will remain Zero at all levels of CO2. The logical inference of this is that life cannot be supported on the planet. Obviously then, something is seriously wrong with the theory.
• Carboxylation is a single enzyme process of an ORDERED reaction of Rubisco with RuBP binding First, producing enediol, and CO2 binding Next with enediol.
• When the reaction rate increases with CO2, CO2 is the limiting the gas exchange and enediol is not limiting.
• At CO2 saturation, enediol is limiting.
• A limitation of enediol represents limitations of either RuP2 Supply or Rubisco, BOTH at CO2 saturation.
• Rubisco is the Final Limit. A Limitation of RuBP-saturated Rubisco at low CO2 is Logically Impossible and Experimentally Unattainable.

It is of interest to note that, consistent with the single-enzyme theory, the hierarchy of limitations is in the opposite direction of the hierarchy of the order of reactions. The order of Farquhar et al model is in conflict with the order of reaction.

I will continue this thread later.

Brad cont…
As mentioned before, Ruuska et al (1998) provided a clarification in the abstract of their article that Rubisco-Limited = RuBP-Saturated. As I have previously pointed out, this description, without a reference to the concentration of CO2, would be unclear, incomplete, and confusing.
In my personal communications with one of the senior scientists of the two-process school, he has expressed his view of the theory of Farquhar et al as:
“The "rubisco" limitation can also be called the RuBP-saturated situation. It often happens at low CO2 since under these conditions rubisco cannot use the RuBP as fast as when CO2 is high.”
This, I assume, is perhaps one of the best definitions of the two-process theory from the view-point of a non-mathematical plant physiologist. To analyze this definition, I would suggest first, to put the orders right. Farquhar et al started with RuBP-saturated Rubisco at low CO2 and called it Rubisco limitation. Let’s start from here. If we go step by step everything will be very clear. We should make sure that we do not jump or miss steps.
1- Carboxylation is a two-substrate ordered reaction, in which RuBP binds first with Rubisco to form enediol.
2- When RuBP is saturating Rubisco, enediol is at its maximum level and not limiting.
3- If enediol is not limiting, the rate of reaction at low CO2 is CO2-limited and should increase with increasing CO2 concentration (as it does).
4- When the response to CO2 stops, enediol will be limiting (the plateau of the curve).
5- A limitation of enediol is the result of a limitation in EITHER Rubisco OR RuBP.
Therefore it is quite simple and clear that:
AT LOW CO2, RuBP is saturating Rubisco, enediol is not limiting and CO2 is the limiting factor, not Rubisco. RuBP is just a co-factor that prepares the enzyme for the reaction with CO2. In gas exchange, the limitations of enzyme and RuBP are inseparable and cannot be readily distinguished. At high CO2, limitation is shifted to enediol, i.e. either RuBP or Rubisco.
The source of confusion is “rubisco cannot use the RuBP as fast“. In my view, carboxylation is the rate of consumption of CO2 not RuBP.

The theory of Farquhar et al predicts a limitation of enediol at low CO2, because Rubisco is limiting, and again at high CO2 because RuBP is limiting, thus no change in the rate of photosynthesis in either case. Therefore, if the rate of photosynthesis stops at CO2 compensation point, there would be no net photosynthesis at any CO2 level above this point. If so, how this model can be used for the estimations of CO2 exchange of ecosystems, global carbon cycle and global warming?

The theory of Farquhar et al is very selective for the definition of limitation. The definition changes as photosynthesis moves from the steep part of the response curve to the flat part. When enediol is limiting at “low CO2” (because of the limitation of Rubisco), the rate of carboxylation increases; but when enediol becomes limiting at high CO2 (because of the limitation of RuBP regeneration), the rate of carboxylation stops.

This model cannot be expected to provide a mechanistic basis for the genetic manipulation of plants, life in space, global warming, environmental change, agricultural production and earth’s biota.

The theory of C3 photosynthesis is extended with more emphasis on the nature of carboxylase-oxygenase. The details of this revision will appear shortly.

Dear Hadi;
I saw an article by Don Jewett in The Scientist the other day (Don L. Jewett The Scientist. Volume 19 | Issue 21 | Page 10 | Nov. 7, 2005 http://www.the-scientist.co...) that, in my view, can describe the situation in our field very well, particularly the Langmuir's idea of "Pathological Science". Do you agree with that?
regards

Where is the beef?
Hi Hadi, I saw your article a year ago and said to myself, well, this is another theory, let us see what happens.
A month ago my search brought me to your comment page. It was striking. Your biochemical explanation worked like a miracle for me. Now I can see why the rubisco-limited theory of Farquhar et al is incorrect. There is no photosynthesis. where is the beef?
However, the model of Farquhar et al is used in preference to any other model everywhere. They should have a hard look at what they are doing.

Hi Sergio:
Thank you for the reference. It is very interesting. with regards to your comparison, perhaps if it looks like a duck, walks like a duck, and sounds like a duck you may expect to call it a duck.
thanks anyway.

Hi Todd:
Thanks for your remaks. Glad to hear that you understand the model.
good luck

Hi Hadi,
I have not seen any written response from the senior users or developers of the model of Farquhar et al regarding your model. Don't you think that they should have given some response? Do you know of any relevant published remark? It will be interesting to know their response if you have had any direct communication.
Regards
Edwin.

Hi Edwin;
Thank you for your question. In the archived comments section you will find some of the remarks that I have received and I have reported them anonymously.

My other direct contacts and feedbacks have been from a presentation that I had in Gordon Research Conference on CO2 Assimilation in Plants: Genome to Biome in September 2005 ( S4-P37 at http://www.grc.uri.edu/prog... ), where as you can see from the participants many leaders of the research community in CO2 assimilation were present, including Suzanne von Caemmerer as Co-chair of the conference.

You may know that GRC is a small gathering of about 100 researchers, some with their graduate students. It is usually held in a remote area to have the opportunity for an intense, and face to face frank discussion of the subject area. Participation is by invitation only, and to encourage new ideas and frank dialogues, the contents of the discussions and remarks are not quoted after the conference, particularly if somebody has made a “foolish” comment.

My presentation was an extended version of the model that has been posted in this site, plus a critique of both the theory and the model of Farquhar et al. Both areas were discussed in detail individually or in groups, and of course with Dr. von Caemmerer and some of her colleagues, and also in the general session.

To make sure that I am fully observing the confidentiality policy of GRC, I can only say that I did not receive any disagreement with my analysis of the model of Farquhar et al.

I don’t know of any published comments concerning my theory to date. However, considering that the authors of theory of the two-process model and their colleagues responded very strongly (Collatz et al 1990, Plant Cell and Environment, 13, 219-225) shortly after the publication of the previous version of the model given by Farazdaghi & Edwards (1988a,b), I don’t think their lack of response could be blamed on their shyness or ignorance.

The big problem now is PhD and research students; research grants, and a large number of projects in agriculture, genetic engineering, global carbon cycle, global warming, climate change, ecological and environmental modeling, and ….., all of which are based on the component of Rubisco reaction and photosynthesis of Farquhar, von Caemmerer and Berry (1980).
As the problem won’t go away by itself, the best policy in my view is to accept it, correct it, and move on.

On April 28, one of the readers, Gord, sent me the following email:
…. Do you know that the international computer service of BNL-DOE-UIUC for simulation of Farquhar model of C3-Photosynthesis has stopped? If it were because of the model they could have kept the service and only change the model. Your model has been under full inspection, inside and out, by our department of mathematics too.
However, your model does not include a temperature function. Do you have any particular preference?

Hi Gord,
Thanks for the mail, you had three points:

a- I inquired about the service on May 2nd as I wanted also to make some comparisons with new sets of data. I received a reply on May 8, 2006, from “FACE photosynthesis” that “Unfortunately, this service is no longer available.”

b- The more inspection the better. This is exactly the reason that I have made the pre-publication copy of my work available for inspection and comments.

c- I think that the effect of temperature on biochemical reactions is to a large extent clear. But Rubisco is much more complex as it reacts with both CO2 and O2, plus a number of side reactions and interactions with Light and CO2 for activation by Rubisco activase and carbamylation with CO2.
I do not have a particular preference.

However, my observation is that the model of Bernacchi et al (2001) provides good fit according to the paper. But I see a number of points with regards to the structure of model.

1) The authors have totally left, what I call fictitious Jmax, out of the model. This is in my view a positive point as the maximum rate of CO2 assimilation at light saturation is rarely dependent on Calvin cycle capacity for regeneration of RuBP. This makes the model distinguished from those other ones that go into the detailed biochemical characteristics of this invisible character. But there are two other points that are not so positive.

2) They use a Michaelis-Menten type model with one competitive substrate inhibition that is developed by Haldane (1930) and call it Farquhar et al (1980) model. They should have been more accurate. Farquhar et al model is the collection of two equations, one of which a Michaelis-Menten type model for CO2 in competition with O2, and another one an electron transport equation with a maximum of Jmax; and these two equations are bridged by a convexity factor. Therefore, a Michaelis-Menten equation by itself is just Michaelis-Menten model not Farquhar et al model. Furthermore, Michaelis-Menten equation is not an Enzyme-Limited model, thus it is highly inaccurate to attach a "Rubisco-Limited" title to this equation. The limitation of enzyme, when limiting, is always reflected at the plateau of the response curve.

3) The model is based on “the generic responses of the six parameters Vcmax, Vomax, Gamma* (G*), Ko, Kc and Rd”.

However, G* is by itself a hybrid quantity, not a constant parameter.

G*= [(Vomax.Kc)/(Vcmax.Ko)].O

G* is the concentration of CO2 at which the rate of CO2 assimilation is equal to the rate of CO2 production through oxygenation. Therefore, G* by itself includes the effects of all the kinetic parameters plus the influence of temperature on the solubilities of both CO2 and O2.
Such interdependencies in variables cannot be allowed in mathematical or biochemical modeling based on regression.
This was mainly for you to watch in your choice of a temperature function.

If you are interested to participate in the discussion on Farquhar, von Caemmerer and Berry model at ECOPHYS discussion forum you can visit
http://www.nrri.umn.edu/eco...
and select ECOPHYS discussion forum.

There has been a discussion about the validity of the theory and model of Farquhar et al the result of which is summarized below.

Major deficiencies of the biochemical model of Farquhar, von Caemmerer and Berry (1980) and its defense by Collatz, Berry, Farquhar & Pierce (1990):

The model of Farquhar et al assumes that, the steady state carboxylation rate is limited by two independent processes: The capacity of RuBP saturated Rubisco at low CO2 and the capacity of RuBP regeneration at high CO2. A Michaelis-Menten equation with respect to CO2 is used for the Rubisco-limited reaction with a maximum of Vcmax (Rubisco capacity), and an asymptotic equation with respect to radiation for RuBP regeneration limitation with a maximum of Jmax.

In my view, under steady state conditions, Michaelis-Menten equation is not applicable; RuBP that is used is regenerated and the energy that is used is for RuBP regeneration is a fraction of the total energy used in Calvin cycle, i.e. 9ATP/(28ATP+18NADPH), (see Farazdaghi & Edwards 1988). Therefore, neither this small fraction of energy can become dominant and limiting, nor the total energy used in the Calvin cycle can be attributed to RuBP regeneration, which disregards net CO2 fixation.

A brief summary of the contradictions and deficiencies of the theory and model of Farquhar et al for the Rubisco-limited and RuBP-regeneration-limited components of the model is given as follows:

A: The Rubisco-Limited component:
1) The theory is incorrect. The Rubisco-limited assumption of the theory of Farquhar et al at CO2 compensation point means that, according to Blackman law, photosynthesis will not increase by any other factor except by increasing the Rubisco level. As the amount of Rubisco is constant, according, net photosynthesis remains zero and will nor change at any higher CO2. This is obviously incorrect, as it does not support higher life on this planet. The concept of enzyme limitation at low substrate is contrary to the principles of Michaelis-Menten and enzyme kinetics, because the limitation of enzyme appears at the plateau of the curve through the maximum enzyme capacity (Vcmax).

2) The application of the limitation law by Farquhar et al is selective. According to Blackman law, when a factor is limiting the rate of reaction stops and it will not change unless by increasing the amount of limiting factor. In Farquhar et al model:
a) When Rubisco is limiting, assimilation rate increases with increasing CO2 concentration.
b) When RuBP regeneration is limiting, the rate of reaction stops at plateau of the photosynthesis response curve.

The two conditions for limitation described in “a” and “b” are contradictory to each other; the first one is against Blackman law, and the second one is consistent with the law.

3) The model uses Michaelis-Menten equation for steady state Rubisco-limited reaction. There are two types of inconsistencies with enzyme kinetics in this assumption:
a) Michaelis-Menten model is not compatible with enzyme limitation at low substrate and the authors should invent a compatible model for their theory.

b) Michaelis-Menten equation is only applicable to the initial velocities of the transitional state of CO2-limited reaction not to the steady state reaction.

Major deficiencies of the model of Farquhar et al continued…

4) Laisk (1985) experimentally demonstrated that the steady state velocity of Rubisco reaction does not follow Michaelis-Menten equation and its maximum rate is 30% to 40% of the maximum velocity of the transitional reaction. This evidence was ignored by Farquhar et al and the other promoters of the model.

5) Farazdaghi & Edwards (1992) also provided both theoretical and experimental evidence that the steady state maximum rate of carboxylation, Vmax (in-vivo), cannot exceed ˝ of its transitional (in-vitro) Vcmax. This was a significant evidence for the invalidity of Farquhar et al model. This evidence was also ignored by the modelers and their associates.

6- von Caemmerer et al (1994) found that there was a difference between the shapes of the CO2 response curves of transgenic tobacco plants with reduced Rubisco that followed Michaelis-Menten curve, and the wild type plants whose response curve deviated from that of Michaelis-Menten. Von Caemmerer (2000) writes:

“This provides unequivocal evidence that the CO2 assimilation rates at high CO2 partial pressures and high light are limited by the supply of RuBP.” They have concluded that when RuBP is not limiting, the response curve should follow Michaelis-Menten equation and the reaction would be Rubisco-limited. This firm conclusion by modelers that was based on the interpretation from the theory of Farquhar et al brought acceptability to both the theory and the conclusion. In my view, this has misled other researchers and delayed exploring the real reasons for this anomaly.

7- Ruuska et al (1998), which included Laisk and von Caemmerer among the authors, repeated (in part) the experiments of Laisk (1985) and showed that, for wild type plants, only the transitional rate of Rubisco reaction followed Michaelis-Menten equation, and its steady state velocity deviated sharply from the Michaelis-Menten curve at less that 50% of Vcmax. This was consistent with the previous findings of Laisk (1985) and Farazdaghi & Edwards (1992). Farquhar et al chose to ignore this finding too.

B: Limitations of energy or electron transport for RuBP regeneration:

Farquhar et al assume that at the plateau of A/Ci curve, RuBP Regeneration limits photosynthesis and consider that, a hypothetical entity, Jmax, limits RuBP regeneration.
1- Contrary to their theory, Farquhar et al use an equation that includes the total energy used in TP pathway, RuBP production and activation of Rubisco, not the component of energy used in RuBP regeneration. This loose treatment of limitation creates a disparity between the theory and the model that has been confusing some researchers. On the basis of the theory, Harrisson et al (1998) and thereafter Christine Raines and her associates, rightly, searched for a limiting factor in the RuBP regeneration pathway. They showed that positive or negative changes in SBPase, an enzyme of the RuBP regeneration pathway, produced similar responses in photosynthesis, which made this enzyme a possible candidate for consideration as Jmax. However, if SBPase is accepted as the controller of Jmax, then the energy used for its activation and reaction is far less and cannot match the total energy that is used in the equation of Farquhar et al or von Caemmerer (2000) for RuBP regeneration.

2- Collatz et al (1990) excluded Jmax from their equation for electron transport requirements of RuBP regeneration and used a linear function for electron transport. However, the quantum requirement of the model is not limited to that of RuBP regeneration.

3- Evans & Farquhar (1991) used the equation for “Mehler reaction” as their model of choice for electron transport with a plateau of Jmax. But, Ruuska et al (2000 Journal of Experimental Botany 51, 357-368.) announced that there was “little evidence for Mehler reaction”. Heber (2002, Photosynthesis Research 73: 223–231) confirmed this for C3 photosynthesis. These evidences indicated that the modeling efforts of Evans and Farquhar (1991) did not help settle the problems of the second process in Farquhar et al model.

4- Wullschleger (1993) analyzed the data of carboxylation of 109 C3 species and found that contrary to the assumption of Farquhar, von Caemmerer & Berry (1980), Jmax and Vcmax are not independent parameters. This was in conflict with the independence of the two processes of Farquhar et al, which was defended very strongly by Collatz et al (1990). A unique explanation was advanced by the modelers, that both Vcmax and Jmax must be controlled by a third factor. But they never attempted to verify this hypothesis experimentally or theoretically. Instead they considered Jmax as a constant proportion of Vcmax.

5- In search of Jmax, Price et al (1995) considered GAPDH (glyceraldehydes-3-phosphate dehydrogenase), the enzyme for triose-phosphate pathway, was the Jmax. This is one step before the RuBP regeneration, but does it matter?

6- The existence of Jmax was so obvious to Lloyd et al (1995) that based on Farquhar & von Caemmerer (1992), they provided an equation for variations of Jmax with temperature, which included the “energy of activation” for this unknown and obscure parameter.