Francisco responses to Dr. Klein

Updated: Feb 3

“Research is to see what everybody has seen and to think what nobody has thought.”

– Albert Szent-Györyi, Nobel laureate

Dear Dr. Klein,

Below you will find two historical notes to let you know that my colleague and I embrace your academic hostility since we recognized that it’s a natural component of the paradigm shifting process. Also, I include my responses to your comments that attempt to ridicule our work.


Francisco Arencibia-Albite, Ph.D.

Historical notes on the process of paradigm shifting

  1. The Existence of atoms put forth by Austrian Physicist Ludwig Boltzmann (1844-1906).

Today the existence of atoms, the idea that all matter is compose of tiny particles, is something that we accept without question but back in Boltzmann time there were notable eminent physicists who viewed Boltzmann’s atomic theory with intense hostility as most of them believe that atoms were entities that did not exist. For instance, during one of Boltzmann’s lectures on atoms (in Vienna) the great Austrian Physicist Ernst Mach stood up and said to the audience “I don’t believe that atoms exist!”.

  1. The existence of blood circulation put forth by the English medical doctor William Harvey (1578-1657).

Today we take for granted that the heart muscle pumps blood trough blood vessel but back in Harvey time (17th century) the prevalent accepted theory was that human blood was continuously produced by the liver. In 1628 he publishes the book De Motu Cordis showing that the latter idea was entirely false yet his contemporaries did not accept his theory and ridiculed his claims with great hostility. Few years before his death Harvey was lucky to see how his ideas began to gain acceptance by the medical establishment.

Reponses to Dr Klein’s comments:

Dr. Klein comment: “I have no intention of debating the actual MBM. If I were convinced that the underlying rationale was firmly established (i.e. that low-carb is superior) then that would be a different story and we could hash out MBM on its merits.”

Response: The underlying rational of the MBM has nothing to do with low-carbohydrate diets. As clearly explained in the introduction of our article, the MBM originates from my mathematical investigation of the central claim of the energy balance theory (i.e., if body weight is stable around some mean value then the average energy intake equals the average energy expenditure). In this analysis, I found, through the use of principles of analytical biochemistry and linear algebra, that energy balance is – in fact – impossible (see [1] for a detailed explanation). This is a mathematical finding and not rhetorical argument or opinion that one may try to support or contradict with empirical data. Therefore, in order to disproof the argument you will need to look for incorrect assumptions or operations in the published computations that lead to “paradigm shifting” conclusion that the energy balance is incorrect. This finding does not violate the First Law of Thermodynamics since this Law allows for open systems, such as the human body, to experience a substantial negative energy balance while the system’s mass remains unaltered (see Figure 1 in [1]). In effect, in the original work, I showed that body weight could be stable in the presence of a constant negative energy balance of about –200kcal (Figure 6 in [1]).

As an alternative to the incorrect energy balance theory, I proposed a mass balance model (MBM) for body weight fluctuations [1]. This model describes daily body weight fluctuations as an imbalance between daily mass intake (decomposed in energy-providing mass and non-energy providing mass) and daily mass excretion (i.e., daily elimination of macronutrient oxidations products). This model fitted weight loss data under distinct dietary compositions [1]. Hence, this model does not attempt to defend one type of diet over any other possible diets. One of its predictions is, however, that in isocaloric weight loss regimens where the associated food mass is the smallest, will result in the largest weight and fat loss. Therefore, the MBM foresees that a low-carbohydrate diet will result in greater weight and fat lost in contrast to a low-fat diet of identical energy content (i.e., isocaloric), since a given level of energy intake always requires substantially less food mass as the energy proportion from fat increases—a consequence from fats high caloric density compared to carbohydrate or protein.

Reaction to the concerns raised by the phrase “vast collection”

In your attempt to dismiss our work, your discourse mainly concentrates in the references linked to a single sentence taken from the abstract: “A vast collection of evidence shows, however, that low-carbohydrate diets typically result in much greater weight and fat loss than isocaloric low-fat diets.”

In your article, you explain why you believe that 5 out of the 6 references at the end of latter sentence are totally worthless, as they are, according to your expert knowledge, plagued with problems that invalidate the claims of greater weight and fat loss. Then to ridicule our work further, you claim that we are unaware that our “vast collection” of references contains an article by Hall et al. [2] that, according to your interpretation, contradicts the claims of greater weight loss and fat loss. However, table 3 of Hall et al. [2] shows that weight loss is significantly greater in the low-carbohydrate diet (–1.85±0.15kg vs –1.3±0.16kg, p-value = 0.022 <0.05), but DXA fat loss measurements are statistically identical (–0.529±0.13kg vs –0.588±0.14kg, p = 0.78 > 0.05) and not greater for a low-fat diet group as you incorrectly portrayed. Additionally, in this same work, DXA measurements were the only true direct measurement of fat loss as the presented fat balance numbers are indirect estimates computed with the following formula

(Fat balance) = (Fat Intake) – (Fat Oxidation)

where (Fat Oxidation) =1.63xVO2 – 1.64xVCO2 – 1.84x(Urinary Nitrogen) (see Hall et all methods).

Therefore, it was perfectly reasonable to include this article as part of our “vast collection”, as the phrase “greater weight and fat loss” is logically equivalent to “greater weight loss or greater fat loss or both”.

Apparently, Hall et al. [2], you, and many others are unaware of the giant inconsistency of this work: Hall paper’s table numbers contradict its provocative title. Specifically, if we use the Hall et al. [2] table numbers to compute the cumulative fat balance, then fat oxidation is, in fact, much greater in a low-carbohydrate diet than in a the low-fat diet.

Let me illustrate:

At the end of the six days the low fat diet group had lost an average of – 588g of fat (see table 3 in [2]). Thus, fat balance is negative with a value of

Fat balance = (9 kacl/g) x (– 588g) = – 5,292kcal

Now as daily fat intake was 17g/day (see table 2 in [2]) the total fat intake over 6 days is

Fat intake = (17g/day) x (6 days) x (9 kacl/g) = 918kcal

Therefore, according to the Fat Balance Equation, the net fat oxidation over the six days was

(Fat Oxidation) = (Fat Intake) – (Fat balance) = 918kcal – (–5,292kcal) = 6,210 kcal

Performing the same computations for the low-carbohydrate group gives

Fat balance = (9 kacl/g) x (– 529g) = – 4,761kcal

Fat intake = (108g/day) x (6 days) x (9 kacl/g) = 5,832kcal

(Fat Oxidation) = (Fat Intake) – (Fat balance) = 5,832kcal – (– 4,761kcal) = 10,593 kcal

Consequently, a low carbohydrate diet leads to substantially increased fat oxidation than a low fat diet – contrary to what the title of that paper claims.

Dr. Klein comment: “Hypocaloric conditions: A meta-analysis of 20 controlled underfeeding studies by Hall and Guo [16] actually found a slight fat loss advantage to lower-fat diets in protein- and energy-matched comparisons. (I wonder why these weren’t referenced in the MBM paper?)”

Response: The MBM fits the hypocaloric conditions. This is shown in the original publication of the MBM [1] and is simulated in Figure 1 of our article. Notice that Figure 1 D shows that the MBM takes into account that the energy expenditure of the low carbohydrate diet is frequently smaller than that of the low-fat diets. Apparently, you did not read it carefully, as the article by Hall and Guo was referenced in the discussion section (see reference [18] in our article).

Dr. Klein comment: “Eucaloric conditions: Metabolic ward-based diet comparisons by Leibel et al [17] that equated protein and total energy failed to show differences in bodyweight maintenance despite wide variations in the proportion of carbohydrate and fat intake.”

Response: The point of our study is this eucaloric condition. In the method section of our paper, after the description of the MBM, we also describe the Hall’s energy balance model that is used in the NIH Body Weight Planer [3] ( In Figure 2, we run the MBM and Hall’s energy balance model through the same hypothetical isocaloric conditions. Also, with both models, we recreated the onset of type 1 diabetes in the absence of insulin therapy. The results of this computational contrast is surprising to say the least. Furthermore, in Figure 3, we basically repeat Figure 2 but with real data from the recent feeding trial by Kong et al. [4], and our simulations indicate that the MBM predictions match perfectly the Kong data, whereas those of Hall’s energy balance clearly do not.

Dr. Klein comment: “Hypercaloric conditions: If it was all about mass balance and not energy balance (as Manninen explains here), then controlled overfeeding studies would show LESS weight/fat gain with the fat-dominant energy surpluses. More explicitly, 44% less grams of fat are required to equal the caloric load of carbohydrate grams (carbohydrate = 4 kcal/g, fat = 9 kcal/g), so less nutrient mass is present in the higher-fat condition. Contrary to what the MBM would predict, tightly controlled isocaloric overfeeding comparisons show no difference in weight gain, with a tendency toward greater fat gain via the fat-dominant surplus [18, 19].”

Response: The overfeeding duration in these trails were not greater than three weeks and thus is possible that a longer treatment period may allow for statistical significance to emerge. Figure 1 in Horton et al. suggests that this is indeed very likely. On the other hand, it is hard for me to trust your judgment, as your ability to do elementary arithmetic is clearly subnormal for a PhD. Let us analyzed your erroneous train of thought by computing how many grams of fat are required to generate 4kcal: In doing so we get

(4kcal of fat) x (1g fat)/(9kcal of fat) ≈ 0.44g of fat

By definition, the percentage change is

{ ([New value] – [Old value])/ [Old value] } x 100 = {(0.44g – 1g)/1g} x 100 = – 56%

which is clearly not 44% as you incorrectly claim. In other words, in order to supply the same amount of energy present in 1g of carbohydrate we need 56% less grams of fat not 44% less.


  1. Arencibia-Albite F. Serious analytical inconsistencies challenge the validity of the energy balance theory. Heliyon. 2020; 6(7):e04204.

  2. Hall KD, Bemis T, Brychta TR, Chen KY, Courville A, Crayner EJ, et al. Calorie for Calorie, Dietary Fat Restriction Results in More Body Fat Loss than Carbohydrate Restriction in People with Obesity. Cell Metabolism. 2015; 22: 531.

  3. Hall KD, Sacks G, Chandramohan D, Chow CC, Wang YC, Gortmaker SL, Swinburn BA. Quantification of the effect of energy imbalance on bodyweight. Lancet. 2011; 378(9793):826-37.

  4. Kong Z, Sun S, Shi Q, Zhang H, Tong TK, Nie J. Short-Term Ketogenic Diet Improves Abdominal Obesity in Overweight/Obese Chinese Young Females. Front Physiol. 2020; 11:856.

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