Saturday, May 21

Total Ketogenic Ratio (TKR)

The degree of ketosis produced by a particular diet has been long determined by the Ketogenic Ratio (KR), proposed by Woodyatt (1):

KR = K / AK

where, K represents the ketogenic factors and AK represents the anti-ketogenic factors. 

Experimentally determined values for each dietary component are expressed by the equation:


f = dietary fats in grams
p = dietary protein in grams
c = dietary carbohydrate in grams

Another easier way to determine the KR was proposed by Metcalf and Moriarty:

KR = f / p + c

The formula doesn't take into account the antiketogenic properties of some amino acids but gives an approximate result to the Woodyat equation. 

A paper published by I.A. Cohen (2) adressed the issue brought by these equations: they only apply to isocaloric conditions because they fail to take into account the utilization of energy stores in a hypocaloric diet, underestimating the degree of ketosis of a given diet. The Woodyatt equation then is referred as the Dietary Ketogenic Ratio (DKR), representing the effect of the dietary components on ketosis. 

The formula proposed by Cohen tries to model the impact of weight reduction dieting under ideal conditions, that is, the utilization of stored lipid without the catabolism of protein, scenario normally reached after a few days of fasting and/or low carbohydrate-high fat dieting. 

The Cohen formula is derived from the Woodyatt equation, in a series of simple, mathematical steps giving the new equation:


e = total energy expenditure in calories
p = dietary protein in grams
c = dietary carbohydrate in grams

There are some limitations of this equation, as stated by the author:

1. It needs further evaluation for proving the hypothesis.
2. It describes an ideal situation in which any energy deficit is met entirely by stored lipids. 
3. Dietary energy established by bomb calorimetry may exceed from the energy obtainable by the organism consuming that diet.
4. Energy efficiencies brought about by dieting, as well as changes in the use of dietary nutrients for non-energy uses may alter the expected outcome. For instance, subjects who have not utilized particular metabolic pathways for an extended period may show changes in energy utilization over time.
5. Urinary loss of ketones is not accounted for in these formulae.
6. The nutrient mix itself, as well as the state of the organism may influence the ability to fully utilize the energy available in the consumed nutrients.
7. There is inter-individual variability for achieving the same degree of ketosis. Genetic factors and differences in intestinal flora may alter this parameter.
8. Woodyatt analysis of the ketogenic and anti-ketogenic properties of protein depends upon the proportions of specific amino acids, raising the possibility of differing properties depending upon protein sources. This may necessitate having to alter Woodyatt's constants depending upon protein mix.
9. Differences on both the absorption and utilization of fats resulting from the types of fat included in the diet might alter the response, ie. saturated vs. unsaturated, polyunsaturated vs. monounsaturated, inclusion of MCT or the presence of abnormalities in individual gall bladder functioning.
10. The antiketogenic effects of carbohydrates in food might be altered by the rapidity of their conversion to glucose, as expressed in their glycemic index. The timing of meals may alter the results, particularly if individual feedings varied greatly in their ketogenic to anti-ketogenic properties. For example, meals that contained an isolated bolus of carbohydrate might be expected to rapidly decrease ketosis, even when the total amount of carbohydrate would not be expected to do so when evaluated over a 24-h period. 
11. Ketosis is but one factor among many in weight-loss dieting. The behaviour of any particular factor, by itself, should not imply suitability nor superiority. 

Let's see some examples. 

Asume that an hypocaloric diet consisting of 100g of protein, 70g of fat and 20g of carbohydrate, for an energy expenditure of 2000kcal:

KR (Woodyatt) = 1.28
TKR (Cohen) = 2.09

The energy supplied by the diet in this example is 1110 kcal, which creates a 900kcal deficit. This additional fat increases the production of ketones, not accounted by the Woodyatt equation.

If we up the protein intake to 150g while maintaining calories, we get:

KR (Woodyatt) = 1.00
TKR (Cohen) = 1.65

So even if we consider a PSMF (Protein Sparing Modified Fast) type diet, 200g of protein with 20g of fat and 20g of carbohydrate, we get:

KR (Woodyatt) = 0.79
TKR (Cohen) = 1.37

While the Woodyatt formula might underestimate the level of ketosis, it is probable that the Cohen formula overestimates it, specially in obese and overweight subjects. 

ResearchBlogging.orgCohen IA (2009). A model for determining total ketogenic ratio (TKR) for evaluating the ketogenic property of a weight-reduction diet. Medical hypotheses, 73 (3), 377-81 PMID: 19410378

Sunday, May 8


Metabolic efficiency can be defined as the capacity for producing useful energy with the least amount of metabolic by-products and heat. In a machine, for example, efficiency can be measured as the ratio of the work done to the energy supplied to it. You can do more with less. There are other definitions of metabolic efficiency around the web such as the capacity for fat utilization for a given activity. 

For aerobic metabolism, the main pathway for ATP production in eukaryotes, there are two substrates which compete with each other: glucose and fatty acids. Amino acids can also be used but are not (or should not) be an important source of fuel. For knowing which fuel is more efficient (giving the higher amount of energy per mole, joule per mole) we must review the pathways for glucose and fatty acid catabolism before they converge into the Krebs Cycle.

Glucose oxidation, ie. glycolysis, is the pathway for oxidizing glucose to pyruvate. The preparatory phase of glycolysis requires the "investment" of two molecules of ATP. This is "payed off" in the following steps, producing 4 ATPs. So the net gain of the conversion glucose --> pyruvate is 2 ATPs. This process also produces 2 NADH+.  Pyruvate must be converted to acetyl CoA, producing one more NADH+ and CO2. So the total oxidation of one molecule of glucose to acetyl CoA yields:

1 glucose molecule to 2 pyruvates: 2 NADH+
2 pyruvates to 2 Acetyl CoA:  2NADH+, 2CO2

Total = 4 NADH+ plus 2CO2

On the other hand, fatty acid oxidation is relatively simpler. Once triglycerides are hydrolyzed, free fatty acids are taken up by cells. In the cytosol, they are esterified to conezyme A to form a fatty acyl CoA. The fatty acyl group is transferred to carnitine and moved across the inner mitochondrial membrane by an acylcarnitine transporter protein. Once in the matrix side, the fatty acyl group is released from carnitine and reattached to another CoA molecule. The mitochondrial fatty acyl CoA is oxidized in a series of reactions to produce Acetyl CoA. The conversion of a fatty acid to acetyl CoA yields (taking palmitate as an example):

1 palmitate to 1 palmitoyl CoA: 2 ATP
1 palmitoyl CoA to 8 Acetyl CoA: 7 FADH2 + 7 NADH+

Overall, in these preliminary reactions before entering the Krebs Cycle we have that 1 molecule of glucose can yield 2 Acetyl CoA while 1 molecule of palmitate can produce 8 Acetyl CoA. Oxidation of glucose until this step produces 2 molecules of CO2 and 4 NADH+, while oxidation of palmitate produces an equal number of FADH2 and NADH+, 7.

Once acetyl CoA reacts with oxaloacetate, forming citrate, it enters the Krebs Cycle. This pathway produces 3 NADH+, 1FADH2, 1 GTP and 2CO2. So, overall we have:

1 molecule of glucose produces: 

2 Acetyl CoA
6 CO2
10 NADH+

Ratio NADH+:FADH2 = 5:1

ATPs produced from complete oxidation: 30-32 (assuming 2.5 ATP from NADH+ and 1.5 ATP from FADH2)

1 molecule of palmitate produces:

8 Acetyl CoA
16 CO2
31 NADH+
15 FADH2
Ratio NADH+:FADH2 = 2:1 (depending on carbon length)

ATPs produced from complete oxidation: 108 (assuming 2.5 ATP from NADH+ and 1.5 ATP from FADH2)

The final electron acceptors are the coenzymes NADH+ and FADH2 which transfer electrons to the mitochondrial respiratory chain. Understanding this process is of utmost importance for understanding the differences between glucose and fatty acid metabolism. For a basic tutorial in oxidative phosphorylation please read this

Electrons carried by NADH+ are transferred to Complex I, also called NADH dehydrogenase. Complex II, succinate dehydrogenase, is the same enzyme encountered in the Krebs Cycle, which oxidizes succinate and transfers electrons to FADH2. Studies have shown that Complex I and complex III are the main producers of ROS in the electron transport chain (1, 2, 3, 4)*. So, the ratio of NADH+:FADH2 is important for the potential ROS production in the mitochondria. Because glucose generates 5 times more NADH+ than FADH2, complex I activity is increased. Fatty acid oxidation produces only twice the amount of NADH+ than FADH2, shifting to a more balanced utilization between complex I and complex II. There are other ways to pass electrons into the respiratory chain. In the first step of the beta oxidation pathway, catalyzed by acyl-CoA dehydrogenase, electrons from the substrate are transferred to the FAD of the dehydrogenase, then to electron-transferring flavoprotein (ETF), which in turn passes its electrons to ETF:ubiquinone oxidoreductase. This enzyme reduces ubiquinone directly, without the need for other complexes. Glycerol-3-phosphate derived either from glycerol or from glycolysis is oxidized by glycerol-3-phosphate dehydrogenase and reduces ubiquinone directly. 

The overall message is that glucose's complete oxidation involves more complex I activity, ultimately promoting more ROS production by the mitochondria. A more in depth review of the implications of glucose and fatty acid metabolism, and mitochondrial complex utilization in aging and disease can be found in this paper by Mobbs et al. (yes, the same guy from the nephropathy reversal study):
"Therefore shifting away from glucose utilization toward lipid and amino acid utilization would be expected to substantially reduce the production of reactive oxygen species, without necessarily reducing ATP production. As described below, other beneficial effects also occur as a result of this altered pattern of glucose fuel use, including a shift toward producing antioxidizing NADPH and increased protein and lipid turnover, which reduces the accumulation of oxidized protein and lipids."
Ok, so we have seen why depending on fat as an energy source seems a better idea than depending on glucose. But what about ketones?

Kurt Harris thinks ketosis is metabolically stressful. Considering that the ketogenesis pathway only demands one molecule of NADH+ and one H2O, I dont see the "stressful" part.

Let's see how ketones alter mitochondrial energy metabolism**. Remember that the respiratory electron transport chain is the process which generates ATP by creating an electrochemical proton gradient. Electrons carried through redox couples are ultimately combined to H+ and O2 to form H2O. The total energy available from the movement of electrons up the respiratory chain is determined by the difference between the variable redox potential of the mitochondrial NAD couple and the O2 couple (this is because the first step in the chain is NADH dehydrogenase and the last step is production of H2O). We know experimentally the reduction potential of both couples (5): 

[NAD]/[NADH+] couple: -0.28V
[O2]/[H2O] couple: +1.2V
So we can calculate the total energy yield given by:

∆G' = -nF∆E

Where: n is the number of electrons, F is 96.485 kJ/mol/V (Faraday's constant) and ∆E the difference between potentials. Replacing in the equation with the values we have:

∆G' = -(2)(96.485)(0.92)
∆G' = -177.5324 or -178kJ/2mol

The energy of the proton gradient created by the electron transport chain is given by: 

∆G' [H+] cyto/[H+] mito = RTln[H+] cyto/[H+] mito + FEmito/cyto

Where  Emito/cyto is the electric potential of the mitochondrial relative to the cytosolic phase.

3 ATPs are generated by the transport of one electron pair through the respiratory chain. Since the maximum energy available from the redox reactions of the chain is -178kJ, the energy available for the synthesis of each ATP cannot be more than -59.2kJ/mol (178/3). Experiments done on different cells have shown that this energy is in the range of -54 to -58kJ/mol (very efficient). 

As the electrons liberated by complex I are carried by coenzyme Q to complex III, the difference between the redox potential of the [NAD]/[NADH+] mitochondrial couple and the coenzyme Q couple determines the energy of the proton gradient generated by the mitochondria. This difference determines the energy of hydrolysis of ATP generated by the mitochondrial F1 ATPase. 

bOHB and AcAc are in near-equilibrium with the free mitochondrial [NAD]/[NADH+] ratio. Veech and colleages showed that the metabolism of ketone bodies in the heart produced a reduction of the mitochondrial NAD couple and oxidation of the coenzyme Q couple, increasing the redox span between the two couples, making more energy available for ATP synthesis because: 

∆G = -nF∆EQ/NADH

In this classic study (6), the authors found that***:
"The Eh7 of the mitochondrial NAD couple, Eh7 NAD+/NADH (Eq. 16), was -280 mV and decreased to about - 300 mV on addition of insulin, ketones, and the combination.
The ratio [fumarate2-]/[succinate2-] increased about 1.5-fold on addition of insulin, about 2.5-fold on addition of ketones, and about 4-fold on addition of the combination (Fig. 1). Taking this change to indicate the redox state of the [Q]/[QH2] couple, which is the cofactor for the succinate dehydrogenase (EC reaction, the observed increase in [fumarate2-]/[succinate2-] indicates a 1.5- to 4-fold oxidation of mitochondrial [Q]/[QH2] on addition of insulin, ketones, or the combination. The Eh[Q]/[QH2], calculated from the succinate dehydrogenase reaction (Eqs. 20-22, Fig. 2), increased progressively from -4 mV during perfusion with glucose alone to + 15 mV on the addition of insulin and ketones.
When the oxidation of the mitochondrial Q couple was combined with the reduction of the mitochondrial NAD couple resulting from these additions to the glucose perfused hearts, the estimated energy available in the transfer of 2 e from the mitochondrial NAD to the Q couple (Eq. 23 and Eq. 24) catalyzed by the NADH dehydrogenase multienzyme complex, ∆G QH2/NAD+, increased from -53 kJ/2 mol e during perfusion with glucose alone to -60 kJ/ 2 mol e with addition of insulin and ketones. This increase was paralleled by an increase in the cytosolic free energy of ATP hydrolysisGATP (Eq. 7 and Eq. 8), determined independently using NMR spectroscopy, which increased from -56 kJ/mol in control hearts to about -59 kJ/mol on addition of insulin or insulin plus ketones. 
The potential between mitochondrial and cytosolic phases, E mito/cyto (Eq. 9, Fig. 2, Table 3), was -143 mV in hearts perfused with glucose alone and unchanged on the addition of insulin but decreased to -120 mV on addition of ketones or -130 mV on addition of the combination. "
Summarizing (from the study data)****: 

For ketones (without insulin):
Eh7 NAD+/NADH = -299mV or -0.299V
Eh7 Q/QH2 = +7.8mV or 0.078V
Cytosolic pH = 7.05
Mitochondrial pH = 7.52

∆G = -nF∆E
∆G = -(2)*(96.485)(0.015-(-0.3))
∆G = -59.2 kJ/2mol

For glucose:

Eh7 NAD+/NADH = -280mV or -0.28V
Eh7 Q/QH2 = -0.4mV or -0.004V
Cytosolic pH = 7.05
Mitochondrial pH = 7.09

∆G = -nF∆E
∆G = -(2)*(96.485)(-0.004-(-0.28))
∆G = -53 kJ/2mol

Recall that the energy of the proton gradient is calculated by:

∆G' [H+] cyto/[H+] mito = RTln[H+] cyto/[H+] mito + FEmito/cyto

Expressing ∆G in terms of pH instead of concentration, we get:

∆G' [H+] cyto/[H+] mito = 2.3RT (∆pH) + FEmito/cyto

where, R is the gas constant (8.315 x 10^-3 kJ/mol.K) and T the absolute temperature (in this study, 311.15K).  

For ketones, Emito/cyto = -0.12V, so:

∆G = 2.3 (8.315*10^-3)(311.15) (∆pH) + (96.485)(-0.12)
∆G = (5.9 kJ/mol) (∆pH) + (-11.52)
∆G = (5.9 kJ/mol) (7.05-7.52) + (-11.52)
∆G = -14.2 kJ/mol

For glucose, Emito/cyto = -0.14V, so:

∆G = 2.3 (8.315*10^-3)(311.15) (∆pH) + (96.485)(-0.14)
∆G = (5.9 kJ/mol) (∆pH) + (-13.5)
∆G = (5.9 kJ/mol) (7.05-7.09) + (-13.5)
∆G = -13.7 kJ/mol

The mean calculated ∆G of cytosolic ATP hydrolysis was:

∆G ATP = -57.6 kJ/mol for ketones
∆G ATP = -56.6 kJ/mol for glucose

Concluding from this data we see that ketones cause a decrease in the potential between the mitochondria and cytosol (ie. Emito/cyto) while increasing the ∆G of ATP hydrolisis, paralleled by the increase in ∆G QH2/NAD+ and ∆G[H+]. Increased efficiency. 

But why bOHB is such a "superfuel"? This can be illustrated in the following table (7):

The table above shows the heats of combustion for different nutrients metabolized by the Krebs cycle. As shown, there is a wide variation in the inherent energy of different C2 units which enter the cycle, derived from different sources. For instance, as we have seen, one molecule of pyruvate produces 15 ATP. The ∆G' of ATP hydrolisis cannot exceed 59-60kJ/mol and the range of variation in cells is very narrow, less than 10% (-53 to -60kJ/mol). So, by simple maths, for producing 15 ATP, -795 to -900 kJ/15 moles are needed (15*-53; 15*-60). There are only -778kJ available from pyruvate, so the ∆G' of the ATP produced is of low energy (-778/15 = -51kJ/mol). C2 from fatty acids (ie. palmitate) have too much inherent energy to be accomodated in the 15 ATPs, metabolically implausible (-1247/15 = 83). If we look at the table, bOHB has -1021kJ/C2, only 13% excess energy (-1021/15=68). Compared to pyruvate, bOHB is more reduced (ie. more H+ per C). 

When interpreting this data, one obvious question arise. If the inherent energy of palmitic acid is greater than bOHB, why does palmitic acid is not a "superfuel"? The answer lies in the nature of beta oxidation. If we remember the sites for entering the respiratory chain, we can see that some reducing equivalents produced by the oxidation of fatty acids enter the chain via the ETF:ubiquinone oxidoreductase, resulting in a loss of approximately 1 of the 6 possible ATP produced, because of its redox potential (8). The remaining reducing equivalents are metabolized in the Krebs cycle normally, but in contrast with metabolizing bOHB, the Q couple is reduced and not oxidized, decreasing ∆E available for ATP synthesis. Last but not least, free fatty acids produce enzymatic/transcriptional changes which account for the difference in efficiency between palmitic acid and bOHB. Elevation of plasma FFA induce the expression of uncoupling proteins (9, 10) and peroxisomal beta-oxidation (11). 

Summing up

The response Dr. Harris gave me a couple of months ago included some statements like:

"It [bOHB] is only efficient if you think the steps it took to get it don't count."

""Glycolysis" is anaerobic and only happens by itself when speed is necessary - like weight lifting."

"Ketosis is an adaptive state that beats the alternative of glycogen depletion or muscle wasting that it is designed to counter. This makes it "good". In the same way, muscle wasting to keep your brain supplied with glucose is "good". Good in the sense of beating the alternatives. That does not mean we should seek to live continuously in either state, though does it?"

I hope that after this post (and after comparing the "alternatives"), my position on the subject is clear.

* This is a subject of much debate. Studying ROS production by mitochondria under physiological conditions is not an easy task. Ultimately, every complex is capable of producing ROS. 
** This explanation is summarized from the referenced article by Veech. A nice article on the subject can be found here.
*** Eh stands for the redox potential of a half reaction. Eh7 = Eh at pH 7.
****Im omitting some units for the sake of clarity. 

ResearchBlogging.orgSato K, Kashiwaya Y, Keon CA, Tsuchiya N, King MT, Radda GK, Chance B, Clarke K, & Veech RL (1995). Insulin, ketone bodies, and mitochondrial energy transduction. The FASEB journal : official publication of the Federation of American Societies for Experimental Biology, 9 (8), 651-8 PMID: 7768357
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