The formulas widely used to calculate fat oxidation (FATox) in grams per minute and carbohydrate oxidation (CHOox) in grams per minute are the following:

FATox (g/min) = 1.67 x VO₂ (L/min) – 1.67 x VCO₂ (L/min)

CHOox (g/min) = 4.55 x VCO₂ (L/min) – 3.21 x VO₂ (L/min)

VO₂ and VCO₂ are placeholders for the measured values of inhaled oxygen and exhaled carbon dioxide expressed in liters per minute. These formulas were presented in a paper from Frayn. Later papers have done various adaptations but these ones are still mostly in use.

Frayn, K. N. (1983). Calculation of substrate oxidation rates in vivo from gaseous exchange. Journal of Applied Physiology, 55(2), 628–634. doi:10.1152/jappl.1983.55.2.628

https://journals.physiology.org/doi/abs/10.1152/jappl.1983.55.2.628

They are used in many different forms of research and particularly in exercise physiology studies during steady state and ramp up tests.

It is important to understand what we are measuring and if these measurements can be fully attributed to what we are trying to calculate.

A first misconception, perhaps due to measuring oxidation rates mainly during exercise research, is that most people may think this is the full amount of FATox and CHOox attributed to the working muscle.  Because of the input variables VO₂ and VCO₂, the formulas are for whole body oxidation.  It is therefore problematic if you want to determine how fuel availability for the skeletal muscle itself influences skeletal muscle oxidation and the performance depending on it.

A second misconception is that it would represent the whole amount of energy required to perform the exercise.  The formula is designed only for what is oxidized thus for the energy generated in the mitochondria where the oxidation takes place.  Not for what is generated outside of the mitochondria where ATP is produced without consuming oxygen (O₂).

The heart and brain also increase energy consumption during exercise and therefore also respond with increased energy production.  The heart needs to pump around blood to deliver the energy to the working muscle.  The brain has to generate muscle contractions through nervous system impulses which require ATP.  As intensity increases, more impulses need to be generated.

“The potential mechanisms of lactate in mediating exercise-enhanced cognitive function: a dual role as an energy supply substrate and a signaling molecule”

https://nutritionandmetabolism.biomedcentral.com/articles/10.1186/s12986-022-00687-z#:~:text=Concretely%2C%20enhanced%20neuronal%20activity%20during,higher%20energy%20demand%20of%20neurons.

My main concern is the following: Are the formulas correct in trained athletes and are they correct under ramp up tests? Ramp up tests produce most of the substrate oxidation scaling results of which you will see some examples further down the article.

To be correct:

• We must be able to attribute all inhaled O₂ to the oxidation of fat and carbohydrate substrates.
• We must be able to attribute all exhaled CO₂ as a direct result from FATox and CHOox

I could only find research from Frayn looking at oxidation in sedentary situations and in sick patients.  So I think it is reasonably safe to assume that the formulas have not been validated in athletes, let alone exercising athletes with variable intensities.  Athletes have gone through a lot of energetic optimization and therefore could deviate from the formulas considerably. If there are any other variables that also take up O₂ or produce CO₂ then we should know and we should know by how much these variables can fluctuate to see if they are considerable enough.

A paper from Wilkerson et al provided max VO₂ and VCO₂ values for the experimental group and control group during a ramp up test.  

Working with the values from the control group, I could calculate the following values for their max FATox and CHOox.

FATox (g/min) = 1.67 x 3.93 (L/min) – 1.67 x 4.79 (L/min) = -1.4362 g/min

CHOox (g/min) = 4.55 x 4.79 (L/min) – 3.21 x 3.93 (L/min) = 9.1792 g/min

Here the results lead to a negative value of -1.4362 g/min for FATox.

Stopping FATox completely, the result should lead to zero g/min. Not a negative value. It should also be questioned when the body requires the maximum available energy, does it make sense to shut off one source of fuel? Even if it would be a slower fuel, you’d still let it contribute to the total. Unless fat causes glucose to be oxidized at a slower rate and shutting down fat would allow glucose to speed up much faster. Towards the end of this article we’ll have seen sufficient material to understand what is really going on.

“Influence of dichloroacetate on pulmonary gas exchange and ventilation during incremental exercise in healthy humans”

https://doi.org/10.1016/j.resp.2009.07.004

https://www.sciencedirect.com/science/article/abs/pii/S1569904809001876

Frayn already pointed out in the paper that protein needs to be accounted for and so does gluconeogenesis (GNG).  

Corrected for protein, measured via urinary nitrogen, the formulas are the following:

FATox (g/min) = 1.67 x VO₂ (L/min) – 1.67 x VCO₂ (L/min) – 1.92 nitrogen (g/m)

CHOox (g/min) = 4.55 x VCO₂ (L/min) – 3.21 x VO₂ (L/min) – 2.87 nitrogen (g/m)

As you can imagine, urinary nitrogen cannot be tested during an exercise test to understand protein metabolism during that exercise.

Variable Sources

As the key focus here is what consumes O₂ and what produces CO₂, we’ll look at various sources and influences that cannot be attributed to FATox and CHOox.  As my question particularly pertained to athletes, I’ll try and stick as close to athletes as possible but data may not always be available.

Brain glutamate oxidation

I’ll be short on this one as there is little data relevant to our case. It is a study in mice that shows glutamate oxidation goes up during exercise. We should consider the possibility that the brain in humans also increases glutamate oxidation during exercise.  And we don’t know how that effects urinary nitrogen excretion.

“Exercise increases mitochondrial glutamate oxidation in the mouse cerebral cortex”

https://doi.org/10.1139/apnm-2016-0033

https://cdnsciencepub.com/doi/10.1139/apnm-2016-0033

Thus estimates on the contribution in metabolism during exercise is unknown. We cannot even do a wild guess.

Amino acid oxidation during exercise

Although other amino acids are oxidized, the following paper looked at leucine specifically.  The daily leucine requirement would be around 14mg/kg body weight/day.  This means 1.05g/day for a 75kg adult. Or 0.0007291666667g/min.  What the paper points out is that on average there is a 3.5 fold increase from rest to exercise or 0.002552083333g/min for +/- 2 hours at 45% of VO₂max.  This is a low intensity.

Using the above formulas with nitrogen this can already mean a 0.5% correction for CHOox and 1% for FATox just from leucine alone at low intensity.

The paper refers to the suggestion to have higher daily protein intake for endurance athletes (1.6g protein/kg/day) versus bodybuilders (1.2g protein/kg/day) because of the higher protein metabolism. 

“Amino Acid Metabolism During Exercise and Following Endurance Training”

https://link.springer.com/article/10.2165/00007256-199009010-00003

This is an important indication. Total amino acid utilization, whether directly oxidized or converted to glucose should be measured and may differ greatly between trained and untrained individuals, high carbohydrate and very low carbohydrate dieters, stable intensity for a long duration versus ramp up exercise tests.

This means that the values for nitrogen in the formula should not be neglected. Research is needed to understand how much gram per minute at various intensities is oxidized. A urinary sample is not sufficient.

Gluconeogenesis

Lactic acid to pyruvate can be ignored as lactic acid is essentially a temporary phase.  Pyruvate is converted to lactic acid and (somewhere else) changed back to pyruvate without affecting the O₂ or CO₂ balance.

Alanine and other amino acids their pathway to pyruvate are difficult in order to find out if that affects the O₂ consumption or CO₂ production.

The pathway oxaloacetate to phospho-enolpyruvate to glucose could have an impact as it produces CO₂.  It can be sourced from amino acids and odd carbon fatty acids. The amino acids can enter the TCA cycle at various places.

GNG needs to be further detailed to see how much of an impact it can have.  The production volume is influenced for our target athletes at increasing intensity so worthwhile to consider.

We see here that training enhances GNG during exercise up to 0.75mg/kg/min of glucose produced which would equate to 56.25mg/min for a 75kg adult.  The study also points out that this effect is trainable.

“Endurance training increases gluconeogenesis during rest and exercise in men”

https://doi.org/10.1152/ajpendo.2000.278.2.E244

https://journals.physiology.org/doi/full/10.1152/ajpendo.2000.278.2.E244

The above study for the GNG rate used sedentary individuals.  We can expect higher rates in highly trained athletes. 

A study looking at 2 different diets shows us in well-trained athletes that the endogenous glucose production increased from a sedentary value of around 1.1 mg/kg/min to around 2.8 mg/kg/min at a steady intensity of 72% of VO₂max.  Thus 127.5mg/min for our 75kg person or more than double versus our non-trained individuals.

“Gluconeogenesis during endurance exercise in cyclists habituated to a long‐term low carbohydrate high‐fat diet”

https://doi.org/10.1113%2FJP271934

https://physoc.onlinelibrary.wiley.com/doi/epdf/10.1113/JP271934

This is a considerable amount of glucose produced but we cannot assess the impact thus far as we have no clear measurement of its CO₂ contribution.

Pyruvate Carboxylation

There are 2 ways for pyruvate to end up in the citric acid cycle.  One is through its pyruvate dehydrogenase conversion into acetyl-CoA which produces a CO₂ molecule.  This CO₂ production is accounted for in the formula  The second is via pyruvate carboxylation which uses bicarbonate and results in the consumption of a CO₂ molecule so that pyruvate ends up as oxaloacetate.  This second pathway is not accounted for in the formulas and we have no idea how much of pyruvate carboxylation is going on. Let alone understand the effect in athletes during a ramp up test.

“Formation of oxaloacetate from pyruvate and carbon dioxide”

https://pubmed.ncbi.nlm.nih.gov/13840551

https://www.jbc.org/article/S0021-9258(18)69442-6/pdf

“Mechanism of the acceleration of CO2 production from pyruvate in liver mitochondria by HCO3-”

https://doi.org/10.1152/ajpcell.1997.273.1.c92

https://journals.physiology.org/doi/abs/10.1152/ajpcell.1997.273.1.C92

Fat

In Frayn’s paper he uses palmitoyl-stearoyl-oleoyl-glycerol (C₅₅H₁₀₄O₆) as a basis for the calculation.  This is the complete fat including the glycerol backbone.

• palmitic acid: C₁₆H₃₂O₂ 
• stearic acid: C₁₈H₃₆O₂
• oleic acid: C₁₈H₃₄O₂

If you sum up the 3, you’ll see there is C₃ and H₂ added due to the glycerol backbone.  The chemical formula for glycerol is C₃H₈O₃ but that is in its detached form.  As you can see in the picture below, the 3 acyls each share an oxygen atom so there is 1 hydrogen removed for each. So it works out as 102 from the acyls – 3 to make the binding + 5 from glycerol thus 104.

The oxidation gives us C₅₅H₁₀₄O₆ + 78 O₂ → 55 CO₂ + 52 H₂O so 55 / 78 = 0.7 RER

What this tells us is that the glycerol backbone of the fat is also part of the equation for FATox thus the formula calculates fat in its complete form oxidized per minute, not just fatty acids. Glycerol is a sugar alcohol, not a carbohydrate, not a lipid.

This doesn’t mean the equations need to be changed.  It just needs to be well understood what they represent.

When the adipose tissue breaks down fats, fatty acids are detached from glycerol and end up in circulation as free fatty acids which are picked up by albumin and transported to where the energy is required.  Inside the cell fatty acids and glycerol exist separately on their pathway to oxidation.

C₃H₈O₃ + ? O₂ → 3 CO₂ + 4 H₂O

Glycerol cannot be oxidized directly, it first has to be enriched with a phosphate so it actually costs an ATP molecule to become glycerol-3-phosphate (C₃H₉O₆P).  Further reaction to pyruvate (C₃H₄O₃) now yields an ATP molecule.  As you can see we still end up with 3 carbon atoms and 3 oxygen atoms so we haven’t consumed O₂ or produced CO₂.  

When fatty acids are turned into acetyl-CoA and similar for glucose and glycerol, the rest of the process is the same.  Where they differ is in how they become acetyl-CoA.  Yet with glycerol, it has entered into the pathway to pyruvate.  Glucose oxidation starts consuming O₂ and producing CO₂ from pyruvate onwards.  So shouldn’t glycerol metabolism be accounted for as glucose oxidation? Without glycerol the RER would be less than 0.7.

It may be a negligible volume on a high carb diet but dietary preference towards a high fat low carb diet can lead to significant changes in volume.

Ketones

Ketones are problematic to account for.  In the liver the fatty acids will undergo beta oxidation to form acetyl-CoA.  Acetyl-CoA can now end up in 3 different pathways.  A first is in the TCA cycle to generate ATP, a second is conversion to acetoacetate.  From here it has 2 different paths. A) reduction to beta-hydroxybutyrate (3HB, C₄H₈O₃) or B) decarboxylation into acetone.

In order to know what the net consumption of O₂ and production of CO₂ is of FATox, we need to know how much acetone is produced and how much 3HB is metabolised.

Acetone escapes via sweat and evaporation.  It is not measured while each acetone does represent 1 CO₂ molecule escaping from the body.

3HB results in 2 molecules of acetyl-CoA.  Each using 1 O₂ and producing 2 CO₂.

They originated as fatty acids where you need 4x acetyl-CoA (each consuming 1 O₂) to form 3HB.  That brings the RER to 4 CO₂ / 6 O₂ = 0.66

3HB oxidation is not accounted for in the formulas.  How much can we expect in athletes and especially in athletes on a low carb high fat diet where ketogenesis is at a higher level?

A paper from Volek et al shows us that FATox is significantly higher as a variable of diet.

They did not perform a ramp up test but we get to see their level of serum 3HB.  It gives us an indication of the contribution but we do not know by how much it is contributing.

“Metabolic characteristics of keto-adapted ultra-endurance runners”

https://www.sciencedirect.com/science/article/pii/S0026049515003340

If we want to know how much fat and glucose is oxidized then we need to correct it for 3HB oxidation as the RER is different. In the athletes above we see 0.6mmol/L as a minimum serum level.  It does not tell us how much is being produced and most importantly how much is oxidized.

Frayn’s paper makes an interesting quote:

Because both AcAc and 3-OHB are almost entirely dissociated at physiological pH an equivalent amount of hydrogen ion will be produced. This raises a difficulty in that it is not clear whether these hydrogen ions quantitatively displace an equivalent amount of CO₂ from bicarbonate (discussed in Ref. ES), so that the correction to the gaseous exchange can only be placed between 2 extremes.

3-OHB or 3HB does not simply dissociate.  The second element in the quote is very relevant to our question.  Bicarbonate can be an extra source of CO₂.

Bicarbonate as a CO2 Buffer

One of the problematic features is that during high intensity the RER value (VCO₂/VO₂) can exceed 1 as we have seen an example of in the introduction.  This means more CO₂ is produced than O₂ inhaled but how is that possible as none of the known metabolites have this property when they produce ATP?

“during intense exercise, RER values can be larger than 1.2 due to generation of carbon dioxide from anaerobic energy metabolism, in excess of that from aerobic metabolism.”

https://www.roomcalorimeters.com/understanding-indirect-calorimetry

But anaerobic metabolism, ATP generated when glucose is converted to pyruvate, does not produce CO₂!  

CO₂ that is produced as the result of oxidation reacts to bicarbonate + hydrogen in the blood.  In reverse the bicarbonate reacts with hydrogen to produce CO₂ and water (H₂O).  This system can react in both ways to maintain a steady blood pH. At low intensities this is a neutral operation.  However, as intensity goes up, hydrogen appearance in the blood increases which means that the bicarbonate buffer starts to release more and more CO₂.

The following study measured baseline bicarbonate in elite runners.  A value of around 27.4 mmol/L was measured.

“The effects of a novel bicarbonate loading protocol on serum bicarbonate concentration: a randomized controlled trial”

https://jissn.biomedcentral.com/articles/10.1186/s12970-019-0309-4

In the following study they could associate the odds of diabetes with the level of plasma bicarbonate where the quartile medians were 19.5, 21.4, 23.1 and 25.3 mmol/L.

“Plasma bicarbonate and risk of type 2 diabetes mellitus” 

https://doi.org/10.1503%2Fcmaj.120438

https://www.cmaj.ca/content/184/13/E719

As you can see there is variation in the serum level of bicarbonate depending on health status and likely also on athlete status.  The following study from Wilkerson et al where they measured starting and end value of bicarbonate, we can perform a rough calculation of how much CO₂ would be released from this bicarbonate reduction.

0.0003 liters of CO₂ = 8.066×10^18 molecules of CO₂

We go from 24.2mM/L to 16mM/L bicarbonate in the control group

Assuming an equivalent molar concentration of CO₂ to bicarbonate thus 8.2mM extra CO₂ at the maximum effort or 4.93815603e+21 molecules.

That would equate to around 0,1836 liters of CO₂ extra when calculating 4.93815603e+21 / 8.066×10^18 * 0.0003

Thus the 4.79 VCO₂ would need to be corrected to 4.6 VCO₂.  If the 3.93 VO₂ remains the same then the RER changes from 1.219 to 1.17 so we still don’t have the right correction.

This means the following for our formulas:

before bicarbonate correction:

• FATox (g/min) = 1.67 x 3.93 (L/min) – 1.67 x 4.79 (L/min) = -1.4362 g/min
• CHOox (g/min) = 4.55 x 4.79 (L/min) – 3.21 x 3.93 (L/min) = 9.1792 g/min

after bicarbonate correction:

• FATox (g/min) = 1.67 x 3.93 (L/min) – 1.67 x 4.6 (L/min) = -1.1189 g/min
• CHOox (g/min) = 4.55 x 4.6 (L/min) – 3.21 x 3.93 (L/min) = 8.3147 g/min

A correction of 0.33 g/min on FATox and -0.86 g/min CHOox.  Do keep in mind here that I have attributed the full reduction in bicarbonate at the point of maximum effort which is not correct. Yet still we didn’t end up with an RER of maximum 1.  These are crude calculations so do not take it as true correction methods but merely as an indication that the formulas are not correct for ramp up measurements.

“Influence of dichloroacetate on pulmonary gas exchange and ventilation during incremental exercise in healthy humans”

https://doi.org/10.1016/j.resp.2009.07.004

https://www.sciencedirect.com/science/article/abs/pii/S1569904809001876

A paper looked at estimation of bicarbonate contribution to CO₂ in healthy untrained individuals. The test was done at 2 different intensity levels.  1 level where there is no extra contribution and one where there is contribution as the intensity was between LAT (lactate threshold) and VO₂max.  They calculated the contribution from the buffer as 23% and they did not exercise to maximum effort.

If I would take our previous numbers and apply a 23% correction, thus 4.79 becomes 3.6883, then we get the following result:

before bicarbonate correction:

• FATox (g/min) = 1.67 x 3.93 (L/min) – 1.67 x 4.79 (L/min) = -1.4362 g/min
• CHOox (g/min) = 4.55 x 4.79 (L/min) – 3.21 x 3.93 (L/min) = 9.1792 g/min

after bicarbonate correction:

• FATox (g/min) = 1.67 x 3.93 (L/min) – 1.67 x 3.69 (L/min) = 0.4008 g/min
• CHOox (g/min) = 4.55 x 3.69 (L/min) – 3.21 x 3.93 (L/min) = 4.1742 g/min

Again, the idea is to run some rough calculations to see what the possible impact can be.  The paper also showed that as the exercise continued at the same intensity, lactic acid rose and therefore also the contribution of CO₂ to the buffer.

“A method for estimating bicarbonate buffering of lactic acid during constant work rate exercise”

https://doi.org/10.1007/bf00392036

https://link.springer.com/article/10.1007/BF00392036

The main takeaway point is that bicarbonate is a major contributor to CO₂ and should not be neglected. But also here we lack sufficient research to know by how much we need to correct the formulas.

Oxygen Consumption

I think the case is now sufficiently supported to cast doubt on the accuracy of the formulas for athletes engaging in a ramp up test but let’s look at it from a different angle now.

One of the reasons why we can suspect that there is more going on than just a few marginal errors will be explored by looking at an example study where the VO₂ data was provided during a ramp up test.

Highly trained professional athletes were used in the following research authored by San-Millán and Brooks.

“Assessment of Metabolic Flexibility by Means of Measuring Blood Lactate, Fat and Carbohydrate Oxidation Responses to Exercise in Professional Endurance Athletes and Less-Fit Individuals”, 2017, San-Millán, Brooks

https://doi.org/10.1007/s40279-017-0751-x

https://link.springer.com/article/10.1007/s40279-017-0751-x

Below is a reconstruction of the oxidation rate from table 2 in the study which used the same formulas from our introduction:

I first convert the grams per minute to calories per minute to see what the formulas mean in terms of caloric requirement for the given power output:

So far that looks relatively OK although there is a minimal relative reduction visible between 250 and 300 watt. Next I wanted to validate the O2 requirements.

The chart above, from the study, shows a strong linear correlation between workload and VO₂ in these trained athletes.  The caloric value/workload seems to be in line with the VO₂/workload correlation as it also gives us a fairly linear progress.

Based on the grams per minute oxidation of fat and carbohydrate, provided by the formulas, we can perform the calculation towards O₂ requirement to support that oxidation.

For example, oxidation of 1 mol of glucose yields a net gain of 38 high-energy phosphate bonds1 while utilizing 6 mol of O2, or 6.3 high-energy phosphate bonds per mole of O2. Metabolism of the fatty acid palmitate, on the other hand, yields 129 high-energy phosphate bonds2 while utilizing 31 mol of O2, or 4.1 high-energy phosphate bonds per mole of O2. Therefore, for each mole of O2 consumed, there is a 53.7% higher energy production in the form of high-energy phosphate bonds from the metabolism of glucose than from the metabolism of palmitate.

“Metabolism of Fatty Acids and Glucose”, 2018, Kessler, Friedman

https://doi.org/10.1161/circ.98.13.1350/a

https://www.ahajournals.org/doi/full/10.1161/circ.98.13.1350/a

In the carbohydrate metabolism module, we determine that the oxidation of 1 mol of glucose produces 38 ATP moles, that is, 38 x 7.4 kcal /mol ATP = 281.2 kcal. That is the amount of energy produced by 1 mol, or 180 g of glucose. In other words, 1 gram of glucose produces 1.56 kcal of energy (1.56/g glucose). For a fatty acid, such as palmitic acid, we are able to produce 129 ATP moles per mol of palmitic acid, that is, 129 x 7.4 kcal/mol ATP = 954.6 kal. One mole of palmitic acid equals 256 grams.

https://chem.libretexts.org/Courses/Brevard_College/CHE_301_Biochemistry/09%3A_Metabolism_of_Lipids/9.04%3A_Oxidation_of_Fatty_Acids

That gives us the following elements to perform the conversion:

1 mol glucose	=	180 g
1 mol glucose	generates	38 ATP
1 mol glucose	utilizes	6 mol O2
1 mol C:16	=	256 g
1 mol C:16	generates	129 ATP
1 mol C:16	utilizes	31 mol O2

And that results in the following chart:

The result is not the same linear trend.  It makes sense that O₂ requirement lowers with a greater shift towards CHOox but we saw in the VO₂/workload chart that there is a linear trend in O₂ inhalation.  What is happening with the extra O₂?  Or is there no extra O₂ and instead are the grams per minute calculations wrong for fat and carbohydrate which is supported by the material we’ve seen before?

Lactic acid and pyruvate buffers

Another factor to consider is that with increasing intensity, more lactic acid and pyruvate is produced.

Whether glucose is first converted to pyruvate on to lactic acid (anaerobic) back to pyruvate and acetyl-Coa or glucose is converted to pyruvate and further to acetyl-Coa, it does not make a difference in O₂ consumption.

What does make a difference is that with increasing lactic acid and pyruvate, this is formed to produce ATP while no O₂ is consumed and no CO₂ is formed.  This again raises questions regarding the linear VO₂.

As I’m critically investigating the formulas, I also have to wonder if this linear VO₂/workload trend makes sense.  Shouldn’t we expect that generating force gets exponentially more difficult?  Do we have a linear scaling efficiency?  The VO₂/workload seems to imply that.  Even more strange is the reduction in O₂ requirement with the increasing intensity (according to the formulas).

Instead I believe the linear O₂ represents the linear scaling of substrate oxidation but there is a missing component of anaerobic substrate metabolism which together would create a more correct exponential picture of total substrate metabolism. But as we’ve seen, the formulas are only for oxidation.

Isotopic Tracing

Finally there is one study that confirms our investigation by looking at labeled glucose as a carbon source.

The study compared all the different formulas and compared them with their own tracing results.  It should be noted that this graded test was done with increments of 10 minutes.  This is much longer than the 3 or 5 minute increments typically employed. I’ll get back to that towards the end.

In the figures below, PC and nPC stand for protein component and non-protein component.  Meaning the results are adjusted for protein or not in the different formulas.  In the result for the tracing, CHOox is not adjusted as that is where the tracing showed actual measurement but FATox is slightly adjusted as it is still based on a calculation.  The protein contribution was determined via urine samples immediately before and after exercise.

I do find the calculation results to be odd at 100% as suddenly all formulas get into agreement with the isotope, except for Jeukendrup for CHOox nPC.

Carbohydrate 

Fat

What we can see for FATox is that there is a continuous increasing trend towards 100% VO₂max and the calculations are often wrong by 0.1g/min at best and Frayn is about 0.15g/min too low.  For CHDox the formula is off by about 0.8g/min too much in estimation.

“Concordance between 13C:12C ratio technique respect to indirect calorimetry to estimate carbohydrate and Fat oxidation rates by means stoichiometric equations during exercise. A reliability and agreement study”

https://doi.org/10.14814%2Fphy2.14053

https://physoc.onlinelibrary.wiley.com/doi/full/10.14814/phy2.14053

Theory

If we look at what is presented by Jeukendrup et al.  From looking at these figures one would assume that FATox is basically shut off.

But the paper states the following explanation accompanying the above figures:

The dotted line is where fat oxidation can no longer be accurately calculated.  The point where fat oxidation = 0 in the graph represents the intensity where RER equals 1.  However, it is not possible to calculate fat oxidation accurately at that intensity.

They provided the following explanation in their paper:

As discussed above, at higher exercise intensities (above intensities corresponding to maximal lactic acid steady state) when glycolytic flux is high, the increase in (H⁺) will be buffered by (HCO₃-) and ultimately excess (non-oxidative) CO₂ will be excreted through hyperpnea.  When this occurs, the calculated rates of fat oxidation will be flawed.  We have reported that fat oxidation rates start to deviate at approximately 75% VO₂max when CO₂-dependent (indirect calorimetry and CO₂-independent (isotomes) methods are compared suggesting that at intensities of 75% VO₂max or higher indirect calorimetry may not result in accurate calculations of fat oxidation.  Fatmax, however, occurs at lower exercise intensities and the determination is therefore not affected by excess CO₂ excretion.

“Measurement of Substrate Oxidation During Exercise by Means of Gas Exchange Measurements”

http://doi.org/10.1055/s-2004-830512

https://www.thieme-connect.de/products/ejournals/abstract/10.1055/s-2004-830512

It is interesting that they pinpoint that intensity of 75% VO₂max.  This is the point at which the formulas send the FATox downwards.  In the isotopic tracer study we see that CHOox flattens out at 93%, 97%, 100% while FATox continues to rise.  In that same isotopic tracer study, FATox looks steady at 73% and 85% which is around that point where accuracy starts to fail.  

We have now seen enough evidence to support that the formulas are not correct for what they try to measure.  It does not look like FATox reaches a peak and then drops to zero as intensity further increases. Rather it will stay at that level and may further increase to support the increase in energetic demand.

There are 2 arguments that would argue against a further increase:

1. FATox does depend on carnitine for bringing it into the mitochondria which is hinder by the available CoA pool 
2. The beta oxidation process produces NADH which acts as a negative feedback for the dehydrogenase enzymes in the TCA cycle.

Let’s handle these in the next section.

NADH

Previous investigation (https://designedbynature.design.blog/2022/08/10/fat-metabolism-slows-down-the-tca-cycle/) showed me that the NADH concentration works as a negative feedback on the dehydrogenase enzymes.  These enzymes make the TCA cycle work.

What should be understood is that pyruvate depends on pyruvate dehydrogenase to form acetyl-CoA.  Fatty acid beta-oxidation produces NADH but it does not depend on a dehydrogenase enzyme to form acetyl-CoA so for fatty acids there is no negative feedback.  

This means that when the TCA cycle produces a lot of NADH, pyruvate will be diverted to lactate and fatty acid beta oxidation will continue to form acetyl-CoA.

This is likely the reason why we noted in the isotopic tracer study a flattened CHOox at the highest intensities while FATox continues to increase.

The consequence of diverting pyruvate to lactate is that the reaction with NADH produces NAD⁺ and lactic acid. It lowers the NADH level.  This lowers the negative feedback and allows the TCA to run faster.  

Lactic acid will then leave the cell which is a convenient way of disposing hydrogen (H⁺) and maintaining cellular pH. In the blood serum it will then react with bicarbonate as we have seen.

So lactic acid production is required to increase ATP output from the TCA cycle.  But in order to do that you need to divert glucose down the lactate pathway.  Thus the only other abundant source of acetyl-CoA to sustain the higher turnover in the TCA is coming from fatty acids.  

The higher the energy needs, the more glucose needs to be turned into lactic acid to increase the ATP output from the TCA when the energy needs exceed oxidative capacity versus what the NADH concentration allows for.

Is it possible that this 75% VO2max represents this zone where that NADH concentration does not allow further increase in mitochondrial ATP output and therefore we see FATox temporarily steady at this level?

Consider that glucose to pyruvate produces 2 NADH and the 2 resulting pyruvate each produce 1 acetyl-CoA and each conversion also produces 1 NADH.  So 1 acetyl-CoA derived from glucose produces 2 NADH.  For beta-oxidation, 1 acetyl-CoA requires the production of 1 NADH. In this respect, fatty acids are a better source as they produce less negative feedback.

Carnitine

The following diagram shows that carnitine requires free CoA to do its work.  As we can understand now from all of the information above, the volume of acetyl-CoA produced by both fatty acid to acetyl-CoA and glucose (to pyruvate) to acetyl-CoA drains the CoA pool and as such gets to a level where long chain fatty acids are slowed down for import.

“New insights concerning the role of carnitine in the regulation of fuel metabolism in skeletal muscle”

https://doi.org/10.1113%2Fjphysiol.2006.125799

https://physoc.onlinelibrary.wiley.com/doi/10.1113/jphysiol.2006.125799

We are looking at another negative feedback system.  If the pool of acetyl-CoA increases (and thus lower free CoA) then less of it should be produced.  It also means that the TCA cycle is running at its maximum capacity given the NADH inhibition and therefor an increasing volume of acetyl-CoA.

If we require more energy, in order to increase the TCA throughput, we have now seen that the production of lactic acid will make it possible and it will likely be proportional to the lactic acid production.  When that TCA cycle can increase then it will free up CoA faster.  This in turn gets into the free pool for carnitine to increase its delivery of fatty acids into the mitochondria for beta oxidation.

Conclusion

The material presented shed some light on the true rate of FATox and CHOox.  Researchers were already aware of the accuracy problems but nobody has come up with a good reliable measurement to adjust for the extra factors.

Historically the formulas together with the 2 arguments (against further increase in FATox) have reinforced each other as validation of the false results so there was no incentive to try and correct the formulas.

Because we know the formulas are incorrect and underestimate the FATox part, therefore the assumptions behind the 2 arguments must also be false and we have seen why they are incorrect.  They may be true up to a certain intensity level.  Yet, as we could see, the inhibition is bypassed by lactic acid production.

Lactic acid takes H⁺ outside the cell into the bloodstream which helps to maintain cellular pH but now blood pH must be protected and therefore H⁺ reaction with bicarbonate will neutralize the acidity and produce CO₂ + H₂O as a result.  Note that water formation requires H⁺ so it is another way to get rid of it.

Likely the biggest contributor to the incorrect calculation is the bicarbonate buffer of which we cannot correctly calculate by how much it interferes with the results.  

Lactic acid is relatively easy to measure.  The formulas can be adjusted for by adding in a factor that represents CO₂ production from bicarbonate through the appearance of lactic acid in the blood.

The NADH production favors FATox for high intensities as it poses less inhibition when more ATP is required.  This more complete picture now helps us understand and accept that FATox continues to rise at the highest intensities.

In addition there are other factors such as protein metabolism and gluconeogenesis of which we do not know the full extent of their contribution and how that scales with intensity.  

A final word on the problem with ramp up tests themselves.

Ramp up tests

The duration of the steps for ramp up tests is also of influence.  The isotopic tracer study incremented intensity per 10 minutes.  Other studies use 3, 4, 5 minutes.

Here’s my own ramp up test using 8 minutes per step with 40 watts increments.

From 16 to 24 minutes you see my lactic acid level go up and the level at 24 is higher than the level at 20 minutes.  This means that even though the workload was identical throughout these 8 minutes, there was not enough time to let lactic acid get to a steady state.  This means there is increasingly more H⁺ brought into the blood without flattening out during those 8 minutes.  

As a result, the time given to each step and also the increment in intensity affects the H⁺ increase and therefore the amount of CO₂ released from the bicarbonate buffer. This is less of an issue with steady state intensity where we can assume that the uptake into bicarbonate and release is in balance.

It should be clear that H⁺ is the important element in this whole story.  This brings us to another advantage of fat metabolism.  Namely that the beta-oxidation results in the production of 1 water (H₂O) molecule per acetyl-CoA produced thus it has a slightly lower production of free H⁺ compared to CHOox. 

I wonder if sweating is partially also intended to help remove excess H⁺ from our body.

I’ll conclude by saying that more research is needed 🙂

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