Calculating the rate for oxidation for 13C breath tracers

Hello, my name is Ken McKenna and today I want to introduce you to calculating the rate of oxidation for carbon-13 breath tracers using data collected from Sable Systems’ Stable Isotope Analyzer. In this talk, I will show you how to combine information about total rates of carbon dioxide production with simultaneous measurements of carbon-13 levels in breath to calculate the rates of tracer oxidation.

In order to calculate the rate of carbon-13 labeled tracer oxidation, one first needs to know the VCO2 and the level of carbon-13 enrichment in the exhaled carbon dioxide at all times. The macro-output of the Promethion system will give VCO2 in milliliters per minute and carbon-13 in breath in terms of per ml. However, these carbon-13 values should not be confused with the actual rates of carbon-13 tracer oxidation which is a mathematical product of VCO2 and carbon-13. This means that even if the carbon-13 in exhaled breath remains perfectly constant over time, the animal is not necessarily oxidizing the carbon-13 label tracer at a constant rate. This second graph illustrates that the actual rate of tracer oxidation is linearly dependent on VCO2 and can vary widely, even if the carbon-13 signal is not changing.

In this example, a single mouse was given identical doses of glucose tracer at 30 degrees Celsius and at 10 degrees Celsius. Note that following the dosing, the raw carbon-13 in breath is substantially lower in the 10 degrees Celsius mouse. However, not surprisingly, the metabolic rate is also higher at 10 degrees Celsius. To account for the differences in metabolic rate, multiplying carbon-13 by VCO2 gives the actual rates of tracer oxidation. The bottom graph illustrates that the rate of glucose oxidation at the two temperatures is far more similar than the carbon-13 signal alone would indicate.

In this experiment, a single mouse was given identical doses of the same carbon-13 tracer for fructose under different experimental conditions. Note how carbon-13 in the breath varies, but VCO2 does not.

In this case then, the rate of tracer oxidation differs solely because of differences in the metabolism fructose.

If we examine a larger data set using eight mice and an even larger temperature range, we see a similar response. Again, note that carbon-13 in the breath is higher at 30 degrees Celsius than it is at 5 degrees Celsius.

At the same time, metabolic rate or VCO2 is over two-fold higher at five degrees Celsius. Multiplying VCO2 by carbon-13 we see that the rate of circulating oxidation at five degrees Celsius is only slightly higher than it is at 30 degrees Celsius. This outcome actually shows that the same mice exposed to cold temperatures are not fueling their increased energy demands using glucose, but rather another fuel (presumably lipids). We will use this data set to take you through the specific calculations that are needed to determine actual rates of tracer oxidation so you can examine carbon-13 tracer oxidation using other experimental interventions and other types of carbon-13 label tracers.

Here is the general equation for calculating the instantaneous rates of carbon-13 tracer oxidation. In order to get specific rates of oxidation in nanomoles per minute, we need to know the carbon-13 in the mouse prior to dosing and the carbon-13 at any given time.

This difference is considered in a unitless value called atom fraction excess or AFE. The background carbon-13 value is the average of carbon-13 in the breath prior to the administration of a carbon-13 tracer. This average must be converted to atom percent following the formula using Pee Dee Belemnite as a standard for the carbon-13 to carbon-12 ratio. Each individual sample measurement must also be converted to atom percent. Once all sample values are in atom percent, we can subtract the background atom percent from each sample atom percent to give us the atom percent excess. To convert atom to atom fractional excess we simply divide atom percent excess by 100.

There are two terms found in the denominator of this equation. K refers to the volume of carbon dioxide produced per gram of tracer oxidized, thus having the units of milliliters per milligram or liters per gram. In practice K can be calculated using the second equation that incorporates the ideal gas law; the number of carbon-13 atoms in each tracer molecule and carbon losses in nitrogenous waste. Most animals will not be oxidizing a given type of molecule exclusively, but rather some infinitely complex mixture of various metabolic fields at any given time. Fortunately, K is relatively insensitive to changes in RER for a given experiment and can be approximated with a value of 1. M is the molar mass of the carbon-13 tracer used and it is used to convert grams of the carbon-13 tracer into moles of tracer.

One additional factor one must account for is the number of carbon-13 atoms in the tracer. The more carbon-13 atoms, the greater the signal for a given dose. We therefore need to account for this. To do so, simply divide T by the number of carbon-13 atoms. In this example, the U-carbon-13 glucose tracer has six carbon-13 atoms while the 1-carbon-13 glucose tracer has one carbon-13 atom. Note how the magnitude of the carbon-13 trace for the U-carbon-13 glucose tracer is almost exactly six times that of the one carbon-13 tracer. Together these calculations demonstrate that VCO2 and the number of carbon-13 atoms contribute significantly to the rate of tracer oxidation.

We hope that you have found this tutorial useful. Here are useful references that show real-world applications of carbon-13 isotope calculations for a multitude of tracers.