Coversion of ppm to mg or mg/kg

I have been trying to understand what ppm stands for and how it relates to rapamycin dose in mg or mg/kg but I don’t really get it. I know that ppm stands for “mg of drug per kg of food”. So 42 ppm is 42 mg of rapamycin per kg of food. But what amount in kilos do a mice eat per day?

If we look at for example at this study. I can’t find the amount of food they ate. This feels little bit strange and it would have been quite easy to measure that or get some kind of average indication of the amount per day. Or is it some other way to convert the ppm to a rapamycin dose in mg or in mg/kg?

UM-HET3 mice housed at UT were fed control, 4.7, 14, and 42 ppm rapamycin diets

ppm stands for “Parts Per Million” - see here:

https://www.adelaide.edu.au/arcpoh/dperu/fluoride/ppm.html

That was the concentration of rapamycin / sirolimus in the food they were feeding the mice.

You have to convert that to mg/kg in terms of dosing that the rats actually received per day I think.

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Is this aligned with what is said in the study above

They were housed at three male mice or four female mice per cage from weaning and at 9 months of age were given a diet containing encapsulated rapamycin at 4.7, 14, or 42 ppm (mg of drug per kg of food)

I tried the below online calculator from ppm to mg/kg. The result was 42 ppm is 42 mg/kg. Does that sound right?

https://www.easycalculation.com/unit-conversion/ppm-mg-kg.php

Its interesting… your calculations are correct, but I think the issue is that we are talking about two different things.

ppm is the parts per million of the total feed the mice are getting that is rapamycin. So, in your example, 42 parts per million in the feed were rapamycin.

But when we talk of dosing specific to a given trial, I believe they usually are quoting the dosing per kg of weight of the mice (not the food) - so its a completely different denominator in the calculation…

for example, in the transient dosing trial of rapamycin at University of Washington they used as high as 8mg/kg - which I interpret as 8mg of rapamycin per kg of mouse weight, and I believe they may be saying that is equivalent to 126ppm - in this table 1 of the document. let me do a little more research on this… I may be wrong.

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OK - so here in the U. Washington Transient Rapamycin paper it says:

We initially used a treatment regimen consisting of intraperitoneal (i.p.) injections of 8 mg/kg rapamycin daily for 90 days. This dose was selected because we have previously found that it increases survival and alleviates disease phenotypes in short-lived mouse models of dilated cardiomyopathy, muscular dystrophy, and the severe mitochondrial disease Leigh Syndrome.

Based on efficacy in the Leigh Syndrome mouse model and serum drug levels in wild type mice, we estimate that this treatment regimen is comparable to dietary delivery of eRapa at approximately 378 ppm (Johnson et al., 2015), or 27-fold higher levels than initially shown to extend lifespan in mice when continuous treatment is initiated at either 9 months or 20 months of age.

So - in this case they are saying that the 8mg/kg injection of rapamycin is approximately equivalent in effect to 378ppm of food-based rapamycin.

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The paper they reference (Johnson et al., 2015) is this one:

C, Johnson BM, Letexier N, McCanta L, Sangesland M, Tamis O, Uhde L, Van Den Ende A, Rabinovitch PS, Suh Y, Kaeberlein M. Dose-dependent effects of mTOR inhibition on weight and mitochondrial disease in mice. Frontiers in Genetics. 2015;6:e16351. doi: 10.3389/fgene.2015.00247.[PMC free article] [PubMed] [CrossRef] [Google Scholar]

and in that paper they state:

To assess the efficacy and effects of high-dose dietary rapamycin, control and Ndfus4 KO animals were fed chow containing 42, 126, or 378 PPM rapamycin beginning at weaning

Levels of circulating rapamycin increased in a linear manner from 14 to 126 PPM at a rate of approximately 3.2 ng/ml serum rapamycin per PPM dietary rapamycin increase, with linearity decaying between 126 and 378 PPM.

Dietary rapamycin reduced developmental weight gain in a dose-dependent manner in control animals, with strength of effect ranging from no observed impact at 14 PPM (data not shown), to a robust and highly significant reduction in body size at 378 PPM that is similar in magnitude to what we previously reported for daily injection of 8 mg/kg

Interesting conjectures on the rapamycin / Blood Brain Barrier issue that is widely discussed with regard to higher doses…

High-dose injection provided the greatest benefit to survival in the Ndufs4 KO model while oral rapamycin at 378 PPM had the strongest impact on developmental weight gain (Figures 3C,D); the bolus provided by injection provides an enhanced benefit over steady dietary delivery in the mitochondrial disease model, perhaps by overcoming blood-brain barrier. Daily IP injection of rapamycin at 8 mg/kg alters neural activity associated with aging (Yang et al., 2012) and robustly reduces whole brain levels of phospho-s6, an indicator of mTOR activity

Effective inhibition of mTOR in the brain may be necessary for the full benefits of rapamycin in both Ndufs4 KO mice and in normative aging.

ah - and yes - here in the paper it confirms my previous understanding of the different dosing calculations - one is food-based, one is mouse-weight based, and here they are identified as equal in terms of the the effect on circulating sirolimus/blood levels:

378 PPM dietary rapamycin (378 ug rapamycin per gram-food) is 27 times the dose used by the ITP, while IP injection requires only 8 ug un-encapsulated rapamycin per gram-mouse weight to achieve comparable circulating levels.

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Great, and if we look at what dose 1mg/kg than that is equal to 47,25ppm (almost 48ppm) as in the study above. The calculation for this is 378ppm / 8 mg/kg = 47,25ppm

Then we come to the conclusion that 1 mg/kg is 47,25ppm. If we now try to calculate the dose on the body weight of the mice for a male in the study at 6 months of age than the weight was around 40 grams (figure 2 in the study). Does this mean that the mg dose for the mice daily was 0,004mg? The calculation for this is 1mg/kg / 1000 = 0,001 mg/gram. 0,001 mg/gram x 40 gram body weight = 0,004 mg of rapamycin daily. It feels like this is wrong. The dose is too low per day or?

Hmm, this calculation seems little bit more right. 42 ppm is 42 mg/kg.

42mg/kg / 1000 = 0,042mg/gram

0,042mg/gram x 40 gram body weight = 1,68 mg/daily

1,68 mg/daily * 7 days = 11,76 mg/weekly

Is this right or is the previous calculation more correct?