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Doubling time: bacterial “compound interest”

By Dr. Davis | April 24, 2020 2 Comments

Remember the kids’ riddle that asks “Would you rather have a penny that doubles each day for a month or $1 million?”

Of course, most kids choose the $1 million. But the penny that doubles every day—$0.01,$0.02, $0.04, $0.08, $0.16 . . . ends up totaling over $5,368,709. Hard to believe at first, but that is the power of doubling or, as financial people call it, “compound interest.”

The same mathematical phenomenon applies to bacterial doubling time: the longer time passes, the more the growth in bacterial numbers: 1, 2, 4, 8,16 etc. (For simplicity, we assume that bacteria don’t die. Of course, this is not true, but the basic principle of increasing numbers over time still applies.)

If graphed, the growth of money—and bacteria—look like this:

(From Jago Trader on compound interest)

One of our favorite bacterial species, L. reuteri, doubles every three hours or so at 100 degrees F, while L. casei that protects us from respiratory viruses doubles every 90 minutes. Replace the days on the X-axis with increments of 3 hours (i.e., 12 doublings) and you have the graph for bacterial doubling time. From the trajectory of this curve, you can surmise that:

  • There is very little increase in bacterial numbers during the first 30 hours of fermentation, the period along the horizontal part of the curve. (Hour 30 coincides with day 25.)
  • There is exponential growth in bacterial numbers starting around hour 30, with faster and faster growth from 30-36 hours.

Why not ferment longer than 36 hours? Although we have not performed thorough analyses, it is likely at some point that all available resources (lactose, prebiotic fiber, etc.) become exhausted and die-off exceeds doublings. Longer times also risk allowing fungal species to appear, since they inevitably seed the yogurt from the air and utensils.

You can also appreciate that, because commercial yogurt is typically fermented for only 4 hours to hasten production, it means that trivial bacterial counts are achieved. It explains why yogurt you buy in the supermarket (with rare exceptions) achieves almost nothing in health benefits.You can boost numbers by starting with higher numbers, but the relative contribution of higher starting numbers are dwarfed by the enormous numbers achieved via extended doubling.

It also means that using my method of lengthening fermentation times and feeding bacteria with prebiotic fibers, not only do you achieve a much richer, thicker end-result, but you also achieve tens to hundreds of billions of bacterial counts that yield real and substantial health benefits.

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Filed Under: Wheat Belly Lifestyle Tagged With: casei, Fermentation, fermented, microbiota, probiotic, reuteri, Weight Loss, wheat belly, yogurt

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About Dr. Davis

Cardiologist Dr. William Davis is a New York
Times #1 Best Selling author and the Medical Director of the Wheat Belly Lifestyle Institute and the Undoctored Inner Circle program.

Nothing here should be construed as medical advice, but only topics for further discussion with your doctor. I practice cardiology in Milwaukee, Wisconsin.

Comments & Feedback...

  1. coldfeat

    April 24, 2020 at 12:08 pm

    Hi

    Maybe I am wrong but doesn’t the volume of half and half figure into this. For example, if you put 10 crushed probiotic pills into 16 oz of half and half versus 32 oz of half and half, wouldn’t that put one doubling in the bank, so to speak. Make that 10 pills into 8 oz. and you’ve got a second doubling. Going the other way, how long would it take 10 pills to turn a GALLON of half and half into “yogurt?’ Been thinking about this because you can turn the starter yogurt into additional yogurt in 5 or 6 hours and it’s usually smoother.

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    • Bob Niland

      April 24, 2020 at 3:15 pm

      coldfeat wrote: «…doesn’t the volume of half and half figure into this.»

      Yes, in terms of the final CFUs per portion.

      The yogurt-like recipes in the WB and Undoctored programs are nominally based on 1 quart or liter. So for a tablet start based on Biogaia® Gastrus®, it would be 10 tablets in 1 qt. If you dilute it by using a half gallon, you’ve lost one doubling period.

      Likewise, you could gain advantage by using more tablets, but it’s expensive.

      I seed my batches (usually ½ gal.) using saved whey, or dedicated saved yogurt, frozen in ice cube trays, and slowly thawed for use. At 2 cubes/qt., these hit the ground running at dramatically higher CFUs, resulting in smooth yogurt and nil whey separation.

      re: «Been thinking about this because you can turn the starter yogurt into additional yogurt in 5 or 6 hours and it’s usually smoother.»

      I’ve never been happy with the results of shorter times (under 24h), no matter how started. I suspect there is more going on than mere population growth in the extended time suggested. Indeed, I run my batches out to 48 hours, but I also double the prebiotic buffer used (inulin) which so far seems to have dodged any die-off effects.
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