Doubling time: bacterial “compound interest”

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.