After checking on a few web sites I managed to follow most of your
argument. Here's one that describes the idea of z-value:
Thermal Destruction of Microorganisms
http://www.foodsci.uoguelph.ca/dairyedu/TDT.html
Actually Bacillus xerothermodurans is the same as ATCC 27380. It's
the name applied to it by Bond and Favero. There is a small difference
in the D values in the references I cited because they were measured
by different researchers Bond and Favero for one and Youvan, Watanabe,
and Holmquist for the other.
I looked over the references again and found that Bond and Favero did
calculate the z-value for the organism. It appears in the reference:
Thermal Profile of a Bacillus Species (ATCC 27380) Extremely
Resistant to Dry Heat.
Bond and Favero
Applied Microbiology, vol. 29, no. 6, June 1975, p. 859-860
"When log D was plotted against temperature (Fig. 2), a Z-value of 15
C was obtained from the best-fit regression line of data points
(corrrelation coefficient = -0.997). This value was somewhat lower
than expected, since the dry-heat Z-value of several commonly studied
and much less resistant spore cultures range from 18 to 27 C(6)."
p. 860.
They get a Z-value of 15 C, close to the value you calculated. As you
indicated this would mean very few of the spores would be expected to
survive at 300 C, a temperature at which Paul Brown was still able to
find infectivity with the scrapie infectious agent. However, Bond and
Favero do mention that the estimated survival rate becomes more
inaccurate for short time periods, say of minutes based on measured
rates at hours.
Another curious effect observed by Bond and Favero is that most
spores have higher survival rates in their natural soil than when
tested on growth media. The natural conclusion to draw is that the
soil somehow provided an insulating effect. However, Bond and Favero
tested this by using sterile soil and found this did not increase the
survival rate. The conclusion they drew is somehow the presence of the
other microbes in the soil somehow provided further heat protection
for the microbes.
This is discussed in the article:
Dry-Heat Inactivation Kinetics of Naturally Occurring Spore
Populations
Bond, Favero, Petersen, and Marshall
Applied Microbiology, vol. 20, no. 4, Oct. 1970, p. 573-578.
As they remark in the abstract to the article:
"These results question the rationale both of assuming logarithmic
death and of using decimal-reduction values obtained with subcultured
standard reference spores in the derivation of dry-heat sterilization
cycles for items contaminated with naturally occurring spore
populations."
p. 573.
Bob Clark
enigl at aol.com (Davin C. Enigl) wrote in message news:<3ca978c2.15717433 at news.earthlink.net>...
> On 1 Apr 2002 03:54:54 -0800, rgregoryclark at yahoo.com (Robert Clark)
> wrote:
>> >Thanks for the response.
>> Thank *you* for the data and for contacting me.
>> -- Davin
>> I will, below, attempt to calculate the z-values for Bacillus sp. ATCC
> 27380 and Bacillus xerothermodurands.
>> >Morphology of Extremely Heat Resistant Spores from Bacillus
> >sp. ATCC 27380 by Scanning and Transmission Electron
> >Microscopy
> >Youvan, Watanabe, Holmquist
> >Life Sciences and Space Research, vol. 15, 1976, p. 65-72.
> >ABSTRACT
> >Bacillus sp. ATCC 27380 is a recently discovered aerobic
> >mesophile, isolated from surface soil, that produces spores with
> >extreme resistance to dry heat: the length of time to 90% kill is
> >139 hr. at 125 C and 13-17 hr. at 138 C.
>> We have two sets of two D-value data-points from which to make our
> calculations. Two points are the minimum for a z-value calculation.
> We can easily see right-off-the-bat that 139hr and 13-17hr is about a
> one log reduction (in time 13 x 10 = 130, 17 x 10 = 170, actual is 139
> so it is in the same log) per 13 degrees C (from 138 - 125 = 13).
> Unfortunately, we will not be able to also get a r, or r^2 correlation
> coefficient with only two points. However, for illustration, I will
> calculate as if we have more than two points. I will convert hours
> into minutes because of the short D-values at higher temperatures.
> Later we may need to convert minutes into seconds, but for now let's
> just "think" in minutes.
>> D-values:
>> 1) 125C = 139hr D-value converted into minutes, we get 139hr x
> 60min/hr= 8340 minutes.
> 2) 138C = 13hr, which is 13hr x 60min/hr = 780 minutes.
> 3) 138C = 17hr, which is 17hr x 60min/hr = 1020 minutes.
>> [and , 4) 150C = 2.5hr = 150 minutes. I am not going to use the ATCC
> note D-value that claimed (Why is it not in the paper cited?) 150C =
> 2.5hr (150 minutes, log base-10 = 2.1761) D-value. Note that is is
> the same for B. zerothermodurans. But, if ATCC 27380, with n =3,
> gives a z-value = 14.30C and an r = -0.09968 and r^2 = 0.9936 (if 138C
> = 13hr is used), then, if 138C = 17hr, I get a z-value = 14.33, r =
> -1.000 and r^2 = 1.000 (which is the highest correlation possible).]
>> The z-value is the negative reciprocal of the slope of the thermal
> death time curve, where the D-values are expressed as log-base 10
> values. So, we convert our D-values in minutes into log base 10
> values times (still minutes).
>> 1) 8340min becomes 3.9212min for 125C
> 2) 780 becomes 2.8921 for 138C
> 3) 1020 becomes 3.0086 for 138C
> [4) 150 becomes 2.1761 for 150C]
>> Plotting this in a linear regression (least squares method), we get:
>> 1) and 2) data gives a y-intercept of 13.8164, and a slope of -0.0792,
> and the negative reciprocal is a z-value of 12.6 degrees C. So, if we
> want to lower the minutes of heat exposure by one log, we need to
> increase the temperature by 12.6C.
>> 1) and 3) data gives a y-intercept of 12.6962, and a slope of -0.0702,
> and the negative reciprocal is a z-value of 14.25 degrees C. So, if
> we want to lower the minutes of heat exposure by one log, we need to
> increase the temperature by 14.25C.
>> [Data can be entered starting with the highest D-value and proceeding
> to the lowest, since psychologically, we want increasing temperature
> and a falling (negative) slope of the line.]
>> Say we want to know how the temperature we will need reduce the spores
> down to <1 CFU, given a reasonable procesing time. If we take the
> data from 1) and 3) -- the worst data case -- and go up in temperature
> starting from 138C, here is what happens:
>> 138C + 14.25 = 152.25C. At 152.25C we will go from 3.0086 (1020
> minutes to kill one log) to 2.0086 (is about a 102 minute D-value).
> From 152.25 + 14.25 = 166.5C will give about 10 minute D-value.
> Continuing, 166.5 + 14.25 = 180.75C gives a 1 minute D-value and
> 180.75C + 14.25 = 195C gives a 1/10 minutes (6 seconds) D-value,
> finally with one more z-value added on, we get 209.25C with a 1/100
> minute (0.6 second) D-value.
>> 138C = 1020 minutes (D-value)
> 152.25C = 102 minutes
> 166.5C = 10.2 minutes
> 180.75C = 1.02 minute
> 195C = 0.1 minute (6 seconds)
> 209.25C = 0.01 minutes (0.6 seconds)
> 223.5C = 0.001 minutes (0.06 seconds)
> etc. . .
>> The reason I have stopped here is because in the Brown et al paper,
> they say the second stage of the medical waste destruction chamber has
> a 2 second residence time at 1000C. Later I will use a 10-D rather
> than a 12-D sterility assurance concept.
>> >Organism: Bacillus xerothermodurans (Bond and Favero)
> >Bacillus xerothermodurans sp. nov., a Species Forming
> >Endospores Extremely Resistant to Dry Heat.
> >Bond and Favero
> >International Journal of Systematic Bacteriology, vol. 27, no. 2,
> >April 1977, p. 157-169
> >. . . dry heat (D_125C = 139 hours, D_130C = 54 h,
> >D_135C = 24 h, D_145C = 8 h, D_150C = 2.5 h; where D = time
> >at temperature effecting 90% reduction in viable count);
>> 1) 125C = 139hr D-value converted into minutes, we get 139hr x
> 60min/hr= 8340 minutes.
> 2) 130C = 54hr, which is 54hr x 60min/hr = 3240 minutes.
> 3) 135C = 24hr, which is 24hr x 60min/hr = 1440 minutes.
> 4) 145C = 8hr, which is 8hr x 60min/hr = 480 minutes.
> 5) 150C = 2.5hr, which is 2.5hr x 60min/hr = 150 minutes.
>> Log Conversion:
>> 1) 125C = 3.9212 D-value time in minutes
> 2) 130C = 3.5106
> 3) 135C = 3.1584
> 4) 145C = 2.6812
> 5) 150C = 2.1761
>> L.R.:
> y-intercept = 12.0762
> Slope = -0.0656
> r = -0.9934
> r^2 = 0.9869
> z-value = 15.25 degrees C.
>> So, comparing the two Bacillus spores, we need (only) a z-value of one
> more degree C per a one D-value change for B. zerothermodurans than
> for the ATCC 27380 Bacillus sp. (15.25C vs. 14.25C respectively).
>> 150C = 150 minutes (D-value)
> 165.25C = 15 minutes
> 180.5C = 1.5 minutes
> 195.75C = 0.15 minute (9 seconds)
> 211C = 0.015 minute (0.9 seconds)
> 226.25C = 0.0015 minutes (0.09 seconds)
> 241.5C = 0.00015 minutes (0.009 seconds)
> etc. . .
> --------------
> So, for ATCC 27380, if we start with an absolute count of 10^10 spores
> (10-D sterility assurance concept for food canning), we would expect
> at 223.5C, 10 logs of spores x (times) the D-value of 0.06 seconds =
> 0.6 seconds to kill down to the <1 CFU level.
>> And, for B. zerothermodurans, if we start with an absolute count of
> 10^10 spores, we would expect at 226.25C, 10 logs of spores x (times)
> the D-value of 0.09 seconds = 0.9 seconds to kill down to the <1 CFU
> level.
>> We, need a higher temperature (or more time, or in the above example .
> . . both) for B. zerothermodurans to get the same count as ATCC 27380.
>> [We do this with "naked" spores on a flat surface such as an aluminum
> self-adhesive tape. The entire tape is removed from the oven and
> cultured in a special liquid spore-recovery broth. We usually use two
> spore count levels, 10^5 and 10^6 CFU.
>> Using the count level target of "<1 CFU", on repeating this
> experiment, I would expect at least one sterility test would be
> positive in ten-thousand runs, because this is like a "most probable
> number" method, the standard is actually 3 positives/10,000 at 10^6.
> In practice we use a sterility assurance level that gives us . . . 3
> or fewer positives in 10,000 tests with a 6-log inoculum of spores.
> 10^6 using 10^4 = 10^10.
>> ******************************************************************
> ==========
> How to calculate these linear predictive models:
>> The temperature required to decrease the spores by one log (which is a
> 90% reduction) is called the "z-value" and is used in heat processing
> of food. For instance, if 125C has a D-value (kills one log, 90%) in
> 139hr (8340 minutes) and 138C has a D-value of 17 hours (1020
> minutes), after converting the D-value times into log base-10, then
> the "z-value" is the negative reciprocal of the slope of the linear
> regression line formed by these two points which is 14.25 degrees C.
>> 1. Clear summation registers.
> 2. Type-in the highest log base-10 of the D-value: 3.9212
> minutes, press enter.
> 3. Type-in the temperature for that D-value: 125C, press
> summation
> 4. Type-in the lowest log base-10 D-value: 3.0086 minutes, press
> enter.
> 5. Type-in the temperature for that D-value: 138C, press
> summation.
> 6. Press L.R. to get y-intercept. 12.6962
> 7. Press exchange x<>y.
> 8. Slope is displayed: -0.0702
> 9. Press 1/x to display the reciprocal of the slope: - 14.2450
> 10. The negative of this is: 14.25 degrees C. This is what we can
> call a z-value in degrees C.
> 11. This is the temperature needed to lower the D-value by one log
> (log of the minutes).
>> The above is for the HP11C calculator.
>> The z-value is common to heat processing. It finds the temperature
> required to lower the exposure time by one D-value (here, the D-value
> are expressed in logs base 10.) We however, measure our D-values in
> time i.e., hours, minutes, or seconds.
>> This is useful since you can now "tailor make" a heat process and be
> close to what you want from the start. Then, you perform a
> validation, because, sometimes the real-world does not match the
> mathematical idealized formulas.
> ---------------------------