Barrett, M. J.

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INVESTIGATIONS n ... ro A. 
DIFFUSION K)DEL OF 
DRY BEAT STERILIZATION 
Interim Report 
Contract NASw-1734 
for 
Rational Aeronautics and Space Adminis tration 
Of lice of Biosciences 
Prepared by 
M. J. Barrett 
May 5, 1969 
EXOTECH INCORPORATED 
Systems Research Division 
525 School Street, S.W. 
Washington, D.C. '20024 
1105 
TRSR-041 
, . 
ABSTRACT 
The analytical model described in thi9 study formalizes the hypothesis 
that dry heat inactivation of microorgan~sms is closely related to the 
water content of the spore and its micro-~~v1ronment. Exper:~ntal 
data are examined relative to this model and it appears to be valid. 
This model ib aimed At overcoming the well known defici2ncies of the 
logarithm model. 
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INTRODUCTION 
Seva':al recent investigations have related environmental con-
ditions other than temperature to miCTobial 8por~ survival under heat 
aterilization. &-turrell and Scott, Angelotti, and RE'id have shown strong 
dependency of dry heat death rates on ambient relative humidity and on 
water content of the spore*. Hunnell and Ordall have fmlnd that hf'nt causes 
.pores to exude calcium and dipicolinic acid (DPA) prior to dE'llth. witHe 
Alderton, Thompson, and Snell show that spores i!l. aqucNls SURpenl'lio!l hAVE' 
improved heat resistance when calcium ions are present. 
In aJdition to these correlations with environmental conditions 
during sterilization, spore survival shows correlations with environment.11 
conditions that prev(.i1ed when the spore formed. Vinter shows l.eat re-
sistance is affected by calcium and cystine availability during sporulation; 
Murrell and Warth show correlations of heat resistance with five diffE'rent 
s~bstances found in the spore. 
These investigations show the importance of cnvironment on heat 
6terilization charaCi:eristics. A simple chemical reaction does not appear 
to be the complete me~ltanism for spore destruction. Rather, a sequence of 
transport of chemicals, notably water, occurs and modulates the rate at 
which chemical reactions destroy the viability of the spore. 
In this report we present a diffusion-denaturation nodel of 
spore heat resistance that actempts to correlate vith the water effects 
observed, and to provide 6 basis for determining the efficiency of proposed 
dry-heat sterilization plans. Such a model is immediately useful in a dry-
heat £terilization program, and also offers promise of eventual under-
standing of the remarkable resistance of spores to heat. 
*References are listed at the end of this report. 
------
DIFFUSION MODEL 
A model to predict the water content of a sp0re as a function 
of time, temperature and initial water concentration w;thin the spore 
ha. be.~ developed. The Ae8umptione mada are that heat deactivation in 
spores is due to protein denaturation and that the rate of this reaction 
is controlled by the water con~ent of the spore core. 
A spore is composed of an outer coat (cortex plus spore coats) 
and a central core (cytoplasm) which is the dormant micro-organ{sm. The 
r.ortex protects the core from physical damage, chemical contamination 
and rapid w~tting by the environment. The cortex is mainly composed of 
mucopeptide polymers CWarth et aI, 1963) with the chains twisted and 
coiled or interwoven (Mayall and Robinow 1957). Th~ coat is mainly pro-
tein with a high cystine disulphide bond content (Vincer 1961). 
The heat resistance of spores is assumed to rest in the ability 
to control the amount of water internal to the spore. A contractile cor-
tex system (Lewis~ Snell snd Burr 1960) would provide a mechanism to de-
hydrate the Qytoplasm and maintain it in this state. Chemical val'iation 
in the mucopeptide of the ccrtex and in the amount of Cu ++ or Ca-DPA 
(Young 1959) binding to the mucopeptide which may cause the contraction, 
rould result in differences in the degree of contraction .and therefore in 
the final water content of the apore, resulting in ma~k~d difference in 
heat resistance. 
In the development of this diffusion model we have assumed a 
simplified spore structuLe composed of an outer coat of negligible thick-
ness at a radius surrounding a ~pherical, homogeneous 0nc. 
Water transport thru the spore can be descrihed by the well known 
diffusion equation 
(1) 
where C is the concentraticn of water/cm3 , as a function of po~ftinn ~nd 
time. 0 is a diffusion coefficient depending on the medium. 
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cytoplasm 
vcell coat 
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-.-
----'-
cortex 
Figure 1. !-:Orie 1 of Spore 
1. 
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- ---_._------- ---- -----.-----. -. -
For a simple example, assume the initial water content in a 
spherical spore is distributed radially according to 
b ~ TTr rC(r) ~ - sin --- -
TT . b \sin 2:r J (2) 
where C(r) is the water concentration at a distance r from the center of 
the 'pore, and b is the radius of the .pore (see Fig 1). This expression, 
as seen in Figure 2, corresponds to a distribution that is peaked in the 
outer portion of the spore, and can be coneidered as approximating the 
case where a spore contains more water than an optimum amount. This ex-
cess water is stored in th~ cortex. 
Applying the diffusion equation to this initial distribution re-
sults in the time variation shown in Figure 3. Water diffuses inward to 
the cytoplasm, and the spore gradually loses water to the medium. As a 
result, the initially-dry central region reaches a peak concentration of 
water that occurs around a time t given by 
~ 1.5 (3) 
where D is ~~e diffusion coefficient of the sys~em. This simple model 
assumes D to be :-dependent of position. As a result, it approximates the 
situation when the s~'re is burie~ !n an appropriate medium, since norma1iy 
one would expect ~he dif£u~{on coefficient of water outside Cl spore to dif-
fer from D inside the spore. 
Data have been reported by Angel6tti (1966) for the thermal ster-
ilization of spores in 1ucite. These data (Fig 4) indicate the death rate 
to he greatest at about 1.5 hours after cormnencing to heat the spores at 
12SoC. Using this value for t, in the above equation, we arrive at an es-
timate for the diffuaion coeffi6ent at 12SoC: 
-6 2 D r:: 1.2.10 (cm Ise~) (4) 
Thie estimate is in reasonable agreement with values for diffusion of protein 
molecules in water (Clark, p. 138). Our example requires the opposite: water 
molecule diffusion in protein, which has an unknown diffusion coefficient, 
B 
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nC 
2.2 
2 
1.8 
1.6 
-
1.1 • 
1.2 
1 
.8 
. /) .. 
.4 
.2 
.2 .4 .6 .8 
( ~) 
Figure 2. Water ['istri~utio:;, i!1 the Spore 
For t=o, b [ n r rC = - sin-TT b 
1 . 2nr] 
- '2 Sl.n ~ 
• , 
1 
...,... .. 
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TTC 
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1.8 
1.6 
1.4 
1.2 
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--_._-,-- _._. ------,----
.2 .6 
kt 
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1.2 
--r-
1.4 
Figure 3. Concentration of Hater. at center of spore. as a fUllction 
of heating time. 
1. 
-------------------- - --.---... --.... ----_ ... -..._ ...... _-_. --
1 
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1/). 
(hra) 
7 
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4 
3 
2 
1 
1 2 
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3 
T --'~-l--'·r-l-.. I---r---.-l 
4 5 6 7 8 9 10 11 12 
t (h1"s) 
Figure 4. Apparent chanGe in resistance of B. globigii 
in lucite after times E in hours at 1250 C 
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and f'urthe ..... aS11:" .lS this coefficient doeR not differ ,:n'atly from wat£'r 
diffusion in luctte. 
One method of evaluclting the diffusion coeffIcient, whi ch is 
necea5ary 1f • diffusion model is to bcapplicd to dry sterilizntion, i. 
to lock at wet sterilization curves. Such curves are shown 'tn Figure 5 
for four temperatures. Tn wet he&t, the spores should absorb water to 
some maximllm. Then, the denaturation of proteins in the spore, wi.th this 
water preBcnt, results in a straight logarithmic curv~ for survivors, as 
a function of time of heating. 
Such a description fits the curves shown. The knee of each 
curve repre~~nts the time at which the cytoplasms of the spores are in 
equilibrium with the external water. For a purely exponential buildup of 
water, this occurs about when three relaxation times have passed, accord-
fng to d1ffu(~ion kinetics. The diffusion coefficient calculated by this 
method can be fitted to a formula 
r H = 60 !< cal 
D H/RT where ~ R = 1.98 D= e , T temp(' Ta ture (OK) (5) 0 = D := Constant 0 
Results of the calculations are shown in Figure 6, to[ethAr with the diffu-
sion coefficient calculated as Eqn. 5. The two sets of experiments seem 
to be in fair agreement, and indicate initial success in applying a diffu-
sion model to the data. 
-,--.. ~ ..... - ..... -'-''"i'-".-~ __ .~-""" -_ .. ,.~ .... , ",'." - . __ .- --- -_._------_ .. 
, ,5"l 5-J ~ .. " ~ 
] T .. i/oC D 12 12 hr 
] 4 \ 4 ~ ~ III III ) J ~ ~ 
III III 
.-4 .-4 
l ,tJ ~ :1 .... r> r> T • 95°C 
00 3 tID 3 
. .9 
.9 D - 32 nd.n .. ] 
.J 
J 2 2 - -f'~- ,---.------, ·--r· .. ,--, 0 1~ 20 30 40 50 60 70 80 0 20 40 nO 80 100 11.0 1:.0 1GO 
TilDe" (hr) Time - (min) 
a 5- 5~ 
I T 0:: 104°C T co 1210C D loa 14 min D .. 0.50 min 
a 
4 J 
D 
4 
~ ~ 
a III CII .0 .0 ~ . 9 
z Z 
III III 
a rf 3 rf ,.D ,.D 3 III III 
.... .... 
> > 
s· 
b/) 00 
.3 .9 
D 2 2 
I I --, I I I I I , ,--, 
D 
0 10 20 30 40 50 60 70 80 0 10 20 30 '.0 50 60 70 80 
Time 
-
(Din) Time 
-
(aee '. 
Figure r ~. Wet Sterilization Curves (Data from Fox, Edcr and Pflug 1967) 
) 
;1 
J 14 
.J 11 
12 
1 11 
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• 9 
8 
.., 
Cd 
'J ~ ~ 0 
.... 
• 
7 1 =' 'H "" .... A 
6 eo 1: 
0 5 
• 
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.... 
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2 
1 1 
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0 
A in luci~t::: 
[ 
2.50 2.55 
Figure 6. 
----.£ 
--'- ----
2.60 2.65 2.70 2.75 2.80 2.85 
_. 1 3 
•. 10 
T 
Ilog Dl plotted versus lIT 
(Estimates ~ased o~ wet heat data by Fe.x, Eder, Pflug) 
(A: estiJaate from dry heat, by An.gelottl) 
... _------ ~ --- -- ---- ---- ------
r 
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IMPLICATIO .. S OF THE K>DEL 
The correlation of water activity with spore resistance in-
dicates that the death mechanism is a denaturatbn of some vital pro-
tein. Much the .... correlation h •• bee~ observed between protein de-
naturation and water content. Furthermore, the reaction is generally 
of first-order kinetics, resulting in a logarithmic curve zuch as is 
frequently sean for thermal die-off of spore populations. 
The vital protein is clearly in the cytoplasm, since the 
outer portions of the spore, shedded during germinati"J!1, are not vital. 
This outer portion, the cortex, appears to squeeze water from the cyto-
plasm durir~ the formation of the spore, and thereby provides that there 
vil~ be a residual concentration that is near the optimum for heat re-
sistance. 
Part of the beat resistance of spores has been shown to be 
due to calcium dipicolinate, manufactured during the formation of the 
spore, and present in the cytoplasm. Ca-DPA is a chelating agent. Pre-
sumablyp the vital protein hds sensitive bonds that are protected by 
Ca-DPA and other sensitive bonds protected by water molecules. 
Germination of the spore presumably requires that the protein 
be rid of these protections. Excess water c~n remove the Ca-DPA; the 
attached water molecules may separate thermally~(heat shock). These 
separatioD3, if reverSible, would be of little help to germination un-
lesf: the protecting molecules str:f.pped from the protein were to ·leave 
the cytoplasm. This is the argument for diffusion: it allows proteins 
to react with enzymes, etc., in the germInation process without hin-
drance from the former bond-protecting agents. At the same time, the 
proteins become more sensitive 1;0 heat. 
Diffusion is the rarti,om movement of molecules. It is charac-
terized by straight-line paths between molecule interactions, and arbitrary 
change of directicn after the interaction. The net result of the ran-
dom motion is a movement of lII.,lecules from regiOns of high density t) 
regions of low density. FrecLuently, these interactions are mere colli-
sions. In such a case. thf! diffusion constant D is po:-oportional to 
temperature. A less frequent situation is wh~r~ the collisions involve 
chemical reactions. The molecule moves tn a straight line, collides 
and "sticks" to a fixri obstacle, is freed by the action of heat, and 
moves off in an arbitrary directi~n. This kind of diffusion, charac-
terized by a diffusion constant as given in Eq. 5, appears to fit the 
process of water diffusing through thE spore cortex. 
The environmental conditions prevaUing dudng .por~ forma-
tion have been shown to affect the subsequent resistance of the spore to 
heat. This, too, is as the model would imply. There is no known 
mechanism by which tbe spore can control the water concentration in the 
cortex and spore coats. As a result, the moisture content of these 
regions will vary 80 that they are in equilibrium with external con-
ditions. When the spore is heated, the contents of theB~ regions can 
diffuse inward and outward to affect the heat sensitivity of the spore. 
These two mechanisms - diffusion and chemical rEactions of 
proteins - appear responsible for the survival probability of spores as 
a fun~tion of humidity, temperature and time. Much work remains in the 
analysis of their quantitative aspects. What are the equilibrium moisture 
contents of spores? What is the water distribution inside the spore? 
What are the surface transfer properties? Does the Ca-DPA diffuse, too? 
What is the protp.in denaturation reaction that occurs? ~ many pro-
tein molecules must denature before the spore becomes nonviable? The 
answers to these questions require further study. Many pravious experi-
ments, unfortunately, are of U.ttle help since not all the pertinent 
variables were measured. 
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RECOMHE;NDATIONS FOR FUfURE WORK 
1. Moisture Cont~nt Analysis 
Measurements of the ~:l.stlt~·e content of spores arc nceded. 
For ea.~ in comparing results of different environments. only on~ 
species (B. s·,btilis var. niger is the accepted norm) should be used 
and standard harvesting, washing, and drying procedur~s employed. Se-
lection of procedures is a subject for discussion, bu'- Rtandard ;7.at fon 
vill permit studies of the results to be concentrated on the envIron-
mental effects. 
The envirotlJllents to which thE spores are equilibrated can 
vary in temperature, in humidity, and in length of time of equiHbration. 
Down-side and up-side equilibration need separate stuclies, in view of 
the ''hysteresis'' effect observed. The rate at "hich spores give off 
vater during an analysis, together with the cumulative water emission, 
ahouldo be measured. 
These measurements should be analy~ed to see whether they con-
fo~ to the hypotheses discussed in this report. Evaluations of dif-
fusion coefficients and surface transfer effects should be possible. 
2. Correlation of Moisture and Sterilizability 
~ heat sterilization, with moisture content as a parameter, 
has b~enomeasured with uncertain results. The understanding gained 
from the analysis above should provide benctmarks for future measure-
ments of spore sterilization rates. The early work s~m~~imes suffered 
from a lack of determin~tion of the pressure or the relatiVe ~umidity 
during sterilization. The substrate deserves attention: if it has 
good water transference properties it can affect the experiment signi~­
icantly. 
With knowledge of moisture transfer properties in the ~pore, 
on i:s s\.&dace, and through the eavirorunent, it should be possible to 
13 
design crucial experiments where the moisture content and temperature 
of the spores are known quantities. The die-off of spores under these 
conditions should be measured. Such experiments include: 
(a) Spores i~ vacuum. The moisture .transfer outside the spores 
Is a relatively easy calculation. 
(b) Spores in non-permeable materials (e.g. epoxy). With different 
initial moisture contents, spores hould show different die-offs, but 
each experiment should provide ne~rly logarithmic curves. 
(c) Spores in air. MOisture transfer is affected by the relative 
humidity and this can be varied in a sequence of experiments. 
(d) Spores of different initial Aw in air. 
----~ ~-- - - -- -
- .. . 
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REFERENCES 
1. Alderton, G.; Thompson, P. A.; and Snell, N.: "HE'at Adaptation and 
Ion Exchange in Bacillus Megateriure Spc~~s"(l964) Science 143, 141-143. 
2. Ana_lotti., R.: "Ecology and Thennal Inactivation of Microbes in and 
on Interplanetary Space Vehicle Components" Fourth Quarterly Report 
of Progress on Rese.1rch Project R-36-015-001 March 1966, 1967, 1968. 
3. Black, S. H.; Hashimoto, T.: and Gerhardt, P.: "Calcium Reversal of 
the Heat Susceptibility and Dipicol1nate Deficiency of Spores Formed 
Endotrophical1y in Water" (1960) Can. J. Microbiol 6 212-224. 
4. Clark, W. M.: ''Topics in Physical Chemistry" p. 138 (1948) The 
Williams and Wilkins r.o., Baltimore. 
5. Halvorson, H. and Howitt, C.: ''The Role of DPA in Bacterial Spores" 
(1961) Spores II H. Halvorson (ed) Burges Publishing Co., Mir.neapolis. 
6. Hunnell, J. W. and Ordall, Z. J.: "Cytologica_1 and Chemical Changes 
in Heat Killed an~ Germinated Bacterial Spores" (1961) Spores II 
H. Halvorson (ed) Burges Publishing Co., Minneapolis. 
7. LewiS, J. C.; Snell, N. S.; and Burr, H. K.: '~ater Permeability of 
Bacterid Spores and the Concept of ~ Contractile Cortex" (1960) 
Science 132: 544-545. 
8. Maynall , B. H. and Robinow, C. F.: "Observations with the Electron 
Microscope 'on the Organization of the Cortex of Resting and Germinating 
Spores of Bacillus Megaterium" (1957) J. Appl.Bacteriol. 20 333-341. 
9. Murrell, W. G. and Scott, W. J.: ''The Heat Resistance of Bacterial 
Spores at Various Water Activities" J. Gen. Microbiol. (1966) 43, 
411-425. 
10. Slepecky, R. and Foster, J. W.: "Alteration in Metal Content of Spore 
of Bacillus Megaterium and the Effect on Some Spore Properties" (1959) 
J. Bact~riol.78 117-123. 
11. Vinter, V.: ''The Fe ~ation of Cystine-Rich Structure in Sporulating 
Cells and its Possible Role in the Resistance of Spores" (1961) Spores 
II H. Halvorson (ed) Burges Publishing Co., Minneapolis. 
12. Warth, A. D.; Ohye, Dw F.; and Murrell, W. G.: ''The ComposHion and 
Structure of Bacterial Spores" (1963) J. Call. Bio.16 579-592. 
13. Young, I. E.: '~ Relationship Between the Free Amino Acid Pool, 
Dipicolinic Acid and Calcium from Resting Spores of Bacillus megaterium" 
(1959) Can. J. Microbfnl. 5 197-202. 


Investigations into a diffusion model of dry heat sterilization Interim report

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