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ARTICLES: FORMULATION ANDENGINEERING OF BIOMATERIALS

Novel Methods for Storage Stability and Release of Bacillus Spores

Iryna B. Sorokulova, April A. Krumnow, and Suram PathiranaDept. of Anatomy, Physiology and Pharmacology, College of Veterinary Medicine, Auburn University, Auburn, AL 36849

Arnold J. MandellDept. of Neuroscience, Psychiatry and Behavioral Sciences, Emory School of Medicine, Atlanta, GA 30322

Dept. of Psychiatry, School of Medicine, UCSD, La Jolla, CA 92037

Dept. of Mathematical Science, FAU, Boca Raton, FL 33431

Vitaly VodyanoyDept. of Anatomy, Physiology and Pharmacology, College of Veterinary Medicine, Auburn University, Auburn, AL 36849

DOI 10.1021/bp.22 Published online September 17, 2008 in Wiley InterScience (www.interscience.wiley.com).

Bacillus subtilis spores were immobilized in activated charcoal and tapioca and filled with acacia gum. These formulations were tested for spore stability during storage at tem-

peratures ranging from 408C to 908C and for bacterial release. Thermodynamic analysisshowed that immobilization of spores in acacia gum significantly increased their viabilitycompared with unprotected spores. The viability was further increased when suspensions of spores in acacia gum were added to granules of charcoal and tapioca. The number of thespores released after storage was also increased when spores were treated with acacia gum

prior to immobilization in tapioca and charcoal. Formulations of Bacillus spores with acaciagum and porous carriers (charcoal and tapioca) prolong the anticipated shelf-life of sporeseven under ambient temperature and provide slow and steady bacterial release consistent with their high viability.

Keywords: acacia gum, shelf life, Arrhenius and Eyring equations, Gibbs free energy,enthalpy-entropy compensation

Introduction

Bacteria of the Bacillus genus are usually considered to

be very stable due to their formation of spores. The experi-

mental data,1 however, indicate that only a few individual

Bacillus spores from an initially large population can sur-

vive for years. In particular situations, it is important to

store Bacillus spores without significant changes in their

titer during long-term storage. For example, bacteria of the

Bacillus genus are widely used as highly effective pro-

ducers of antibiotics, enzymes, aminoacids, and vitamins.2

Various Bacillus strains are known for their roles as probi-

otics for humans and animals, biopesticides, bioinsecticides,

and biological indicators.2,3 Such strains-producers require

special methods of storage to maintain a stable level of

spore viability. Some of them, such as the biopesticide

strains, should be formulated in such a way as to ensure the

slow release of spores.4 To avoid a decrease in their

numbers, Bacillus spores are frequently frozen, freeze-

dried, or refrigerated in aqueous suspensions or buffers.5

Even under these conditions, some Bacillus spores show a

significant loss in viability.6 Numerous formulations that

make use of a variety of polymers have been used to pro-

long the shelf life of spores.7

The two aims of this study are (1) to explore the effective-

ness of preserving of Bacillus spores in new formulations

using charcoal and tapioca as carriers along with acacia gumpolymers to increase shelf-life and the slow and steady

release of spores, and (2) to use thermodynamic characteris-

tics of new formulations under various storage conditions for

the prediction of spores viability.

Materials and Methods

Bacterium

The bacterium used as an experimental model was type

strain Bacillus subtilis ATCC 6051 that was obtained from

American Type Culture Collection (Manassas, VA). B.Correspondence concerning this article should be addressed to V.

Vodyanoy at [email protected].

Biotechnol. Prog. 2008, 24, 1147À1153 1147

VVC 2008 American Institute of Chemical Engineers



subtilis is regarded as a model Gram-positive organism for

genetic and physiological studies.8

Spore preparation

A fresh, overnight culture of B. subtilis ATCC 6051 was

spread-plated on Difco Sporulation Medium.9 The plates

were then incubated at 378C for 5 days. Sporulation was

assessed by phase contrast microscopy which revealed$99% phase bright spores. Spores were collected by flood-

ing the surface of the culture with sterile distilled water fol-

lowed by scraping with a sterile cell spreader (Daigger,

Vernon Hills, IL). Spores were then washed twice with ster-

ile distilled water followed by centrifugation at 19,837g for

40 min. To eliminate vegetative cells, they were heated at

808C for 20 min. Spores were then stored in sterile distilled

water at 48C until needed. Plates were incubated at 378C

overnight and the titer of spores was determined by plating

serial dilutions of spore suspension onto nutrient agar (NA)

plates.

Spore carriers and preparation of the protective biopolymer

Activated charcoal (Sigma, St. Louis, MO) and granu-

lated tapioca (Frontier, Norway, IA) were used as carriers

for B. subtilis spores. Acacia gum (Colloids Naturels

International, Rouen, France) was used as the protective

polymer. The solution was prepared by mixing the poly-

mer powder with sterile water in concentrations of 15%

(w/v). The solution was stirred and heated at 808C until

the powder was completely dissolved. It was then filtered

using two Brew Rite1 coffee filters (Rockline Industries,

Sheybogan, WI) in a Buchner funnel with vacuum filtra-

tion and autoclaved at 1208C, 20 PSI for 15 min, cooled

and stored at 48C.

Formulation of spores in the carriers and polymer

All the formulations were prepared using the Fluid Bed

System (Applied Chemical Technology, Florence, AL) at an

outlet temperature of 708C:

1. Tapioca þ spores, TþS: 75 mL of the spore suspension

was diluted with 300 mL of sterile water and dried with

375 g of tapioca.

2. Tapioca þ (spores þ acacia gum), TþSA: 75 mL of

the spore suspension was diluted with 300 mL of the 15%

solution of acacia gum and dried with 375 g of tapioca.

3. Charcoal þ spores, CþS: 75 mL of the spore suspen-

sion was diluted with 300 mL of sterile water and dried with375 g of charcoal.

4. (Charcoal þ spores) þ acacia gum, CCSþA: 375 g of

charcoal was mixed with 75 mL of the spore suspension.

The solution of acacia gum was prepared by adding 75 mL

of sterile water to 300 mL of the 15% (w/v) acacia gum

solution. The charcoal-spores preparation was then dried

with the acacia gum solution.

5. Charcoal þ (spores þ acacia gum), CCþSA: 75 mL of

the spore suspension was diluted with 300 mL of the 15%

solution of acacia gum and the mixture dried with 375 g of

charcoal.

Freshly prepared spores were used in all formulations.

The moisture content in prepared formulations was deter-

mined by Karl Fisher titration.10

Heat resistance test for spore viability

B. subtilis spores in the formulations described above

were tested for resistance to degradation at a range of

temperatures. The spore formulations were put in 50-mL

Falcon tubes (Becton Dickinson, Franklin Lakes, NJ), each

containing 500 mg of the formulation. Spores (S) and

spores with acacia gum (SþA), prepared in the same ratio

as in the formulations, and were used for the storage as a

control. Tubes with the varying formulations were placedin incubators at temperatures of: 40, 55, 60, 65, 75, 80, 85,

and 908C. Enumeration of viable spores was performed for

all formulations before placing for storage and at the pre-

determined time intervals during the storage. Five millili-

ters of cold sterile water were added to each tube and

mixed thoroughly. Samples containing charcoal and tapioca

were homogenized using the Tissue Tearor (model 985-

370; Biospec Products, Racine, WI). Decimal dilutions in

sterile water were prepared and appropriative dilutions

were plated onto NA (Difco, BD, Sparks, MD). Plates were

then incubated at 378C for 18–24 h. The number of spores

(colony forming units, CFU) was counted for each time

point and their mean and standard deviation were calculated

in triplicate or more.

A thermodynamic model of the thermal degradation

of spores

The apparent rate of degradation of spores during dehydra-

tion at constant temperature can be described by first-order

kinetics

dN

dt ¼ ÀkN (1)

where N is the concentration of spores being degraded, k represents the first-order rate constant, and t , the time of the

thermal drying. The solution of the equation (Eq. 1) can be

expressed as

N = N 0 ¼ eÀkt (2)

where N 0 is the initial concentration of spores and N / N 0 rep-

resents the ratio of the concentration of degraded spores to

the initial spore concentration. This fraction defines the ratio

of viable of spores. Taking the logarithm of both sides of

Eq. 2, one obtains

logð N = N 0Þ ¼ À2:303 Â kt (3)

A plot of the left-hand side of Eq. 3 vs. time (t ) yields an

estimate of k from the slope. The Arrhenius equation11 can

be used to express the temperature dependence of the first-order activation kinetics:

k ¼ Ae Ea RT (4)

where R is the universal gas constant, Ea represents the appa-

rent activation energy, and A is the pre-exponential Arrhe-

nius factor. Taking the logarithm of Eq. 4 yields

log k ¼ ÀEa

2:303 RÂ

1

T þ log A (5)

If the logarithm of k in Eq. 5 is plotted against the re-

ciprocal of temperature, 1/ T , then the slope of this graph

yields the activation energy ( Ea), the thermal activation

level of transitions from spore viability to nonviability.

1148 Biotechnol. Prog., 2008, Vol. 24, No. 5



The r ate c onstant of the spore degra da tion proce ss

depends on the thermodynamic activation parameters of

this transition state and can be described by the Eyring

equation12:

k ¼k BT

he

ÀDG RT ¼

K BT

heDS R e

ÀD H RT (6)

where k is the rate constant, DG is the standard Gibbs freeenergy of activation, h is Planck’s constant, DS is the stand-

ard entropy of activation, D H is the standard enthalpy of

activation, k B is the Boltzmann constant, R is the gas con-

stant, and T is the absolute temperature in Kelvin. Taking

the logarithm of both sides of Eq. 6, one obtains

logk

T

¼ log

k B

h

þ

DS

2:303 RÀ

D H

2:303 RÂ

1

T (7)

If the plot of the left-hand side of Eq. 7 vs. 1 / T is linear,

one can compute the value of D H from the slope, DS from

the ordinate intercept and the Gibbs free energy of activation

by the relation:

DG ¼ D H À T DS (8)

From Eq. 4 we can define the energy of activation as

Ea ¼ À R@ ln k

@ 1T

À Á (9)

The substitution of k in Eq. 9 with the k equivalent relation

in Eq. 6 and differentiation of this new expression with

respect to 1/ T shows that the Arrhenius (Eq. 4) and the Eyr-

ing (Eq. 6) expressions can be related as

Ea ¼ D H þ RT (10)

and

A ¼ek BT

h

eDS R (11)

Taking the logarithm of both sides of Eq. 11, one obtains

log A ¼ logekT

h

þ

DS

2:303 R(12)

suggesting a linear relation between the logarithm of the

Arrhenius frequency factor and entropy of activation

obtained from the Eyring equation for the transitional state.

The first-order kinetic model (Eq. 3) was used to deter-

mine the best fits of the data with the apparent rate constant

k . The Arrhenius and Eyring equations were then applied to

the data in order to determine Ea, A, DG, D H , and DS of the

temperature-dependent viability transitions.

Enumeration of spore release

Each sample consisting of 1 g of the indicated spore for-

mulations was put in 50-mL Falcon tubes containing 10 mL

of sterile water, mixed and maintained at room temperature.

Before sampling for the determination of spore number, the

tubes were mixed again and 0.5 aliquots of supernatant were

removed at predetermined times. To maintain constant vol-

ume, 0.5 mL of sterile water was added to the tubes after

each sample was removed. Serial 10-fold dilutions of eachsample were prepared in sterile water and plated onto NA.

The plates were then incubated at 378C for 18–24 h. The

mean and standard deviation of the number of released

spores were calculated for at least triplicate determinations.

Results

Characterization of the formulations

The number of spores in the various formulations pro-

duced using the fluid bed system varied slightly, ranging

from 4.2 Â 108 to 7.9 Â 108 CFU/g. The moisture content

was low in all the formulations, varying from 0.21% Æ

0.01% in the products with tapioca to 1.4% Æ 0.06% inthose containing activated charcoal.

Heat resistance of spores on different carriers

The decrease in spore viability in time was dependent on

temperature and the presence or absence of the acacia gum

polymer and the carrier used. Figure 1 shows the typical de-

pendence of spore viability as a function of time at different

temperatures exemplified by the data obtained for spores that

were first suspended in acacia gum and then combined with

charcoal. The degradation rate followed first order kinetics

in time across almost all temperatures. The apparent rate

constants for spore degradation in the various formulations

were used to obtain linear Arrhenius and Eyring plots con-stants with Eqs. 5 and 7 and shown in the corresponding

Figures 2a,b. These plots were then utilized for the calcula-

tion of Ea, A, DG, D H , and DS. Those values are shown in

Table 1.

The estimated time for spores to lose one log of their ini-

tial titers at different temperatures was calculated using the

experimental values of the apparent rate constants of spore

degradation in k , 1/day for different formulations and the

Arrhenius equation (Figure 2c). Stability of spores with both

carriers was higher when acacia gum was added.

The highest viability was obtained for spores that were

absorbed by charcoal and filled with acacia gum (Table 1,

Figure 2d). In this formulation, after 2 years of storage at

208C, the predicted viability of spores is 90.5%. At this

Figure 1. Viability of spores with acacia gum on charcoal(CC1SA) formulation.

Apparent first-order kinetics of spore degradation at 608C (n),808C (l), 858C (!), and 908C (~), respectively. Points areexperimental data plotted according to Eq. 5, while lines arelinear regressions: R ( P) ¼ À0.61 (\0.1), À0.96 (\4 Â 10À4),À0.96 (\3 Â 10À4), À0.92 (\5 Â 10À4) for 60, 80, 85, and908C, respectively.

Biotechnol. Prog., 2008, Vol. 24, No. 5 1149



temperature, the viability of spores in the control prepara-

tion, without carriers or acacia gum was only 6% (Table 2).

Release of spores

All preparations were tested for spore release from the

carriers. The graph in Figure 3 shows that spores are

released continuously, the number of free spores increasing

in time. The largest number of spores was released from the

formulations containing tapioca and CCþSA. Even after 7

weeks, the number of live spores in the supernatant of these

formulations was 2.6 to 4.0 Â 108 CFU/mL.

Discussion

We have found, as have others, that formulation and stor-

age conditions influence the viability of Bacillus spores.5

Compared with the other experimental conditions, unpro-

tected spores were the most sensitive to storage temperature.

Our data indicate that the rate of degradation, the loss of

spore viability, was highest without polymeric or carrier

Table 1. Thermodynamic Parameters Derived From the Arrhenius and Eyring Equations

Formulation Ea

(kcal/mol) A (1/day)D H

(kcal/mol)DS

[cal/(mol K)]T DS

(kcal/mol)DG, 608C(kcal/mol)

Tapioca þ spores 15.0 3.37 Â 108 14.5 0.8 2.7 14.2Tapioca þ spores in AG* 17.3 1.00 Â 1010 17.4 9.3 3.1 14.3Charcoal þ spores 18.7 1.60 Â 1010 18.0 8.4 2.8 15.2Charcoal with spores þ AG† 19.1 2.78 Â 1010 19.9 14.1 4.7 15.2Charcoal þ spores in AG‡ 17.3 2.96 Â 109 16.9 5.1 1.7 15.2Spores þ AG 11.4 1.33 Â 106 9.8 À13.8 À4.6 14.4Spores 7.1 6.58 Â 102 6.2 À25.9 À8.6 14.8

* Spores were first suspended in acacia gum (AG) and then combined with tapioca. † Charcoal was first loaded with spores and then coated with acaciagum. ‡ Spores were first suspended in acacia gum and then combined with charcoal.

Figure 2. Estimated viability of spores by Arrhenius and Eyring equations.

(a) Arrhenius plot. Points are experimental data plotted by Eq. 5, lines are linear regressions: R ( P) ¼ À0.96 (\0.04). (b) Eyring plot. Points are ex-perimental data plotted by Eq. 7 and lines are linear regressions. R ( P) ¼ À0.96 (\0.05). (c) Time for degradation of one log of spores at differenttemperatures. (d) Viability of spores at 58C; 1 - Tapioca þ spores, TS; 2 - Tapioca þ (spores þ acacia gum), TþSA; 3 - Charcoal þ spores, CCS;4 - (Charcoal þ spores) þ acacia gum, CCSþA; 5 - Charcoal þ (spores þ acacia gum), CCþSA; 6 - Spores þ acacia gum, SA; 7 - Spores, S.

Table 2. Predicted Viability of B. subtilis Spores in Charcoal andAcacia Gum (CCS1A Formulation) at Different Temperatures of

Storage in Comparison With Unprotected Spores (S)

Time

Viability of spores at different temperatures (%)

58C 208C 408C

CCSþA S CCSþA S CCSþA S

1 month 99.9 95.7 99.6 89.0 96.6 83.03 months 99.8 87.8 98.8 70.4 90.2 57.11 year 99.2 59.3 95.1 24.6 66.3 10.72 years 98.3 35.2 90.5 6.0 44.0 1.13 years 97.5 20.1 86.0 1.5 29.2 0.1




protection. Acacia gum increased the viability of spores.

Combining the polymer of acacia gum with carriers such as

charcoal and tapioca augmented the viability of spores addi-

tionally. Consistent with these findings, the apparent activa-

tion energy, Ea, for degradation of unprotected spores was

smallest among all the spore preparations at 7.1 kcal/mol

(Table 1). This result is in close agreement with the findings

of Bruch and Smith,13 who estimated the Ea for Bacillus

spores on Teflon to be 9.5 kcal/mol. The unprotected spores

also showed the highest negative entropy change, DS, of

À25.9 cal/mol K (Table 1). When spores were dried in tapi-

oca and charcoal, the apparent Ea was increased and the T DS of degradation became positive. Even higher Ea was

achieved when porous carriers were combined with acacia

gum. The apparent Ea peaked at 19.9 kcal/mol at 333 K for

the spore formulations containing activated charcoal and sus-

pended in acacia gum.The energy associated with the change of entropy, T DS,

correlates with the change of enthalpy, D H , keeping the

Gibbs free energy, DG ¼ D H À T DS, minimal, often main-

taining it at a nearly constant. At T ¼ 333 K, in all prepara-

tions, the DG remains within 14–15 kcal/mol (Table 1 and

Figure 4a).

This thermodynamic phenomenon is known as enthalpy-

entropy compensation.14 The enthalpy-entropy compensation

phenomenon is characteristically displayed by a linear graph

of D H vs. DS as revealed in these studies when the experi-

mental results across different formulations were grouped as

in Figure 4b.

The change of enthalpy was positive,D

H [

0, for all for-mulations (Table 1) indicating that the process of spore deg-

radation is endothermic, i.e. it occurs with the absorption of

heat. The value of D H [ 0 for unprotected spores was rela-

tively small, equal to 6.2 kcal/mol. This value is comparable

to the D H [ 0 of 13 kcal/mol found for the unfolding of the

RNA from B. subtilis.15 In contrast, the D H [ 0 of the

Figure 4. Thermodynamic correlates of polymeric system.

(a) The energy associated with the change of entropy (T DS), the change of enthalpy (D H ), and the Gibbs free energy (DG ¼ D H À T DS) at T ¼333 K in samples of different formulations. (b) Enthalpy-entropy compensation for spore degradation in different formulations. Points are experimen-tal data, while a line is a linear regression: R ( P) ¼ 0.996 (\0.001). The line corresponds to the equation D H ¼ DGo þ T o DS, where DGo ¼ 1477kcal/mol and T o ¼ 342 K, the temperature is such that DS ¼ 0. (c) Relationship between parameters of the Arrhenius and Eyring equations (log Aand DS). Points are experimental data, while a line is a linear regression: R ( P) ¼ 0.990 (\0.0001). The line is described by Eq. 11. The experimen-tal slope of the line and Y -intersect, 0.19 Æ 0.2 cal/(mol K), (2 Æ 0.8) Â 108, respectively, compare well with 0.22 cal/(mol K) and 2.35 Â 108,respectively. (d) The apparent activation energy as function of the change of enthalpy as described by Eq. 10. Points are experimental data, and aline is a linear regression: R ( P) ¼ 0.993 (\0.0001). The experimental slope of the line, 0.9 Æ 0.5, compares well with the theoretical slope of the

line that is equal 1.0.

Figure 3. Release of spores from the different formulations intime.




denaturation of proteins may have relatively higher values,

ranging from 20 to 5,300 kcal/mol.16

Low values for D H [0 does not particularize the involvement of a specific cellular

structural domain involved in the process of temperature-de-

pendent spore degradation. There are examples of important

cellular domains with low values for D H [ 0 of degradation

and/or denaturation.17,18 Immobilization of spores in acacia

gum alone significantly increased D H [ 0 from 6.2 to 9.8

kcal/mol. Associated with the T DS[ 0 of this formulation,the degradation of spores was significantly slower than that

of unprotected spores. Embedding spores in the porous car-

riers together with acacia gum was accompanied by even

higher values for D H [ 0, reaching its maximum at 19.9

kcal/mol for the activated charcoal with spores suspended in

acacia gum (Table 1). For the samples containing this for-

mulation, compared with unprotected spores at 58C, protec-

tion from degradation was increased by a factor of $70. As

predicted by Eq. 10, the values of the seven formulation

conditions for D Ea were followed closely by those for D H .Figure 4c demonstrates this good linear fit, R ¼ 0.99, P \0.0001.

T DS changed progressively from negative to increasingly

positive (Table 1) as protective conditions and the stability

of system were increased. When spores were immobilized in

acacia gum, T DS changed from À8.6 to 4.7 cal/(mol K). DS

\ 0 has conventionally been associated with decreases in

molecular rotational and translational degrees of freedom.

DS \ 0 in processes involving aqueous solvents often

involves the dehydration of solvent moieties forming the

interface between the contacting molecules and by release of

cations.19 The small positive or negative DS was observed

depended upon the competition between the DS[ 0 of sol-

vent dehydration and the DS \ 0 of the loss of molecular

translational and conformational degrees of freedom. We

speculate that acacia gum, though manifesting solvent dehy-

dration when dried and polymerized, traps some bound water thus preventing complete dehydration of the spore’s vital

components.

There was a good correspondence between observed val-

ues of the pre-exponential Arrhenius frequency factor, A,

and T DS that was predicted by Eq. 12 and confirmed in Fig-

ure 4d demonstrating a linear relationship between log A and

DS ( R ¼ 0.99, P \ 0.0001). Predicted and experimental

results portrayed in this graph are in a good agreement.

Our experiments showed that the release of spores, as for-

mulated in different carriers, increased in time and was in

the range of 107 – 108 CFU/mL even after 7 weeks of incu-

bation. These results are in good agreement with those

observed for the release of spores in 24 h from B. megate-rium pellets embedded in a variety of formulations.3

The

greatest release of B. subtilis spores was found in the for-

mulations with tapioca. The number of the spores released

after storage was increased when spores were treated with

acacia gum prior to immobilization in tapioca and charcoal.

Similar effect of acacia gum on the release of B. thuringien-

sis spores was observed for formulations containing various

polymers.7

Our investigations have shown that formulation of Bacil-

lus spores with acacia gum and tapioca and/or activated

charcoal as spore carriers significantly increased the shelf

life of the spores. Even after 2 years of storage at 208C the

formulations with acacia gum can protect 90% of spores,

while only 6% of unprotected spores remain alive at these

conditions. These findings are very important especially for

Bacillus probiotic strains because it shows the possibilities

for new probiotic formulations which can keep high rate of

strain viability even under ambient temperatures and do not

require cold chain during transportation.

New formulations with acacia gum together with charcoal

and tapioca cause as well the steady release of spores main-

taining their high viability over the 7-week experiments. It is

significant for improving formulations with Bacillus sporesrequired slow and consistent release of spores (for example,

in biopesticides, bioinsecticides). Thus, obtained results can

be used in the development of new formulations of Bacillus

spores for different biological products.

Conclusion

We found that new formulations with acacia gum and tap-

ioca or activated charcoal considerably increasing the shelf

life of Bacillus spores. For the spores embedded in gum aca-

cia, tapioca, or charcoal, we show that optimizing conditions

can extend spore life times by a factor of 60. Fundamental

Arrhenius and Eyring chemical rate equations, their tempera-

ture dependence, and Van’t Hoff relations that are usually

applied to compensation studies of organic chemical series

and aqueous macromolecular thermodynamics are used for

the analyses of a whole living cell system. We found that

increases in spore viability correlated with conjugate incre-

ments in enthalpy and entropy and negligible changes in

Gibbs free energy. The experimental results are consistent

with theoretically calculated data. These findings indicate the

possibilities for creating of new products, including Bacillusspores, with prolonged shelf-life and with slow and steady

release of spores. Theoretical and experimental approaches

presented in this study may be used for prediction of viabil-

ity and characterization of the degradation processes in bio-

logics for medicine and agriculture.

Acknowledgments

This research was supported by Aetos Technologies, Inc.,

and by FAA’s Office of Aerospace Medicine, as part of the Air

Transportation Center of Excellence for Airliner Cabin Envi-

ronment Research.

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Manuscript received Nov. 10, 2007, and revision received Apr. 17,2008.

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