# Comparison of human axillary odour profiles obtained by gas chromatography/mass spectrometry and skin microbial profiles obtained by denaturing gradient gel electrophoresis using multivariate pattern recognition

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**ABSTRACT:**SOMs (Self Organising Maps) are derived from the machine learning literature and serve as a valuable method for representing data. In this paper, the use of SOMs as a technique for determining the most significant variables (or markers) in a dataset is described. The method is applied to the NMR spectra of 96 human saliva samples, half of which have been treated with an oral rinse formulation and half of which are controls, and 49 variables consisting of bucketed intensities. In addition, three simulations, two of which consist of the same number of samples and variables as the experimental dataset and a third that contains a much larger number of variables, are described. Two of the simulations contain known discriminatory variables, and the remaining is treated as a null dataset without any specific discriminatory variables added. The described SOM method is contrasted to Partial Least Squares Discriminant Analysis, and a list of the markers determined to be most significant using both approaches was obtained and the differences arising are discussed. A SOM Discrimination Index (SOMDI) is defined, whose magnitude relates to how strongly a variable is considered to be a discriminator. In order to ensure that the model is stable and not dependent on the random starting point of the SOM, one hundred iterations were performed and variables that were consistently of high rank were selected. A variety of approaches for data representation are illustrated, and the main theoretical principles of employing SOMs for determining which variables are most significant are outlined. Software used in this paper was written in-house, allowing greater flexibility over existing packages, and tailored for the specific application in hand.Chemometrics and Intelligent Laboratory Systems. 10/2009; - SourceAvailable from: Kanet WongraveeKanet Wongravee, Gavin R. Lloyd, John Hall, Maria E. Holmboe, Michele L. Schaefer, Randall R. Reed, Jose Trevejo, Richard G. Brereton[Show abstract] [Hide abstract]

**ABSTRACT:**Three methods for variable selection are described, namely the t-statistic, Partial Least Squares Discriminant Analysis (PLS-DA) weights and regression coefficients, with the aim of determining which variables are the most significant markers for discriminating between two groups: a variable’s level of significance is related to its magnitude. Monte-Carlo methods are employed to determine empirical significance of variables, by permuting randomly the class membership 5000times to obtain null distributions, and comparing the observed statistic for each variable with the null distribution. Seven simulations consisting of 200 samples, divided equally between two classes, and 300 variables, are constructed; in one dataset there are no induced correlations between variables, in two datasets correlations are induced but there is no induced separation between the classes, and in four datasets, separation is induced by selecting 20 of the variables to be discriminators. In addition two metabolomic datasets were analysed consisting of the GCMS of urinary extracts from mice both to determine the effect of stress and to determine the effect of diet on the urinary chemosignal. It is shown that the t-statistic combined with Monte-Carlo permutations provides similar results to PLS weights. PLS regression coefficients find the least number of markers but, for the simulations, the lowest False Positives rates.Metabolomics 01/2009; 5(4):387-406. · 4.43 Impact Factor - SourceAvailable from: Anna Cohuet
##### Article: Human Skin Volatiles: A Review.

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**ABSTRACT:**Odors emitted by human skin are of great interest to biologists in many fields; applications range from forensic studies to diagnostic tools, the design of perfumes and deodorants, and the ecology of blood-sucking insect vectors of human disease. Numerous studies have investigated the chemical composition of skin odors, and various sampling methods have been used for this purpose. The literature shows that the chemical profile of skin volatiles varies greatly among studies, and the use of different sampling procedures is probably responsible for some of these variations. To our knowledge, this is the first review focused on human skin volatile compounds. We detail the different sampling techniques, each with its own set of advantages and disadvantages, which have been used for the collection of skin odors from different parts of the human body. We present the main skin volatile compounds found in these studies, with particular emphasis on the most frequently studied body regions, axillae, hands, and feet. We propose future directions for promising experimental studies on odors from human skin, particularly in relation to the chemical ecology of blood-sucking insects.Journal of Chemical Ecology 04/2013; · 2.46 Impact Factor

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Comparison of human axillary odour profiles obtained by gas

chromatography/mass spectrometry and skin microbial profiles

obtained by denaturing gradient gel electrophoresis using multivariate

pattern recognition

Yun Xu,aSarah J. Dixon,aRichard G. Brereton,a,* Helena A. Soini,bMilos V. Novotny,bKarlheinz Trebesius,c

Ingrid Bergmaier,cElisabeth Oberzaucher,dKarl Grammer,dand Dustin J. Penne

aCentre for Chemometrics, School of Chemistry, University of Bristol, Cantocks Close, Bristol, BS8 1TS, UK

bInstitute for Pheromone Research and Department of Chemistry, Indiana University, 800 E. Kirkwood Ave, Bloomington, IN, 47405, USA

cVermicon AG, Emmy-Noether-Str. 2, 80992, Munich, Germany

dDepartment for Anthropology, Ludwig Boltzmann Institute for Urban Ethology, Althanstrasse 14, A-1090, Vienna, Austria

eKonrad Lorenz Institute for Ethology, Austrian Academy of Sciences, Savoyenstr. 1a, A-1160, Vienna, Austria

Received 19 November 2006; Accepted 22 March 2007

Several studies have shown that microbial action is responsible for many compounds responsible for human odour. In this

paper, we compare the pattern of microbial profiles and that of chemical profiles of human axillary odour by using multivariate

pattern matching techniques. Approximately 200 subjects from Carinthia, Austria, participated in the study. The microbial profiles

were represented by denaturing gradient gel electrophoresis (DGGE) analysis and the axillary odour profiles were determined in the

sweat samples collected by a stir-bar sampling device and analysed by gas chromatography/mass spectrometry (GC/MS). Both

qualitative and quantitative distance metrics were used to construct dissimilarity matrices between samples which were then used to

represent the patterns of these two types of profiles. The distance matrices were then compared by using the Mantel test and the

Procrustean test. The results show that on the overall dataset there is no strong correlation between microbial and chemical profiles.

When the data are split into family groups, correlations vary according to family with a range of estimated p values from 0.00 to

0.90 that the null hypothesis (no correlation) holds. When 32 subjects who followed four basic rules of behaviour were selected, the

estimated p-values are 0.00 using qualitative and <0.01 using quantitative distance metrics, suggesting excellent evidence that there

is a connection between the microbial and chemical signature.

KEY WORDS: multivariate pattern comparison; human odour profile; human microbial profile; gas chromatography/mass

spectrometry; denaturing gradient gel electrophoresis.

1. Introduction

It is well known that axillary microflora play very

important roles in human odour production. Previous

studies have shown that the population density of

certain micro-organisms has strong association with the

intensity of odour (Rennie et al., 1990, 1991). Certain

areas of the human body possess a unique odour which

is produced partially by microbial action, especially the

human axillary odour is a combination of secretions

from eccrine, apocrine, apoeccrine and sebaceous glands

together with the local microflora (Sastry et al., 1980;

Sato et al., 1987). Studies have also shown that axillary

odour is absent if Gram-positive bacteria are eliminated

from the skin (Marples, 1969; Gower et al., 1985).

In this study, we compare the pattern of microbial

profiles obtained by denaturing gradient gel electropho-

resis (DGGE) with the pattern of chemical human

axillary odour obtained by gas chromatography/mass

spectrometry (GC/MS) and explore the common trends

between these two types of profile. Samples were taken

from approximately 200 test subjects. Most subjects were

sampled twice for the microbial signature, and five times

for the chemical signature, each sample taken over dif-

ferent fortnights. Our previous studies have shown that

there is strong statistical evidence that both in GC/MS

and DGGE data, reproducible signals exist for individ-

ual characterisation (Penn et al., 2007; Xu et al., in

preparation). In this paper, pair-wise dissimilarity

matrices (both qualitative and quantitative distance

metrics) were calculated on both GC/MS and DGGE

profiles to determine the patterns of these two types of

data. The similarity of these two patterns was evaluated

by the permuted Mantel test. We also transformed the

dissimilarity matrices to sample-latent variable matrices

using Principal Co-ordinates Analysis and then com-

pared the patterns of these two matrices by using a test

based on Procrustes analysis.

*To whom correspondence should be addressed.

E-mail: r.g.brereton@bris.ac.uk.

Metabolomics, Vol. 3, No. 4, December 2007 (? 2007)

DOI: 10.1007/s11306-007-0054-6427

1573-3882/07/1200-0427/0 ? 2007 Springer ScienceþBusiness Media, Inc.

Page 2

2. Experimental

2.1. Test subjects

A total number of 196 subjects participated in this

study. These individuals are from an isolated population

in Carinthia, Southern Austria, belonging to 17 different

families, coded by a single letter (e.g. A). The samples

were taken from July to August, 2005, the odour sam-

ples were collected five times for each subject, once per

fortnight while microbial samples were collected twice,

(on the third and fourth fortnights). In this paper,

we only consider the fortnights when the microbial

and odour samples were collected simultaneously. The

subjects were also asked to fill in a survey when the

samples were taken which contains information about

their living habits, such as when was the last washing of

armpit, and when was the last usage of deodorant as

discussed in greater detail in Section 4. Due to experi-

mental reasons, some subjects only provided one sample

over fortnights 3 and 4 and they were excluded from the

analysis, making the number of subjects reported in this

paper less than the full population. A total of P = 177

subjects are analysed in this study, each sampled twice

to give 2P samples, each with a corresponding GC/MS

and microbial profile.

2.2. Human axillary odour samples collection and

GC/MS analysis

The volatile and semivolatile compounds from arm-

pits were collected by using a newly designed skin roller

device. A stir bar is attached to the device and rolled

over the skin to collect chemical compounds. The stir

bar was then subjected to the GC/MS analysis. Stir bar

sampling on the skin surface is likely to favour com-

pounds which bind in the oily layer present on the

human skin: in fact, the relatively long storage stability

time of 20 days under cooled conditions supports the

hypothesis. Compounds with high volatility and of very

hydrophilic characteristics

against using this sampling approach. During the same

day, reproducibility for typical skin compounds taken

from five individuals was 3–25% (RSD, relative stan-

dard deviation, three samples per individual). The long

term RSD of the internal standard is 14.3%. More

detailed information about the characteristics and the

reproducibility of both the sampling device and the GC/

MS experiments are given elsewhere (Soini et al., 2006).

The GC equipment for quantitative analysis consisted

of an Agilent 6890N gas chromatograph connected to a

5973i MSD mass spectrometer (Agilent Technologies,

Palo Alto, CA) with a Thermal Desorption Autosampler

(TDSA,Gerstel,Mu ¨ lheimanderRuhr).Positiveelectron

ionisation (EI) mode at 70 eV was used with a scanning

rate of 4.51 scans/s over the mass range of m/z 35–350.

The ion source and quadrupole temperatures were set at

230 ?Cand150 ?C,respectively.The separation capillary

wouldbe discriminated

was DB-5MS (20 m·0.18 mm, i.d., 0.18 lm film thick-

ness) from Agilent Technologies (Wilmington, DE).

Samples were thermally desorbed in a TDSA automated

system, followed by injection into the column with a

CooledInjectionSystem,CIS-4.TheTDSAoperatedina

splitless mode. The temperature program for desorption

was 20 ?C (0.5 min), then 60 ?C/min to 250 ?C (3 min).

Thetemperatureofthetransferlinewassetat280 ?C.The

CIS was cooled with liquid nitrogen to )80 ?C. After

desorption and cryotrapping, the CIS was heated at

12 ?C/s to 280 ?C with the hold time of 10 min. The CIS

inlet was operated in the solvent vent mode, with a vent

pressure of 14 psi, a vent flow of 50 mL/min, and a purge

flow of 50 mL/min. The temperature program in the GC

operation was 50 ?C for 1 min, then increasing to 160 ?C

attherateof5 ?C/min,followedbythesecondrampatthe

rateof3 ?C/minto200 ?C(holdtime16 min).Thecarrier

gas head pressure was 14 psi (flow rate, 0.7 mL/min at

constant flow mode). The GC temperature program

lasted for 52.33 min, with mass spectrometric detection

commencingafteradeadtimeof1.88 min(solventdelay).

To increase throughput, two instruments of identical

specifications were used to analyse the samples. The

configurationofbothinstrumentswasthesame,andtests

had been done to ensure reference samples analysed on

eachinstrumentwereofacceptablesimilarity.Therewasa

slight difference in scan rates between the two instru-

ments, with instrument 1 sampling 13,481 scans over the

analysis period, and instrument 2 sampling 13,460 due to

slightly different software versions. In the mass spec-

trometry software (Agilent ChemStation) a parameter is

set, below which a scan will be recorded as having zero

intensity.Thisisthedetectionlimitoftheinstrument,and

canbe setby theinstrument operator.In this work, it was

set to 300: this number is essentially arbitrary and will

dependonthespecificinstrument,butinthecontextofthe

current study the smallest peaks which were visible above

the noise were of height around 600 units. Typical peak

heights in a mass channel range from 1000 to 100,000

(varyingfromsampletosample).Themassresolutionwas

reduced to unity before analysis. During the analysis,

test runs using quality control samples were performed

on a regular basis to ensure that the instruments were

performing acceptably.

2.3. Microbial sampling and DGGE analysis

2.3.1. Fixation of samples

Microbial samples were taken in Greifenburg (Carinthia,

Austria) from the armpit of different subjects. Sampling

of the axillary microflora of the armpit was performed by

the washing-scrub method of Williamson and Kligman

(1965). A plastic cylinder open at both ends was placed

on the armpit. About 1.5 mL detergent solution was

filled into the cylinder. A glass stirrer was moved with

constant pressure over the skin to detach the micro-

organisms. The solution was removed and transferred to

Y. Xu et al./Comparison of human axillary odour profiles 428

Page 3

a sterilised reaction tube and the procedure was repeated.

The obtained solutions were fixed with ethanol at a ratio

1:1. The total sample volume of 6 mL consisted of 3 mL

sampling buffer containing the microbes (sample) and

3 mL of 96% ethanol.

2.3.2. DNA extraction

About 1.3 mL of the sample was centrifuged (10 min,

14,000 rpm) and the supernatant was discarded. This

step was repeated once, by adding 1.3 mL sample to the

pellet and an additional centrifugation step (10 min,

14,000 rpm). The obtained pellet was washed in 200 lL

1· phosphate-buffered saline (PBS). After centrifugation

(10 min, 14,000 rpm) the pellet was resuspended in

100 lL 6% Chelex? 100 solution (BioRad, Munich,

Germany) according to Rodrı`guez-La ´ zaro et al. (2004),

and incubated at 56 ?C for 20 min. The sample was then

thoroughly mixed and incubated further at 100 ?C for

8 min. Subsequently, the sample was mixed and cooled

for 5 min on ice. Next a centrifugation step (10 min,

14,000 rpm) was performed. The supernatant contain-

ing the DNA was removed.

2.3.3. PCR amplification of target DNA for DGGE

The extracted genomic DNA was amplified using the

forward primer 341F-GC (Muyzer et al., 1993) with a

GC clamp 5¢-CGC CCG CCG CGC GCG GCG GGC

GGG GCG GGG GCA CGG GGG GCC TAC GGG

AGG CAG CAG -3¢ and the reverse primer 518R 5¢-

ATT ACC GCG GCT GCT GG-3¢. The final 50 lL

reaction mixture contained: 2 lL template DNA,

25 pmol primers each, 2.5 U of Taq DNA polymerase

(Promega, Mannheim, Germany), 1-fold PCR buffer

(Promega), 75 mM MgCl2(Promega), 10 mM dNTPs,

(Promega). The PCR protocol included a 5 min initial

denaturation at 94 ?C, 30 cycles of 94 ?C for 0.5 min,

44 ?C for 1 min, 72 ?C for 1.5 min followed by 10 min

at 72 ?C for final extension in a Primus 96 thermocycler

(MWG, Ebersberg, Germany). PCR products were

stored at )20?C until further use.

2.3.4. DGGE analysis

DGGE analysis was performed on DcodeTM-System

(Bio-Rad). Samples were loaded onto a 8% (w/v)

acrylamide gel (37.5:1 acrylamide-bisacrylamide) in 1·

TAE buffer with a denaturant gradient ranging from

20% to 60% prepared in accordance with Muyzer et al.

(1995). (100% denaturant contains 7 M urea and

volume ratio of 40% formamide.)

To standardise DGGE gels, reference standards were

applied to each gel. The reference standard consisted of

a mixture of PCR products of 11 different bacterial

species which are commonly found in human skin

samples (Trebesius et al., in preparation). The banding

pattern resulted from PCR products obtained by the

same primer pair as described above.

The electrophoresis was performed at 60 ?C, initially

at 25 V for 15 min following at 130 V for 4 h. The gel

was silver stained based on Sanguinetti et al. (1994) by

the following procedure. About 150 mL of fixing solu-

tion (10% ethanol, 0.5% acetic acid) was applied to the

gel and shook gently for 3 min. Subsequently, the

gel was incubated for 10 min at room temperature in a

silver nitrate solution (0.2% AgNO3, 10% ethanol,

0.5% acetic acid). After discharging the silver nitrate

solution a washing step in distilled H2O for 2 min

followed. Hereafter, 150 mL of ‘‘developer solution’’

was applied to the gel (3% NaOH containing, 300 lL of

37% formaldehyde) for 5 min, while shaking gently.

The staining procedure was stopped by incubating the

gel for 5 min in 10% ethanol, 0.5% acetic acid solution.

A typical example of a DGGE gel is presented in

figure 1.

2.4. Software

The GC/MS instrument was controlled by Agilent

ChemStation software versions D.01.00 (system 1) and

D.01.02 (system 2). The GC/MS data was exported to

AIA/netCDF (network Common Data Format) format

and then imported into MATLAB (The Mathworks,

Inc., Natick, MA) using a freely available conversion

tool (available at http:// mexcdf.sourceforge.net/). The

stained gel was transferred on an overhead transparency

sheet and documented on a SnapScan 1236 scanner

(Agfa, Ridgefield Park, NJ). The scanning mode was

transparent, 300 dpi and 24 Bit colour. The resultant

pictures were converted to TIFF files for processing and

imported into MATLAB by using Image Processing

Toolbox. All data processing was performed using

MATLAB version 7.0.4.365, Release 14, Service Pack 2.

Figure 1. A typical DGGE gel.

Y. Xu et al./Comparison of human axillary odour profiles 429

Page 4

3. Data analysis methods

3.1. Data preparation

3.1.1. DGGE data preparation

The images of scanned DGGE gels were processed by an

in-house image digitisation software. For each lane

(sample) on the gel, the bands were detected and their

positions recorded. The position of each band was then

corrected with respect to the positions of reference

standards to cope with different separation behaviour

between gels. The detailed description is given in a

separate paper (Xu et al., in preparation) and not

repeated here for brevity.

The main difficulty in this study is the band

assignment. DGGE is a 1-D technique hence the only

useful information for the band assignment is the

position information and there is no spectroscopic or

other information which can help in identifying which

band is which. When there were many lanes and gels, it

is often hard to assign some bands unambiguously, i.e.

when two bands come from different lanes/gels with

slightly different positions, it is difficult to decide

whether these two bands originate from the same

micro-organism or two different ones. However, data

analysis methods such as PCA (Wold et al., 1987;

Brereton, 2003) based on a sample-feature matrix

require each variable to originate from the same

source, otherwise the results will be influenced by the

incorrect assignments of variables. To overcome this

problem, we used a pair-wise dissimilarity matrix

between sample profiles rather than a full sample-

variable matrix since it is much easier to measure the

dissimilarity between two samples as the number of

ambiguous assignment of the bands is small when

comparing two lanes, rather than using global band

assignments. Previously we developed a fuzzy distance

metric to measure this dissimilarity. The metric is

weighted by a fuzzy function and the value of this

function depends on the difference of the positions of

two bands, so it does not require an accurate assign-

ment of each band and tolerates slight imprecision of

the positional information. We briefly summarise the

method here which will be described elsewhere (Xu

et al., in preparation): in this paper we use the square

root of the intensities rather than the raw intensities to

be comparable to the GC/MS data, otherwise the

method is identical.

The first step is to correct the position of bands in

each lane according to a reference lane consisting of

extracts from 11 microbes, the corrected position relates

to how close the bands are to the microbial extracts in

the nearest reference lane, for example a band that is

detected half way between bands 3 and 4 in the reference

lane will be given a value of 3.5. These positions relative

to the reference bands are then used for subsequent

analysis as follows.

The next step is to determine a dissimilarity measure

between the reference band corrected profiles in each

lane. Suppose lane i has Nibands and lane j has Njbands,

and also assume Ni£Nj. A Ni· Njposition difference

matrix is constructed; each row representing the posi-

tional difference of one band in lane i to all the bands in

lane j. The minimum value in each row will be the nearest

band. For each dissimilarity metric calculation, there can

be Nicomparisons at most. However, sometimes two or

more bands in lane i share the same nearest neighbour in

lane j. In such case, we only consider the closest pair and

the others will be discarded (i.e. consider them as unique

bands in lane i). We denote the number of band pairs k

that have been identified as b (b£Ni).

Both quantitative and qualitative (presence/absence

criterion) fuzzy weighted distance metrics are used to

measure the dissimilarity between two DGGE samples.

The quantitative metric takes into account band inten-

sities as well as uncertainties in position using the fol-

lowing equation:

dði;jÞ ¼ 1 ?

P

b

k¼1

s

ffiffiffiffiffiffiffiffiffiffiffiffiffi

P

xik:xjk

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n¼1

p

? wk

??

Ni

xin

P

Nj

n¼1

xjn

ð1Þ

where b is the number of pairs being considered (see

above) each matched pair being denoted by k, where xik

and xjkare the integrated intensities of the band pair k in

lanes i and j. The qualitative distance metric is the

square root of the fuzzy weighted Jaccard distance

(Jaccard, 1908) metric defined as

dði;jÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 ?

P

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 ?

Niþ Nj? b

P

b

k¼1

wk

p

k¼1

wkþ Niþ Nj? b ?P

P

p

k¼1

wk

v

u

v

t

u

u

u

u

u

u

u

t

u

¼

b

k¼1

wk

ð2Þ

The fuzzy weight function wk= H(Ddk) is determined

by the absolute difference in the corrected position (Ddk)

of the band pair k (=1 to p) defined by

wk¼ HðDdkÞ ¼1

2? erfcðA ? Ddk? SÞð3Þ

where function erfc(x) is the complementary error

function(Zwillinger, 1997),

2

xe?t2dt and t is an integration factor, from x to

+¥. S and A are two adjustable free parameters which

control the sensitivity to the positional difference of the

definedbyefrcðxÞ ¼

p?R1

Y. Xu et al./Comparison of human axillary odour profiles 430

Page 5

weight function. With an appropriate setting of S and A

this function has the following properties.

(a) When the difference is small enough, the output is 1

or very close to 1,

(b) when the difference is moderate, the output is

between 0 and 1 and decays exponentially with

increasing Dd,

(c) when the difference is large enough, the output is 0

or very close to 0.

In this paper, S is set to 5 and A to 30. If the corrected

positional difference is closer than about 0.1 they are

assumed to be a perfect match, if differing by more than

0.2 they are assumed not to match at all.

3.1.2. GC/MS data preparation

A peak table was constructed based on all the GC/MS

total ion chromatograms which is a matrix whose rows

correspond to samples and whose columns correspond

to summed peak areas over all significant masses of

the corresponding compounds. The method for peak

identification and alignment has been described in detail

in Dixon et al. (2006). The peaks corresponding to

known background compounds such as siloxanes orig-

inating from stir bars or vial septa were identified based

on their mass spectra and removed from the peak table.

Next, peaks that occur in 4 or less samples in the overall

dataset are removed as they are unlikely to have any

diagnostic significance. A further reduction in the size of

the peak table is performed to consider only those peaks

that are detected in at least 4 out of 5 fortnights in at

least one subject leaving NGCMS =373 peaks in total

over all subjects: this is so as to retain peaks that are

likely to relate to stable biological signatures which are

detected in the majority of samples from one or more

individuals. Finally peak areas were scaled as follows:

the square root of the peak areas were computed, these

peak areas were summed to a constant total of 1 in each

chromatogram. The reason we square root peak areas is

that there can be large peaks in some chromatograms

that could dominate the profile, hence distorting data

after normalisation; a common alternative of log scaling

is not suitable in this study because many peaks are not

detected in chromatograms so a large number of zero

numbers would need to be replaced, square root scaling

is a common alternative for reducing contrasts. More

detailed discussion about these data transformation

methods can be found elsewhere (Box and Cox, 1964;

Huber et al., 2002).

In order to compare the patterns of the GC/MS and

DGGE data, we constructed two pair-wise distance

matrices for each data set, one using qualitative dis-

tance metric and another using quantitative distance

metric. For the quantitative distance between GC/MS i

and j we use

dði;jÞ ¼ 1 ?

P

NGCMS

k¼1

½ðxik? xjkÞ?

xi

k k ? xj

????

ð4Þ

where xikis the normalised square root intensity of peak

k in chromatogram i and xiis the vector containing all

NGCMS(=373) intensities of this chromatogram. For

the qualitative distance we use the square root of the

Jaccard distance (Jaccard, 1908)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

where a are the number of peaks that are common to

both samples, and b and c the number of peaks unique

to one of the two samples.

The reason we square root the distances will be

explained in Section 3.2.2.

dði;jÞ ¼

1 ?

a

a þ b þ c

r

ð5Þ

3.2. Comparison of multivariate patterns

3.2.1. Mantel test

To compare two distance matrices directly, the Mantel

test (Mantel, 1967) is a commonly used and effective

method. Given two distance matrices A and B with

dimensions of N·N, the lower (or upper) triangular

parts of the matrices are unfolded into two vectors:

a ¼ fa11;a21;...aN1;a22;...aN2;...;aNNg

b ¼ fb11;b21;...bN1;b22;...bN2;...;bNNg where amnand

bmnare the mth row and nth column of the elements in

matrices A and B respectively. The correlation coeffi-

cient r between a and b is then calculated.

The significance of the correlation is determined

using a Monte Carlo simulation. The order of the

elements in one vector is permuted while the other

remains unchanged and the correlation coefficient

between these two vectors is calculated. This process is

repeated sufficiently large number of times and the

correlation coefficients obtained by these permutations

are used to form an empirical null distribution. The

significance of the correlation coefficient r calculated

above is computed to provide an indication as to

whether this belongs to the null distribution or not.

For an estimate of the significance of the correlation

coefficient we can calculate the proportion of times the

Monte Carlo simulation results in a correlation coeffi-

cient greater than the observed value r (one tailed test)

or the absolute value is greater than r (two tailed test).

These approximate to probabilities and are denoted by

p values below. In this paper we use the two sided

Mantel test.

and

3.2.2. Multidimensional scaling and the Procrustean test

A major drawback of the Mantel test is that it is not

possible to visualise the data structure as it is based on a

Y. Xu et al./Comparison of human axillary odour profiles 431

Page 6

single number (the correlation coefficient), between two

sets of data. Multidimensional scaling (MDS) is a set of

methods that can transform the pattern represented by a

pair-wise distance matrix back to a matrix of samples

and latent variables. MDS constructs a new sample-

latent variable matrix and the relative configuration of

the data points has been preserved and can be visualised,

if appropriate, by using 2-D or 3-D scatter plots. We

used a common MDS method called Principal Coordi-

nate Analysis (PCO) (Gower, 1966) to transform the

distance matrices to sample-feature matrices. A brief

description of PCO is given below.

Given an N·N symmetric distance matrix D, each

element dijin D represents the distance from sample i to

sample j.

(1)

A ¼ ðaijÞ= ?1

2? d2

ij

??

ð6Þ

(2) Calculate Gower?s centred matrix G using

G ¼

I ?1

N1 ? 10

??

? A ?

I ?1

N1 ? 10

??

ð7Þ

where I is the identity matrix and 1 is a column of 1s of

length N.

(3) Perform eigen-decomposition on matrix G so that

G ¼ Q ? K ? Q0

ð8Þ

where K is a diagonal matrix with eigenvalues on the

diagonal in descending order. Q is a square matrix

whose columns are corresponding orthonormal eigen-

vectors. It is important to point out that the eigen-

values and eigenvectors here are defined by linear

algebra: each pair of eigenvalues k and corresponding

eigenvectorsq of the square

G ? q ¼ k ? q. The definition of an eigenvalue often used

in the chemical PCA literature (Wold et al., 1987;

Brereton, 2003), the sum of squares of scores, has a

similar property to the eigenvalues as defined above:

however unlike eigenvalues in PCA literature, linear

algebra defined eigenvalues cannot be guaranteed to be

non-negative for all types of matrices. A matrix G

having all diagonal elements of K positive is called

positive definite ; if one or a few diagonal elements of

K are 0 and others are all positive G is denoted a

positive semi-definite matrix (p.s.d). In context of PCO,

non-negative eigenvalues can only be guaranteed when

the Euclidean distance has been used for determining

dissimilarities (Gower, 1966).

(4) If l dimensions are desired for modelling the data,

retain the first l columns in Q and first l rows and l

columns in K, the PCO scores matrix T can be

matrixGsatisfies

obtained by T = QÆK1/2with imaginary elements if

there are negative eigenvalues.

It is important to pay special attention to the values of

the diagonal elements of K. If a non-Euclidean distance

is used to construct the distance matrix, it is possible

that one or a few eigenvalues in K are negative. In such

case, the original distance matrix cannot be perfectly

embedded into Euclidean space because some PCs exist

in imaginary space. However, if the magnitude of the

negative eigenvalues is relatively small compared to that

of positive eigenvalues, the negative part is usually

indicative of noise. The rationale behind such method-

ology is given by the Wielandt-Hoffman theorem

(Golub and Loan, 1996): the best approximation of a

matrix G whose eigenvalues K contain negative elements

is by setting all negative elements in K to zero to give a

matrix^K and then reconstructing^G using Q and the new

matrix^K. This method can be justified as noise reduc-

tion so long as the negative eigenvalues are small relative

to the positive ones and has been extensively used in

PCO and kernel learning related literature (Krzanowski

and Marrior, 1994; Graepel et al., 1998; Peres-Neto and

Jackson, 2001; Pekalska et al., 2002). In our study, the

quantitative dissimilarity matrices given by equations (3)

and (4) contain only a few very small negative eigen-

values but Jaccard distance matrices often result in some

very large negative eigenvalues. Fortunately, as dem-

onstrated by Gower and Legendre (1986), although the

Jaccard distance itself is non-Euclidean, the square

rooted Jaccard distance has Euclidean properties and

hence can be perfectly embedded into Euclidean dis-

tance space. The square rooted fuzzy weighted Jaccard

distance sometimes still has some negative eigenvalues

but such imperfection has been largely reduced, reflected

by the ratios of the sum of absolute negative eigenvalues

over that of positive eigenvalues are significantly lower

than before and never exceed 10%, hence we just ignore

all PCs with negative eigenvalues and keep those with

positive eigenvalues. Hence in equations (2) and (5) we

use the square root of the Jaccard dissimilarity metric.

Once the pair-wise distance matrices are transformed

to sample-latent variable matrices using PCO there are

various methods available to measure the correlation

between these matrices. We employ the Procrustean

Test (Jackson,1995) to measure

between the two types of data inputs (GC/MS and

DGGE). The most attractive aspect of this method is

that it is possible to superimpose two patterns on the

same scatter plot and visualise the matching. The test

involves two steps.

the correlation

(1) The Procrustean transformation (Rohlf and Slice,

1990) is performed on one data matrix and the other

used as the target. The transformed matrix as well as

the matching error when it is compared to the target

matrix is calculated as follows. Given two matrices

A and B to be compared, we set matrix A as the

Y. Xu et al./Comparison of human axillary odour profiles 432

Page 7

target and transform B to match A as closely as

possible. The Procrustean transformation involves

three basic operations:

(a) Translation. Column mean centre both A and B and

scale both matrices so that the sum of squares of all

the elements in each matrix equals 1. The mean

vector and the root sum of squares of all elements in

A has is computed for further use, as discussed be-

low. We denote the matrices after the translation as

Ascland Bscl.

(b) Rotation. The rotation matrix R is obtained by

performing Singular Value Decomposition (Gentle,

1998) on the matrix A¢sclBsclto get A0sclBscl¼ USV0,

R = VU¢ and in this application all N non-zero

components are retained. Note that SVD, unlike

eigen-decomposition, always results in a positive

diagonal matrix S.

(c) Scaling. Thescaling

s ¼P

for all the elements in matrix A. The transformed

matrix obtained from B can be calculated by

Btrans¼ s ? Bscl? R þ 1 ? a where a is the row vector of

means of matrix A and 1 is column vector of 1s. The

matching error e is given by e = ||Btrans)A||.

(2) Evaluate the significance level of the matching error

using a Monte Carlo simulation procedure. Like the

Mantel test, a null distribution of the matching error

is derived by permuting the order of samples in one

factorisobtained by

N

n¼1

snn A

k k, where ||A|| is the root sum of square

data matrix (the order of the variables remains the

same) while keeping the other unchanged. Procrus-

tean transformation is performed on this new pair of

matrices and the matching error computed as de-

scribed above. This process is repeated a large

number of times and the matching errors form the

null distribution. The null distribution is then used

to assess the significance level of the observed

matching error and to give p values as described

above for the Mantel test.

Since the matching error can never be negative, the

Procrustean test is always a one-tailed test. One can also

visualise the matching of two most significant compo-

nents of the data matrices by superimposing the

Procrustean transformed matrix with the target matrix

in a 2-D or 3-D scatter plot.

It is necessary to note that the p values of both the

Mantel test and the Procrustean test are estimated

from empirical null distributions which are formed by

using Monte Carlo simulations. If none of the

randomised resampling experiments produced a higher

(or lower) value than the true observed value, the

estimated p value is reported as 0. Such a case sug-

gests that the observed value is significantly different

from the null distribution. However this does not

necessarily mean that the probability of the observed

value derived from the null distribution is actually 0,

i.e. that the null hypothesis can be rejected at 100%

confidence level.

-0.1-0.05

Correlation Coefficient

0 0.050.1

0

200

400

600

800

s t i

H

f o

. o

N

-0.03 -0.02 -0.0100.01 0.020.03

0

200

400

600

800

Correlation Coefficient

s t i

H

f o

. o

N

0.68 0.6850.690.695 0.7

0

200

400

600

800

Matching Error

s t i

H

f o

. o

N

0.9650.970.975

Matching Error

0.98 0.985 0.99

0

200

400

600

800

s t i

H

f o

. o

N

Null DistributionObserved Value

p=0.0914

p=0.3396

p=0.0774

p=0.3483

(a)(b)

(d) (c)

Figure 2. Mantel test and Procrustean test applied to the full data set of 354 samples: (a) Mantel test on qualitative distance matrices; (b) Mantel

test on quantitative distance matrices; (c) Protest on qualitative distance matrices and (d) Protest on quantitative distance matrices. A total of

10,000 permutations are performed and for the purpose of the bar chart, data are divided into 50 equally spaced bins between the lowest and light

values on the graph, the number of hits is the number of time the relevant parameter falls within a bin.

Y. Xu et al./Comparison of human axillary odour profiles433

Page 8

4. Results

The first step was to compare the patterns of the GC/

MS and DGGE profiles by using all 2P (=354 pairs of

samples). The null distributions for the Mantel and

Procrustean test were obtained using 10,000 permuta-

tions. Both the two-sided Mantel test and Procrustean

test suggest that there is a weak correlation (p<0.1)

between these two data blocks when qualitative distance

metrics were used while no significant correlation can be

found when quantitative distance metrics were used. The

results are presented in figure 2, using 50 equally spaced

bins as illustrated.

We then performed such a comparison on each of

the family groups separately. At first sight, the results

for each family give apparently inconsistent conclu-

sions. Some families showed very significant correlation

between two data blocks while some families do not

show any significant correlation at all. When the

qualitative distance metrics were used, the strongest

correlation between the DGGE and GC/MS signals

come from family D (11 members, 22 samples), both

the Mantel test and Procrustean test result in a value of

p = 0, i.e. not a single case in 10,000 random permu-

tations results in such high correlation and the

observed value of correlation coefficient or matching

error of the Procrustean transformation is also far

away from the corresponding null distribution. Family

A (17 members, 34 samples) also shows very strong

correlation at the level of p = 0 but the observed

values are closer to the null distributions compared to

family D. The superimposed PCO scores plots of two

data blocks of these two families are shown in figure 3.

To interpret these graphs, it is necessary to observe

how close the corresponding DGGE and GC/MS

samples appear. Each family member has a unique

identifying number, and the scores of the two samples

from each individual are averaged after the Procrustes

transformation, for simplicity. Note, for example in

figure 3(b) that the two samples for individual 86

appear in the top right corner, 83 in the bottom left

corner, and 91 and 88 are in the middle. Had there

been no correlation we would expect these paired

samples to appear more or less randomly. Families G,

P and Q also show strong correlations (p<0.05);

families B, C, J show weak correlations (p<0.1) but

correlations between the two blocks for families E, H,

L, M, N, O, R, S and U are consistent with the ran-

dom model for the null distribution at a level of

p>0.1. When the quantitative distance metrics were

used, only three families, G, P and Q show correlations

whose p values varied from 0.01 to 0.07. The results

from all 17 families are summarised in table 1.

However it is important to consider that human

odour can be significantly influenced by many environ-

mental factors, so we examined the behaviour surveys

which the subjects filled in when the samples were taken.

We found that there are considerable variations in

human behaviour, such as the time elapsed from the last

armpit washing, the time from the last use of deodorant

or soap and whether the suggested T-shirt (chemical

free) was worn. This variation was suspected to influ-

ence the GC/MS volatile compound profiles. We expect

that such variations can impact subject?s odour, as well

as their microbial profiles. Hence we defined four subject

screening rules to reduce possible influence from envi-

ronmental factors.

(1) The time of the last armpit washing must be between

12 and 48 h.

(2) The time of the last usage of deodorant must be no

less than 48 h.

(3) The suggested T-shirt must be worn before the

sampling.

(4) The suggested soap must be used in the last armpit

washing.

-0.25-0.2-0.15-0.1-0.0500.05 0.10.15 0.2

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

1

2

4

5

7

9

10

15

17

18

20

24

25

27

28

30

31

1

2

4

5

7

9

10

15

17

18

20

24

25

27

28

30

31

GC/MS

DGGE

-0.4 -0.3 -0.2 -0.10 0.10.2 0.3

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

83

84

85

86

86

87

88

89

90

91

92

93

83

84

85

87

88

89

90

91

92

93

GC/MS

DGGE

(a)

(b)

Figure 3. Superimposed scatter plots of PCO scores of the first two

components of the GC/MS data and Procrustean transformed DGGE

data on families A and D. (a) Family A; (b) Family D. Each number in

the figure represents one test subject; the PCO scores of two repeats of

one testing subject have been averaged to avoid making the plots too

crowded.

Y. Xu et al./Comparison of human axillary odour profiles434

Page 9

By applying these four rules, only 32 of the 177

subjects meet all the requirements. The Mantel test and

Protest were applied to these subjects using a null dis-

tribution based on 64 rather than 354 samples. The

results show very strong correlation between two data

blocks at the level of p = 0 with the qualitative distance

metrics and p<0.01 with the quantitative distance

metrics (see figure 4). For comparison purpose, we also

randomlyselected another

remaining 145 subjects that had not obeyed these

behavioural rules (excluding the 32 individuals above)

and did the same experiment and repeat the computa-

tions 10 times with different random selections of sub-

jects. The results showed that 1 experiment resulted in

strong correlation at the level of p<0.01 and 1 exper-

iment resulted in weak correlation at the level of p<0.1

using a qualitative distance metric; 1 experiment resulted

in strong correlation at the level of p<0.05 with the

quantitative distance metric. The results are summarised

in table 2.

We also compared the null distributions for the

qualitative and quantitative distance metrics generated

by Monte Carlo simulation both for the overall popu-

lation and for each family separately. Although the null

distribution generation procedures are exactly the same

and the only difference involves using different distance

metrics, the characteristics of the null distributions are

very different. For the Mantel test, both null distribu-

tions of qualitative and quantitative distances are cen-

tred around 0 as expected (as a correlation coefficient of

0 implies that there is no link between two blocks of

data) but the distributions of the qualitative distance

metrics always appeared to have much larger standard

32subjectsfrom the

-0.4-0.2

Correlation Coefficient

0 0.20.4

0

200

400

600

800

s t i

H

f o

. o

N

-0.2-0.1

Correlation coefficient

0 0.1 0.2

0

200

400

600

800

s t i

H

f o

. o

N

0.4 0.42

Matching Error

0.440.46

0

200

400

600

800

s t i

H

f o

. o

N

0.7 0.750.80.85

0

200

400

600

800

Matching Error

s t i

H

f o

. o

N

p=0

p=0.0082

p=0

p=0.0054

(a)

(c)

(b)

(d)

Figure 4. Mantel test and Procrustean test applied to the selected data set of 32 subjects (64 samples) that obeyed four behavioural rules over the

period of sampling. (a) Mantel test on qualitative distance matrices; (b) Mantel test on quantitative distance matrices; (c) Protest on qualitative

distance matrices and (d) Protest on quantitative distance matrices. A total of 10,000 permutations are performed and for the purpose of the bar

chart, data are divided into 50 equally spaced bins between the lowest and light values on the graph, the number of hits are the number of time the

relevant parameter falls within a bin.

Table 1

The results of Mantel test and Protest on all families

Family

Number

of

subjects

p-value of Mantel testp-value of Protest

Qualitative

distance

metric

Quantitative

distance

metric

Qualitative

distance

metric

Quantitative

distance

metric

A

B

C

D

E

G

H

J

L

M

N

O

P

Q

R

S

U

All

17

15

12

11

8

9

11

10

15

8

10

5

9

10

10

9

8

177

0

0.0571

0.0641

0

0.4075

0.0423

0.3114

0.0912

0.2088

0.5007

0.128

0.1763

0.0016

0.0095

0.4331

0.4053

0.2989

0.0914

0.1676

0.2895

0.2764

0.1457

0.4806

0.067

0.355

0.3181

0.1112

0.5592

0.4324

0.2691

0.0185

0.0139

0.3271

0.4513

0.3587

0.3396

0

0.0615

0.0607

0

0.5837

0.0431

0.2451

0.0634

0.4714

0.5884

0.1076

0.1136

0

0.0032

0.4174

0.4187

0.2985

0.0774

0.1231

0.137

0.2514

0.1512

0.8977

0.045

0.3055

0.2181

0.4755

0.5983

0.3478

0.2919

0.0112

0.0103

0.6425

0.519

0.3056

0.3483

All p-values less than 0.1 are in italic and bold.

Y. Xu et al./Comparison of human axillary odour profiles 435

Page 10

deviation compared to those of the quantitative

distances, i.e. the histogram of the p.d.f. (probability

distribution function) of the null distribution for the

qualitative distance metric is much broader. It may

suggest that for qualitative distance matrices, the per-

mutation process has much higher influence on the

calculated correlation coefficient for each simulation.

For the Procrustes test, matching errors are used to

form the null distribution. The most obvious difference

is that the null distribution for the qualitative distance

always has much lower average (centre of the p.d.f.)

compared to that of the quantitative distance. It sug-

gests that when the qualitative distance metric is used,

the matching error calculated from Procrustes analysis

could be low even if there is in fact no real correlation,

hence should be interpreted only in the light of Monte

Carlo simulations.

5. Conclusion

Based on the results of the Mantel test and the

Procrustean test, it appears that there is no strong cor-

relation for the overall population between microbial

and chemical odour profiles. However when divided into

individualfamilies,some

revealed and it is probable that correlations are over-

whelmed by environmental factors such as the personal

habits and living conditions of the subjects. When we

select individuals whose behaviour follows certain rules,

there is indeed a significant correlation between the

microbial and chemical odour profiles: the differences

between the families could also be interpreted in terms

of the different personal behaviour patterns in certain

family groups. We also notice that in most cases, the

correlation between human odour profiles and microbial

profiles is usually stronger when the qualitative distance

metrics were used compared to quantitative distance

strongcorrelations are

metrics. This is interpreted in part as the amount of

sweat sampled not being precisely controlled and the

method for DGGE gels is only semi-quantitative so

quantitative dissimilarity metrics are more sensitive to

such variations, whereas qualitative patterns based on

presence/absence of microbes and chemicals are more

robust.

Acknowledgements

Alexandra Katzer is thanked for her superb organisa-

tional skills. Hejun Duan of the Centre for Chemo-

metrics is thanked for helping organise the GC/MS

data, and Fan Gong for preliminary help in the micro-

bial analysis. This work was sponsored by ARO Con-

tract DAAD19-03-1-0215. Opinions, interpretations,

conclusions, and recommendations are those of the

authors and are not necessarily endorsed by the United

States Government.

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0.8589

0.4998

0.1501

0.6562

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