Jürgen Breitenbach

Hans Visser

Jan C Verdoes

Albert J J Van Ooyen

Gerhard Sandmann
email: sandmann@em.uni-frankfurt.de

Engineering of geranylgeranyl pyrophosphate synthase levels and physiological conditions for enhanced carotenoid and astaxanthin synthesis in Xanthophyllomyces dendrorhous

Keywords: carotenoid biosynthesis, 3-hydroxy-4-keto-torulene, geranylgeranyl pyrophosphate synthase, light enhancement

The basidiomycetous yeast, Xanthophyllomyces dendrorhous, is one of the very few organisms which can be used for biological production of the carotenoid astaxanthin. crtE cDNA has been cloned from this fungus for engineering of the terpenoid pathway. The function of its gene product as a geranylgeranyl pyrophosphate synthase was established. .X.

dendrorhous was transformed with the crtE cDNA to divert metabolite flow from the sterol pathway towards carotenoid biosynthesis. Transformants were obtained with increased levels of geranylgeranyl pyrophosphate synthase leading to higher carotenoid levels including astaxanthin. Physiological conditions for maximum carotenoid synthesis for wild type and the CrtE transformant were dim light and extra air supply of the shaking culture. These conditions and the transformation with crtE had additive effects and resulted in an 8-fold higher astaxanthin formation as compared to the initial wild type culture without illumination and extra air supply yielding 451 µg/g dry wt within four days of growth.

Introduction

Astaxanthin (3,3'-hydroxy-4,4'-diketo-β-carotene) is an industrially important carotenoid. It is used as feed additive in salmon and trout farming [START_REF] Bjerkeng | Carotenoids in aquaculture: Fish and Crustaceans[END_REF]) and has beneficial effects on human health [START_REF] Hussein | Astaxanthin, a carotenoid with potential in human health and nutrition[END_REF]). The basidiomycetous yeast, Xanthophyllomyces dendrorhous (the sexual state of Phaffia rhodozyma), is the only fungus which synthesizes substantial amounts of astaxanthin [START_REF] Andrewes | 3R,3'R)-Astaxanthin from the yeast Phaffia rhodozyma[END_REF]. Its carotenoid pathway is well established. The major end product is astaxanthin. However, a second product is 3 -hydroxy-4keto-torulene (Vasquez and Santos 1998). This keto carotenoid is formed as a by-product (see Fig. 1 for details). Only three genes cover the whole specific carotenoid pathway from phytoene synthesis to the end products. These are crtYB, a fusion gene encoding a phytoene synthase and a lycopene cyclase (Verdoes et al. 1999a), crtI encoding a phytoene desaturase which forms lycopene and 3,4-didehydrolycopene (Verdoes et al. 1999b) and asy encoding an astaxanthin synthase which converts β-carotene via echineneone (4-keto-β-carotene), 3-hydroxy4-keto-β-carotene and phoenicoxanthin (3-hydroxy-4,4'-diketo-β-carotene to astaxanthin [START_REF] Ojima | Cloning of the astaxanthin synthase gene from Xanthophyllomyces dendrorhous (Phaffia rhodozyma) and its assignment as a betacarotene 3-hydroxylase / 4-ketolase[END_REF]. The function of the latter enzyme is dependent on a specific astaxanthin synthase reductase (Alcaíno et al. 2008).

An alternative or complementary approach to random mutagenesis for high yield strains [START_REF] An | Isolation of Phaffia rhodozyma mutants with increased astaxanthin content[END_REF]) is genetic engineering of the astaxanthin synthesis pathway. In general, genetic modification may increase the flow of precursors into a specific pathway, mediate an efficient conversion of intermediates into the end product and divert a pathway at a branch point much stronger into a desired direction.

First attempts have been made for successful genetic engineering of the carotenoid pathway of X. dendrorhous. Introduction of extra copies of the crtYB fusion gene resulted in transformants with higher total carotenoid content (Verdoes et al. 2003a). This is due to the additional phytoene synthase activity. A second effect observed in the crtYB transformants was a change of the carotenoid composition with a strong decrease of 3-hydroxy-4ketotorulene, the alternative product of X. dendrorhous carotenoid biosynthesis. This can be attributed to the lycopene cyclase part of crtYB gene product.

Feeding of the terpenoid precursor mevalonate to X. dendrorhous resulted in a fourfold increase of astaxantin content [START_REF] Calo | Mevalonic acid increases transastaxanthin and carotenoid biosynthesis in Phaffia rhodozyma[END_REF]. Consequently, we regarded synthesis of GGPP as a substrate for phytoene as a limiting step for carotenoid synthesis as found before for Saccharomyces cerevisiae (Verwaal et al. 2007). Therefore, we engineered X. dendrorhous by over-expressing its own GGPP synthase gene. The resulting increase of astaxanthin formation was analyzed under different physiological conditions i.e. by variation of O 2 supply and illumination.

Materials and methods

Strains, growth and physiological conditions

Xanthophyllomyces dendrorhous strain CBS6938 (=ATCC96594) was grown in 150 ml of a medium containing Bacto-peptone (5 g/l), yeast extract (3 g/l), malt extract (3 g/l), and glucose (10 g/l) in 1 l conical flasks at 20°C on a rotary shaker for 4 days in darkness.

Selection of transformants for G418 resistance was with geneticin (G-418 sulfate, 40 µg/ml) containing agar plates. Light cultures were illuminated with low white light of 1 µmol photons m -2 s -1 . High O 2 cultures were supplemented with extra air at 50 ml/min. Transformation of X. dendrorhous was carried out by electroporation according to Visser et al. (2005).

Escherichia coli strains DH5α, XL1-Blue MFR and JM101 used for genetic manipulations or functional complementation, respectively, were grown on LB medium with ampicillin (100 µg/ml) and chloramphenicol (34 mg/l).

Cloning of the GGPP synthase cDNA and construction of plasmids for E. coli and X. dendrorhous A cDNA library from X. dendrorhous [START_REF] Ojima | Cloning of the astaxanthin synthase gene from Xanthophyllomyces dendrorhous (Phaffia rhodozyma) and its assignment as a betacarotene 3-hydroxylase / 4-ketolase[END_REF]) in E. coli XL1-Blue MFR was screened for a GGPP synthase cDNA by functional complementation and color selection. For this purpose, the library was co-transformed with plasmid pACCAR25ΔcrtE [START_REF] Sandmann | Functional identification of al-3 from Neurospora crassa as the gene for geranylgeranyl pyrophosphate synthase by complementation with crt genes, in vitro characterization of the gene product, and mutant analysis[END_REF], which contains all the genes for the synthesis of zeaxanthin glucosides except the gene for GGPP synthase crtE. Functional complementation with a GGPP synthase cDNA should enable the synthesis of colored carotenoids. An orange pigmented colony was found among 8000 white ones. This X. dendrorhous cDNA was used as template for further plasmids. Plasmid pUC8-2crtE was designed for crtE expression in E. coli. It was constructed by PCR amplification with primers EcocrtEforw 5'-GAATTCATGGATTACGCGAACATCCTC-3' and crtErew 5'-GTCGACTCACAGAGGGATATCGGCTAG-3', and sub-cloned into Toverhang vector pMON38201 [START_REF] Borovkov | XcmI-Containing vector for direct cloning of PCR products[END_REF]. The crtE insert was subsequently excised with EcoRI and PstI and finally ligated into pUC8-2 [START_REF] Hanna | Construction of a family of universal expression plasmid vectors[END_REF]). The plasmid with the crtE cDNA for transformation of X. dendrorhous was obtained by amplification with the primers PcrtEATG 5'-ATATGAATTCATGGATTACGCGAACATCCTC-3' and PcrtETGA 5'-TATAGTCGACTCACAGAGGGATATCGGCTAG-3' which generated EcoRI and SalI cloning sites. The obtained PCR product of expected size (1.1 kb) was ligated into the EcoRI and XhoI sites of vector pPRcDNA1 [START_REF] Ojima | Cloning of the astaxanthin synthase gene from Xanthophyllomyces dendrorhous (Phaffia rhodozyma) and its assignment as a betacarotene 3-hydroxylase / 4-ketolase[END_REF]) yielding pPRcDNA1crtE.

Carotenoid extraction and analysis

Cells of X. dendrorhous were harvested and freeze-dried. Carotenoids were subsequently extracted from these cells with dimethylsulfoxide by heating for 15 min at 60°C. After centrifugation, the extract was transferred into a separator funnel, diethyl ether was added, and the mixture was kept on ice for 3 min before water was added for phase separation. The upper phase was collected to which step by step acetone, 10% (v/v) diethyl ether in petroleum ether (bp 60-80°C) and water were added. Again, the upper phase was collected, washed with water, dried in a stream of N 2 , and re-suspended in acetone. Details of the extraction procedure are given elsewhere (Visser et al. 2005).

Freeze-dried E. coli cells were extracted with methanol by heating for 15 min at 60°C.

The extract was partitioned against 50% (v/v) ether in petrol and the upper phase collected and dried. High-performance liquid chromatography (HPLC) separation of carotenoids was performed on a 25cm HyPurity C18, 5µ column with acetonitrile /methanol/2-propanol (85:10:5, by vol) as the mobile phase. Spectra were recorded on-line with a photodiode array detector. Carotenoid identification and quantitation was carried out with authentic standards.

Results and discussion

Function of crtE and the X. dendrorhous crtE transformation vector

The cloned GGPP synthase cDNA crtE from X. dendrorhous encoded a protein of 375 amino acids. The sequence of the cDNA and genomic DNA is presented elsewhere [START_REF] Van Ooijen | Recombinant material for carotenoid production[END_REF]). The function of the cDNA was determined by pathway complementation in E. coli using plasmid pACCAR25ΔcrtE, which contained all genes for the synthesis of zeaxanthin diglucoside except the GGPP synthase gene [START_REF] Sandmann | Functional identification of al-3 from Neurospora crassa as the gene for geranylgeranyl pyrophosphate synthase by complementation with crt genes, in vitro characterization of the gene product, and mutant analysis[END_REF]. Upon separation by HPLC, only minor amounts of zeaxanthin diglucoside and zeaxanthin of together 4 µg/g dw were detectable due to the very low GGPP pool in E. coli. When E. coli was co-transformed with pUC8-2crtE (for vector map see Fig. 2 top), which was designed for crtE expression, the concentration of the same carotenoids including small amounts of zeaxanthin monoglucoside increased more than 30-fold to 128 µg/g dw. This result indicated that the CrtE from X. dendrorhous indeed is the GGPP synthase as shown in Fig. 1.

After assignment of the crtE cDNA as a GGPP synthase, it was used to construct a transformation plasmid for crtE genome integration and over-expression in X. dendrorhous.

The resulting plasmid is shown in Fig. 2 bottom. Both the crtE cDNA and the nptII gene conferring resistance of transformed X. dendrorhous to geneticin (G418) were flanked by the promoter and terminator of the X. dendrorhous glyceraldehyde-3-phosphate dehydrogenase gene. The crtE transformation vector contained a ribosomal DNA sequence region for multiple copy integration into the X. dendrorhous genome. Integration of the transformation vector was achieved after linearization by the single-cutting restriction enzyme SfiI prior to transformation.

Carotenoid formation in X. dendrorhous CBS6938[crtE] transformants

Since after transformation of X. dendrorhous, variations in the resulting phenotype can be found depending on the number of integrated copies (Verdoes et al. 2003), different CBS6938[crtE] transformants were selected according to the intensity of their pigmentation.

The carotenoids of the three most pigmented transformants are shown in Table 1. They synthesize between 1.3-to 1.5-fold more total carotenoids than the control reaching up to 288 µg/g dry weight. Transcript determinations of crtE in transformant no. 1 revealed a 10 times higher level than in the wild type strain (data not shown). In spite of the resulting enhanced overall carotenoid synthesis, formation of the pathway end product astaxanthin did not increase accordingly. Instead, also keto carotenoid intermediates accumulate. This result indicates that the transformants have a certain limitation in the biosynthesis pathway to astaxanthin for the last steps catalyzed by Asy (Fig. 1). A similar observation was also reported for X. dendrorhous transformants that over-expressed the crtYB gene (Verdoes et al.

2003).

The major terpenoid in fungi is ergosterol. Its synthesis branches off the route to carotenoids at the level of farnesyl pyrophosphate, the substrate for GGPP synthase. The concentrations of ergosterol and carotenoids including colorless phytoene were determined in wild type CBS6938 and the transformant CBS6938[crtE] with over-expressed GGPP synthase (Table 2). In the wild type strain grown without extra air supply, the carotenoid content was substantially lower than ergosterol regardless whether permanently illuminated or not.

Enhanced air supply increased colored carotenoids at the expense of ergosterol. Additionally, the phytoene content decreased. These results suggest a better utilization of FPP towards carotenogenesis and a more efficient conversion within the carotenoid pathway towards the end products. This up-regulation of astaxanthin synthesis with higher O 2 supply may be due to generated singlet oxygen and oxygen radicals [START_REF] Schroeder | Singlet oxygen and peroxyl radicals regulate carotenoid biosynthesis in Phaffia rhodozyma[END_REF]. Another environmental factor which can stimulate carotenogenesis in X. dendrorhous is light (de la [START_REF] De La Fuente | Hightiter production of astaxanthin by the semi-industrial fermentation of Xanthophyllomyces dendrorhous[END_REF]. With our wild type strain, the highest astaxanthin and 3-hydroxy-4ketotorulene concentrations were obtained in the light with extra air supply, which with 452 µg/d dry weight were 5-fold higher than in the dark, culture without extra air. The same tendency was observed for the crtE transformant. Here, we obtained an additive effect between GGPP synthase over-expression, illumination and O 2 supply, which all contributed to increased synthesis of total carotenoids including astaxanthin. In the case of astaxanthin, the yield was 8-fold higher than in the initial wild type culture without illumination and extra air supply reaching a maximum of 451 µg/g dry wt.

Conclusion

Over-expression of crtE is a useful target to divert and enhance metabolite flow into carotenogenesis. In addition, physiological conditions like dim light illumination of and enhanced air supply to the shaking culture all independently contributed to enhanced astaxanthin synthesis in an additive way. Although astaxanthin yield could be strongly increased, its amount accounts only for 43% of total carotenoids even under optimum conditions. Most of the residual carotenoids are keto derivatives which are not completely metabolized into astaxanthin. This finding suggests that asy over-expression should be the next step to increase astaxanthin yield. Previous transformation with additional copies of the crtYB gene was already successful in increasing carotenoid formation (Verdoes et al. 2003).

Therefore, maximum astaxanthin biosynthesis can finally be achieved both by generating a fully genetically engineered X. dendrorhous with additionally expressed crtE, crtYB and asy genes which are likely to alleviate limitations of the carotenoid pathway in combination with advantageous cultivation conditions. This overall genetic approach will represent a decisive step towards the development of X. dendrorhous as a cell factory for astaxanthin production which may economically compete with chemical synthesis. --------------------------------------------------------------------------------------------------------Growth was for 4 days without extra air supply, in the dark at 20°C as shaking cultures.

--------------------------------------------------------------------------------------------------- 198
Means + standard deviation were from 3 to 5 determinations.

--------------------------------------------------------------------------------------------------------------- CBS6938

-Fig. 1

 1 figure legends

Fig. 2

 2 Fig. 2 Transformation vectors pUC8-2crtE for CrtE expression in Escherichia coli (top) and pPRcDNA1crtE for over-expression of geranylgeranyl pyrophosphate synthase in Xanthophyllomyces dendrorhous (bottom).

Table 1

 1 Total colored carotenoids and % distribution of individual carotenoids in

	Xanthophyllomyces dendrorhous wild type CBS6938 (control) and individual crtE
	transformants CBS6938[crtE] (numbers 1, 2, 3).
	Carotenoids (µg/g dw)	Control	1	2	3

Table 2

 2 Ergosterol and carotenoid formation (µg/g dw) in wild type Xanthophyllomyces dendrorhous CBS6938 and a transformant with integrated crtE gene CBS6938[crtE]#1

	Conditions	Ergosterol	Phytoene	TCC	3HO4KT	Astaxanthin
	-

Verdoes JC, Krubasik KP, Sandmann G, van Ooyen AJJ (1999a)


O Adriani

G C Barbarino

G A Bazilevskaya

R Bellotti
email: roberto.bellotti@ba.infn.it

M Boezio

E A Bogomolov

L Bonechi

M Bongi

V Bonvicini

S Borisov

S Bottai

A Bruno

F Cafagna

D Campana

R Carbone

P Carlson

M Casolino

G Castellini

L Consiglio

M P De Pascale

C De Santis

N De Simone

V Di

A M Galper

W Gillard

L Grishantseva

P Hofverberg

G Jerse

S V Koldashov

S Y Krutkov

A N Kvashnin

A Leonov

V Malvezzi

L Marcelli

W Menn

V V Mikhailov

E Mocchiutti

A Monaco

N Mori

N Nikonov

G Osteria

P Papini

M Pearce

P Picozza

M Ricci

S B Ricciarini

L Rossetto

M Simon

R Sparvoli

P Spillantini

Y I Stozhkov

A Vacchi

E Vannuccini

G Vasilyev

S A Voronov

J Wu

Y T Yurkin

G Zampa

N Zampa

V G Zverev

D Marinucci

V Di Felice

A statistical

Keywords: Cosmic-rays, Positron, Classification, Wavelets, Electromagnetic calorimeter

HAL is

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Introduction

Recent measurements of cosmic-ray electrons and positrons carried out by the ATIC [1], PAMELA [2] FERMI [3] and HESS experiments [4], extend the previous balloon-borne [5,6,7,8,9,10], and satellite [11] measurements and represent a breakthrough in cosmic-ray physics. In particular it is well known that an antimatter component that cannot be explained as an effect of a purely secondary production mechanism, could provide insight into the nature and distribution of particle sources in our galaxy [12]. The PAMELA experiment has reported a measurement of the positron fraction, i.e. the ratio of positron flux to the sum of electron and positron fluxes, R = φ(e + )/(φ(e -) + φ(e + )), at energies between 1.5 GeV and 100 GeV, sampled in 16 energy bins. The observations extend the energy range of previous positron measurements and ambiguously show an anomalous positron abundance above 10 GeV. A reliable identification of electrons and positrons has been performed by combining information from independent detectors within the apparatus [2,13]. The main difficulty in the measurement of R is the dominating background flux from protons which is 10 3 (at 1 GV) and 10 4 (at 100 GV), times the positron flux. Furthermore, a precise estimate of the proton contamination in the positron sample is a difficult task.

A widely adopted approach both in high energy physics and astrophysics, consists of an intensive use of simulated signal and background samples to train different multivariate classifiers, such as artificial neural networks and support vector machines [15,16]. It has been demonstrated that such a approach can improve background rejection in the signal sample [17,18]. However this approach can introduce systematic uncertainties which are difficult to estimate, for the real data.

In this paper we present a method used to obtain an updated the PAMELA positron fraction [2] and further statistical procedures, based on wavelet and kernel estimates, in order to estimate the proton contamination in the positron sample. Although our approach is based on well known statistical techniques, we believe this methodology can be of interest because the data analysis is mainly based on the discrimination capabilities of a single detector, i.e. the electromagnetic calorimeter. Previously published results [2] refer to data collected by the experiment between July 2006 and February 2008. Here, we present the methodology applied to larger data set collected between July 2006 and December 2008.

In Section 2 the PAMELA experiment is briefly described. A detailed description of the apparatus can be found in [19]. In Section 3 the discriminating variables used for the analysis are presented. In Section 4 the event selection procedure is described: this is the first phase of the analysis and it involves all the detectors of the PAMELA apparatus. The core of the analysis is described in Section 5. The methodologies developed to estimate the positron fraction R and the statistical and systematic uncertainties are illustrated and applied to the PAMELA data. A summary of the experimental results and the conclusions are presented in Section 6.

The PAMELA apparatus

As shown in Fig. 1, the PAMELA apparatus is composed by the following detectors (from top to bottom):

1. a time-of-flight system (ToF (S1, S2, S3)); 2. a magnetic spectrometer;

3. an anticoincidence system (AC (CARD, CAT, CAS)); 4. an electromagnetic imaging calorimeter; 5. a shower tail catcher scintillator (S4) and 6. a neutron detector.

The ToF system provides a fast signal for triggering the data acquisition and measures the time-of-flight and ionization energy losses (dE/dx) of traversing particles. It also allows down-going particles to be reliably identified. Multiple tracks, produced in interactions above the spectrometer, are rejected by requiring that only one strip of the top ToF scintillator (S1 and S2) layers register an energy deposition (hit). Similarly no hits were permitted in either top scintillators of the AC system (CARD and CAT). The magnetic spectrometer consists of a 0.43 T permanent magnet and a silicon microstrip tracking system. It measures the rigidity of charged particles through their deflection in the magnetic field. During flight the spatial resolution is observed to be 3 µm in the bending view, corresponding to a Maximum Detectable Rigidity (MDR), defined as a 100% uncertainty in the rigidity determination, exceeding 1 TV. The dE/dx losses measured in S1 and the silicon layers of the magnetic spectrometer were used to select minimum ionizing singly charged particles (mip) by requiring the measured dE/dx to be less than twice that expected from a mip. The sampling calorimeter comprises 44 silicon sensor planes interleaved with 22 plates of tungsten absorber. Each tungsten layer has a thickness of 0.26 cm corresponding to 0.74 radiation lengths. A high dynamic-range scintillator system (S4) and a neutron detector are mounted under the calorimeter. The apparatus is approximately 130 cm tall and with a mass of about 470 kg and it is inserted inside a pressurized container attached to the Russian Resurs-DK1 satellite [19].

Figure 1: A schematic overview of the PAMELA satellite experiment. The experiment stands ∼ 1.3 m high and, from top to bottom, consists of a time-of-flight (ToF) system (S1, S2, S3 scintillator planes), an anticoincidence shield system, a permanent magnet spectrometer (the magnetic field runs in the y-direction), a silicon-tungsten electromagnetic calorimeter, a shower tail scintillator (S4) and a neutron detector. The experiment has an overall mass of 470 kg.

The imaging calorimeter

In this analysis the PAMELA silicon-tungsten sampling imaging calorimeter [20] plays a key role, due to its capability to give an accurate topological description of the showers generated by the interaction of the cosmic-ray particles.

Electromagnetic calorimeters have been widely used for particle discrimination in balloon-borne cosmic-ray experiments [5,7,21,22]. The PAMELA an imaging calorimeter is evolution of the instrument used in several balloonborne experiments [22,23,6] and its performances have been thoroughly investigated by means of test beam data and Monte Carlo simulations [20]. It is 16.3 radiation lengths (0.6 nuclear interaction lengths) deep, so both electrons and positrons develop a well-contained electromagnetic shower in the energy range of interest. In contrast, the majority of the protons will either pass through the calorimeter as a minimum ionizing particle or interact deeply in the calorimeter. In fact there is a high probability (>89%) that an electromagnetic shower will start in the first 3 planes of the calorimeter. For hadronic showers, the starting point is distributed more uniformly. Particle identification based on the total measured energy and the starting point of the reconstructed shower in the calorimeter can be tuned to reject 99.9% of the protons, while selecting more than 95% of the electrons or positrons. The remaining proton contamination in the positron sample can be eliminated using additional topological information, including the lateral and longitudinal profile of the shower. Using particle beam data collected at CERN it was previously shown that less than one proton out of 100, 000 passes the calorimeter electron selection up to 200 GeV/c, with a corresponding electron selection efficiency of 80% [20].

Discriminating variable selection

The misidentification of electrons and protons are the largest sources of background when estimating the positron fraction. This can occur if the signof-charge is incorrectly assigned from the spectrometer data, or if electronand proton-like interaction patterns are confused in the calorimeter data. The proton-to-positron flux ratio increases from approximately 10 3 at 1 GeV to approximately 10 4 at 100 GeV and represents the major source of contamination. Robust positron identification is therefore required and the residual proton background must be carefully assessed. To do this a single discriminating variable is considered: the fraction F of calorimeter energy deposited inside a cylinder of radius 0.3 Molière radii. Fig. 2 shows F as a function of deflection (rigidity -1 ). The axis of the cylinder is defined by extrapolating the particle track reconstructed in the spectrometer. The Molière radius is an important quantity in calorimetry as it quantifies the lateral spread of an electromagnetic shower (about 90% of the shower energy is contained in a cylinder with a radius equal to 1 Molière radius), and depends only on the absorbing material (tungsten in this case). The events shown in Fig. 2 were selected requiring a match between the momentum measured by the tracking system and the total detected energy and the starting point of the shower in the calorimeter. For negatively-signed deflections, electrons are clearly visible as a horizontal band with F lying mostly between 0.4 and 0.7. For positively-signed deflections, the similar horizontal band is naturally associated to positrons, with the remaining points, mostly at F < 0.4, designated as proton contamination. The validity of such event characterization was confirmed using the neutron yield from the calorimeter and the ionization (dE/dx) losses measured in the spectrometer [13]. The spillover limit for positrons is estimated from particle beam tests to be approximately 300 GeV. From particle beam tests the spillover limit for positions is estimated to be approximately 300 GeV, primarily due to the tracker resolution. The electron spillover background between 1.5 and 100 GeV is negligible.

Event selection

While the distribution shown in Fig. 2 presents a clear positron signature, the residual proton background distribution must be quantified. It is worthwhile to note that the background distribution was obtained using the flight calorimeter data and there was no dependence on simulations. In order to build a background model, the total calorimeter depth of 22 detector planes was divided in two non-mutually exclusive parts: an upper part comprising planes 1 -20, and a lower part comprising planes 3 -22. The positron component in positively charged events can be significantly reduced by selecting particles that do not interact in the first 2 planes because only 2% of electrons and positrons with rigidities greater than 1.5 GV pass this condition. This requirement selects a nearly pure sample of protons entering the lower part of the calorimeter (planes 3 -22). The event selection methodology was further validated using particle beam data collected prior to lunch and data generated using the PAMELA Collaboration's official simulation program. This simulation is based on the GEANT package [START_REF] Brun | Detector Description and Simulation Tool[END_REF] version 3.21 and The number of events per bin is shown in different colors, as indicated in the color scale. The axis of the cylinder is defined by extrapolating the particle track reconstructed by the spectrometer. The events were selected requiring a match between the momentum measured by the tracking system and the total detected energy and requiring that the electromagnetic shower starts developing in the first planes of the calorimeter.

reproduces the entire PAMELA apparatus.

Calorimeter variables (e.g. total detected energy, and lateral shower spread) were evaluated for the upper and lower parts of the calorimeter. Electrons and positrons were identified in the upper part of the calorimeter using the total detected energy and the starting point of the shower. As an example Fig. 3 shows the energy fraction F , for negatively charged particles in the rigidity range 28 -42 GV selected as electrons in the upper half of the calorimeter (panel a). Panels (b) and (c) show the F distributions for positively-charged particles obtained for the lower (upper) part of the calorimeter, i.e. protons (protons and positrons). The distributions in panels (a) and (b) are clearly different while panel (c) shows a mixture of the two distributions, which strongly supports the positron interpretation for the electron-like F distribution in the sample of positively charged events.

Positron/proton discrimination

As a result of the event selection described in the last section we obtained the distributions of pure electrons, pure protons and a mixture of positrons and protons, as shown in Fig. 3. Starting from these distributions the deter- mination of the ratio R, with the statistical and systematic error estimates, consists of four main steps, as summarized in Fig. 4: 1. estimation of the probability density functions (pdf) for the experimental distributions shown in Fig. 3; 2. construction of a finite mixture density of probability; 3. estimation of the weight of the mixture by means of the maximum likelihood indicator;

4. estimation of the statistical errors by means of a bootstrap procedure.

In addition, an estimate of the systematic uncertainties due to inaccuracies in the background identification is performed.

Pdf estimate

The proton experimental distributions provide information about the background yields. In order to evaluate these distributions and to check possible systematic errors in this phase of the analysis, three different methods have been implemented: beta, wavelets and kernel.

Beta pdf

Since the discriminating variable used for the analysis is the energy fraction F , spanning the interval [0, 1], the rational choice is to fit the experimental distribution with a function spanning in the same interval and with few free parameters, in order to avoid unphysical modeling of the experimental data. We used the beta function [START_REF] Rohatgi | An Introduction to Probability Theory and Mathematical Statistics[END_REF] to fit both electrons and protons. A set of parameters for each rigidity bins is obtained and used for the subsequent steps of the analysis.

Wavelets

In the previous section, the distribution of the energy fraction was fitted by means of a fixed family, i.e. we fitted a parametric law in the statistical jargon. More precisely, we assumed a priori that the experimental distributions we observed should be generated according to a specific (beta) law in [0, 1]. Although the choice of a beta function is natural for random variables in this range, it is important to question how much our final results depend on this assumption, i.e. their degree of robustness when varying the energy fraction distribution over a much greater range of possibilities. Our goal here is to explore the possibility of a nonparametric fit, where there is no a priori assumption on the energy fraction distribution. Over the last fifteen years, the statistical literature has focussed on the estimation of density functions in this broader nonparametric setting. We refer for instance to [START_REF] Hardle | Wavelets, Approximation and Statistical Applications[END_REF] for an introduction to this area of research. A wide consensus has formed on the role of wavelet based methods as the most powerful statistical techniques for nonparametric density estimation. To fit the proton sample, the wavelet thresholding technique with the Daubechies' basis (in particular db3) has been used. A critical step has been to find the best value for the parameter c in (17). We started fixing c = 3, which is often recommended as rule-of-the-thumb choice. We further verified by numerical experiments that our results are very stable for a wide range of fluctuations around this value. The positron-to-electron ratio estimates and corresponding confidence intervals are very close (indeed, in some cases nearly undistinguishable) from those obtained with the parametric fit of the beta distribution.

Kernel estimate

Since the discriminating variable is defined in the bounded interval [0, 1] a beta kernel has been used [START_REF] Xi | [END_REF]. The beta kernel is a non-negative kernel and it is usually considered to estimate probability density functions with compact supports. The number of beta functions generated was equal to the number of bins of the histogram and each beta function had a mean equal to the center of histogram bins. The standard deviation of these functions has been chosen through an application of the Kolmogorov-Smirnov test so that the initial distribution of protons and the modified one were statistically compatible, thereby rejecting the null hypothesis at 5% level.

The beta parameters (p, q) have been calculated inverting (8) and (9). The kernel band-with is assumed to be the histogram bin. The number of events in each histogram of protons has been increased six fold compared to the original histogram. Fig. 7 shows the real protons and the pseudo-proton set for rigidity between 28 GV and 42 GV. Each pseudo-proton sample is then analyzed in the same way as the real protons (in particular with wavelets-fit), obtaining, for each energy bin, a new positron fraction.

Finite mixture density

A finite mixture of distributions is used for modeling data set extracted from not homogeneous population. It is useful to analyze a sample drawn from an unknown mixture of known distributions. In the procedure of the finite mixture distributions an experimental distribution may be approximated as a linear combination of probability distribution functions (pdfs) [START_REF] Everitt | Finite Mixture distributions[END_REF]:

g(x, p) = n i=1 p i f i (x) ( 1 )
where g(x, p) is the pdf to estimate, f i (x) are known pdfs, n is the number of pdfs, p i are the mixing proportions (0 < p i < 1 and n i=1 p i = 1) to estimate. In the present analysis we model, for each energy interval, the distribution of the calorimeter energy fraction (F ) for positively-charged particles as mixture distribution [START_REF] Everitt | Finite Mixture distributions[END_REF] of the positrons and protons pdfs:

g(F ) = pf b (F ) + (1 -p)f s (F ) ( 2 )
where f b (F ) and f s (F ) are the probability density functions for protons and electrons, respectively and the pdfs f b and f s have been determined in the previous section. As a result of this phase of the analysis a set of unknown weights p j , with j = 1,...,16, is obtained.

Maximum Likelihood

In order to find the values of unknown weights p j we used the well know maximum likelihood method. In the present case the likelihood function, (for each rigidity bin), is

L j = m t=1 p j f b (F t ) + (1 -p j )f s (F t ) ( 3
)
where m is the number of independent observations x 1 , x 2 , ..., x m in each rigidity bin. The estimation of the parameters p j is done by maximizing the natural logarithm of (3): As a result of the three steps of the analysis, three different weights of the mixture for each energy bin are obtained. Using the beta functions, the wavelets transform and the kernel technique. In the next section the bootstrap technique is introduced. It has been used to evaluate both the positron fraction R and the statistical errors of the measurements.

∂lnL j ∂p j = 0. ( 4

Statistical error estimates by means of the bootstrap technique

The Bootstrap is a powerful method for analyzing small expensive-tocollect data sets where prior information is sparse [START_REF] Nankervis | [END_REF]. In this method, a set of data is randomly re-sampled many times with replacement. Then statistical indicators, such as the standard error or the confidence interval, are evaluated from these new samples [START_REF] Money | Bootstraping: A Nonparametric Approach to Statistical Inference[END_REF].

This procedure has been used to estimate the statistical error on the ratio R.

Rigidity at

Percent Each experimental distributions for electrons, protons and positivelycharged particles have been re-sampled 1000 times, then the three steps of the analysis procedure previously described have been repeated. For each rigidity bin, a statistical distribution of the ratio R is thereby obtained.

As a first step, M = 1000 bootstrap re-sampling of positives sample were applied. For each re-sample i the unknown parameter p ij was estimated by means of an unbinned maximum likelihood analysis, for each rigidity bin j. As a second step the procedure has been repeated N = 1000 times applying N bootstrap re-sampling of electron and proton sample. So N × M estimations of the number of positron candidates have been obtained. Then, the final number of positron candidates was obtained as:

nj = 1 N N i=1 ( 1 M M t=1 n ti ) ( 5
)
where n ti in the number of positron candidates evaluated by each bootstrap iteration. Therefore also N × M estimations of positron fraction have been obtained. In the present analysis we used the range from the 16th and 84th percentiles of these distributions as the statistical error estimates of the ratio R.

As shown in Table 1 the statistical errors on the points range between 3% and 10% in all bins but the last two and then increase to just under 30% in the highest energy bin. Fig. 9 shows three new estimates of the July'06-December'08 (Beta pdf)

Energy [GeV] 1 10 2 10 )] - (e φ )+ + (e φ )/[
July'06-December'08 (Wavelets pdf)

July'06-December'08 (Kernel + Wavelets pdf)

Figure 9: The positron fraction R obtained using the wavelets-fit (blue), beta-fit (red) and kernel with wavelets-fit (green).

positron fraction, using the different fitting techniques adopted in this study. Moreover, as shown in Tab. 2, the results obtained with the three different background pdfs are consistent with each other.

Rigidity at Mean kinetic energy Extrapolated

φ(e

+ )
φ(e -)+φ(e

+ ) Extrapolated φ(e + )
φ(e -)+φ(e

+ ) Extrapolated φ(e + ) φ(e -)+φ(e + )
spectrometer (GV) at top of payload at top of payload at top of payload at top of payload with beta/wavelets/kernel (GeV) with beta-fit with wavelets-fit kernel with wavelets-fit wavelets-fit and kernel with wavelets-fit. The errors are defined by the range between the 16th and the 84th percentiles in the R distributions.

Systematic uncertainties due to inaccuracies in the background selection

In this section a further procedure aimed to estimate the systematic uncertainties in the positron fraction measurement is presented. Due to the equivalence of the results obtained in the previous section with the three different pdfs, the evaluation of the systematic uncertainties has been performed using only the beta fit.

It is based on a deformation of the experimental distribution of the positively charged particles selected as proton, as shown in Fig. 10. This deformation can be introduced using the weighted bootstrap technique [START_REF] Barbe | The Weighted Bootstrap[END_REF], such as the re-sampled event are chosen to prefer a single part of experimental data set. For each rigidity bin, starting from a proton sample n(F ) with mean x, two new samples, n + (F ) and n -(F ), are generated:

1. n + (F ) with mean x+ > x; 2. n -(F ) with mean x-< x.
In such way, starting from our experimental data two new distribution are obtained. The bootstrap weights are chosen in order to have both n + (F ) and n -(F ) statistically incompatible with n(F ), according to the Kolmogorov-Smirnov test: therefore both n + (F ) and n -(F ) are statistically incompatible with the distribution of events selected as protons. Using n + (F ) and n -(F ) to evaluate the positron ratio we obtained R + and R -. The range encompassing R-R + and R --R is assumed as an estimate of the systematic uncertainty due the inaccuracies in the proton selection. Tab. 3 reports the systematic uncertainties assessed for each rigidity bin. The obtained results show that the systematic uncertainties [R -R + ; R --R] are of the same magnitude as the statistical errors.

Experimental results and conclusions

Fig. 11 shows the positron fraction R obtained trough beta-fit with statistical and systematic errors summed in quadrature, compared with the PAMELA positron fraction previously reported [2]. The solid line shows a calculation by Moskalenko & Strong [START_REF] Moskalenko | [END_REF] for pure secondary production of positrons during the propagation of cosmic-rays in the galaxy. Protonpositron discrimination is provided the imaging calorimeter, the capability to yield a trustworthy estimate of the positron and electron numbers in the cosmic radiation at energies between 1.5 GeV to 100 GeV has been clearly established. Compared to what is reported in [2]: a) new experimental data, b) the application of three novel background models and c) an estimate of the systematic uncertainties has been presented. The new experimental results are in agreement with what reported in [2] and confirm both solar modulation effects on cosmic-rays with low rigidities and an anomalous positron abundance above 10 GeV. Figure 11: The positron fraction R obtained using a beta-fit with statistical and systematic errors summed in quadrature (red), compared with the positron fraction reported in [2] (black). The solid line shows a calculation by Moskalenko & Strong [START_REF] Moskalenko | [END_REF] for pure secondary production of positrons during the propagation of cosmic-rays in the galaxy.

Energy [GeV]

Appendices A. Beta function

The beta function is defined by:

f (x) = 1 β(p, q) x p-1 (1 -x) q-1 . ( 6
)
where p > 0, q > 0, and

β(p, q) is β(p, q) = 1 0 x p-1 (1 -x) q-1 dx. ( 7
)
The mean of the beta pdf is:

x = p p + q (8)
and its variance is:

σ 2 = pq (p + q) 2 + (p + q + 1) . ( 9)

B. Wavelets

A wavelet system is essentially an orthonormal basis which is constructed by dilations and translations of a mother and father function, leading to a multiresolution scheme. The wavelets we are going to implement are those proposed by Daubechies, which are computationally convenient as their support in the real domain is limited. More explicitly, the father wavelet satisfies [START_REF] Hardle | Wavelets, Approximation and Statistical Applications[END_REF]:

ϕ(x) = √ 2 k h k ϕ(2x -k) ( 10
)
where h k are suitably chosen weights ( [START_REF] Fhang | Wavelets in Physics[END_REF]), whereas the mother wavelet satisfies:

ψ(x) = √ 2 k (-1) k+1 h 1-k ϕ(2x -k) (11)
The multiresolution expansion of a function f is then provided by:

f (x) = k α k ϕ k (x) + j,k β jk ψ jk (x) (12)
where α k and β jk are approximation and detail coefficients, respectively, and the elements of the basis are constructed as ψ jk (x) = 2 j/2 ψ(2 j xk), j, k = 1, 2, ... (13) In practice the coefficients α k and β jk are unknown and must be estimated from the data. Given x 1 , ..., x n independent identically distributed random variables with an unknown density f on R, suitable estimators are provided by

α k = 1 n n i=1 ϕ k (x i ), β jk = 1 n n i=1 ψ jk (x i ). ( 14
)
These estimators can be viewed as convolutions of the empirical histograms of the observations with the elements of the wavelets basis. At this stage, an obvious estimator may be proposed, by simply replacing the coefficients α, β in (12) by their sample estimates. This approach -the so called linear wavelet estimator -has however been shown to be suboptimal in general ( [START_REF] Hardle | Wavelets, Approximation and Statistical Applications[END_REF] or [START_REF] Wasserman | All of Nonparametric Statistics[END_REF]). On the other hand, a wide consensus has emerged in the mathematical statistics community on the use of so-called wavelet thresholding techniques. Here, small coefficients are suppressed by introducing a threshold. In particular, in this paper a hard thresholding rule is used. In this case, the estimator for f is defined by [START_REF] Hardle | Wavelets, Approximation and Statistical Applications[END_REF]:

f n (x) = k α k ϕ k (x) + j,k β H jk ψ jk (x) (15)
where the coefficients β H jk are defined by:

β H jk = β jk I(| β jk | > t) (16)
(the indicator function is defined as usual, e.g. I(|X| > t) = 1 if |X| > t , 0 otherwise). The threshold level is chosen to be

t = c logn n ( 17
)
where c > 0 is a suitably chosen constant, and n is the number of observations in our sample. Intuitively, the rationale behind these techniques can be explained as follows. The smaller sample coefficients can be expected to be largely dominated by noise, so dropping them will improve the global performance of the estimates. These argument can be made rigorous, in particular it can be shown that wavelet thresholding estimators yield basically the optimal rate of convergence over a wide variety of loss functions, i.e., they (nearly) minimize over a wide class of functions f and norms . L p the maximum risk

R( fn , f) = max f fn -f p L p (18)
In practice, this means wavelet thresholding techniques enjoy robustness properties which are important in our context. They are sensitive at the same time to large scale features of the unknown energy distribution, and they are also expected to detect the possible existence of small scale effects, such as local density spikes which could affect the final result. We refer again to [START_REF] Hardle | Wavelets, Approximation and Statistical Applications[END_REF] and [START_REF] Wasserman | All of Nonparametric Statistics[END_REF] for further details and discussion.

C. Kernel technique

The kernel estimate is a statistical technique used to obtain an unbinned and nonparametric estimate of the probability density function. In the univariate case, the general kernel estimate of the parent distribution is given by [START_REF] Cranmer | [END_REF]:

f (x) = 1 nh n i=1 K( x -x i h ) ( 19
)
where x i represents the data and h is the smoothing parameter (also called the bandwidth). It is important to note that f (x) is bin-independent regardless of choice of K. K has the role to distribute the contribution of each data point in the evaluation of the probability density function. Instead h have the task to set the scale of kernel.

Figure 2 :

 2 Figure2: Calorimeter energy fraction F . The fraction of calorimeter energy deposited inside a cylinder of radius 0.3 Molière radii, as a function of deflection. The number of events per bin is shown in different colors, as indicated in the color scale. The axis of the cylinder is defined by extrapolating the particle track reconstructed by the spectrometer. The events were selected requiring a match between the momentum measured by the tracking system and the total detected energy and requiring that the electromagnetic shower starts developing in the first planes of the calorimeter.

Figure 3 :

 3 Figure 3: Calorimeter energy fraction F : 28 -42 GV. Panel (a) shows the distribution of the energy fraction for negatively charged particles, selected as electrons in the upper part of the calorimeter. Panel (b) shows the same distribution for positively charged particles selected as protons in the bottom part of the calorimeter. Panel (c) shows positively charged particles, selected in the upper part of the calorimeter, i.e. protons and positrons.

Figure 4 :

 4 Figure 4: Flowchart of the methodology, based on different fitting and bootstrap techniques developed to evaluate the positron fraction R.

Figure 5 :

 5 Figure5: Distribution of the energy fraction for positively charged particles selected as protons for 3 different rigidity bins with a fit to a beta pdf.

Figure 6 :

 6 Figure 6: Distribution of the energy fraction for positively charged particles selected as protons for 3 different rigidity bins with a wavelets fit.

Figure 7 :

 7 Figure7: The distribution of positively charged particles selected as protons (grey) for the rigidity bin 28 -42 GV and the same distribution modified using the kernel method (dark-grey).

Figure 8 :

 8 Figure 8: The distribution of positively charged particles for the rigidity bin 28-42 GV showing 3 pdf fits.

Figure 10 :

 10 Figure10: The distribution of positively charged particles selected as protons for the rigidity bin 28 -42 GV and the same distribution when modified using the weighted bootstrap technique.

  -December'08 (Beta pdf with systematic and statistical errors) O. Adriani et al,[2]

Table 1 :

 1 Statistical errors on the positron fraction R for all rigidity bins.

		error Percent error	Percent error
	spectrometer (GV)	(beta)	(wavelets)	(kernel with wavelets)
	1.5 -1.8	3.2%	2.6%	2.6%
	1.8 -2.2	2.6%	2.9%	2.6%
	2.2 -2.7	2.7%	2.6%	2.6%
	2.7 -3.3	2.9%	3.1%	3.1%
	3.3 -4.1	3.1%	3.9%	3.9%
	4.1 -5.0	3.6%	3.8%	4.3%
	5.0 -6.1	3.9%	5.7%	5.3%
	6.1 -7.4	4.7%	4.8%	4.4%
	7.4 -9.1	4.9%	4.9%	5.0%
	9.1 -11.2	4.7%	5.7%	5.9%
	11.2 -15.0	5.3%	5.0%	5.6%
	15.0 -20.0	6.1%	5.4%	6.3%
	20.0 -28.0	8.1%	7.5%	8.2%
	28.0 -42.0	10.1%	9.5%	11.2%
	42.0 -65.0	13.4%	12.4%	13.0%
	65.0 -100.0	25%	29.5%	25.3%

Table 2 :

 2 Summary of the positron fraction results for the beta-fit,

	0.0670 +0.0017 -0.0017 +0.0016 -0.0016 0.0618 +0.0016 -0.0014 0.0587 +0.0018 -0.0015 0.0546 +0.0020 -0.0020 0.0508 +0.0022 -0.0022 0.0515 +0.0028 -0.0028 0.0535 +0.0022 -0.0022 0.0492 +0.0027 -0.0027 0.0543 +0.0029 -0.0032 0.0518 +0.0031 -0.0035 0.0595 +0.0039 -0.0036 0.0590 +0.0045 -0.0051 0.0592 +0.0071 -0.0074 0.0651 +0.013 -0.012 0.093 +0.034 -0.033 0.132
	0.0673 +0.0021 -0.0021 +0.0018 -0.0018 0.0618 +0.0017 -0.0014 0.0598 +0.0016 -0.0017 0.0540 +0.0019 -0.0021 0.0516 +0.0020 -0.0020 0.0524 +0.0030 -0.0029 0.0520 +0.0024 -0.0025 0.0500 +0.0027 -0.0027 0.0504 +0.0032 -0.0031 0.0541 +0.0032 -0.0030 0.0619 +0.0036 -0.0033 0.0628 +0.0048 -0.0051 0.0651 +0.0079 -0.0077 0.0833 +0.012 -0.012 0.094 +0.035 -0.037 0.109
	0.0639 +0.0017 -0.0017 +0.0015 0.0591 -0.0015 +0.0015 0.0564 -0.0015 +0.0016 0.0549 -0.0016 +0.0017 0.0537 -0.0017 +0.0020 0.0545 -0.0020 +0.0024 0.0602 -0.0024 +0.0024 0.0522 -0.0024 +0.0028 0.0576 -0.0028 +0.0033 0.0570 -0.0033 +0.0032 -0.0033 0.0611 +0.0039 -0.0039 0.0630 +0.0052 -0.0052 0.0645 +0.0073 -0.0074 0.0733 +0.012 -0.013 0.090 +0.028 -0.030 0.106
	1.5 -1.8 1.65 / 1.65 / 1.65	1.8 -2.2 1.99 / 1.99 / 1.99	2.2 -2.7 2.44 / 2.44 / 2.44	2.7 -3.3 2.99 / 2.99 / 2.99	3.3 -4.1 3.67 / 3.68 / 3.68	4.1 -5.0 4.49 / 4.51 / 4.52	5.0 -6.1 5.68 / 5.38 / 5.49	6.1 -7.4 6.78 / 6.80 / 7.02	7.4 -9.1 8.27 / 8.28 / 8.30	9.1 -11.2 10.16 / 10.17 /10.18	11.2 -15.0 13.11 / 13.12 / 13.13	15.0 -20.0 17.50 / 17.51 / 17.51	20.0 -28.0 23.99 / 24.00 / 24.01	28.0 -42.0 34.97 / 35.00 / 34.99	42.0 -65.0 53.43 / 53.44 / 53.48	65.0 -100.0 82.39 / 82.41 / 82.47

Table 3 :

 3 Summary of positron fraction results, obtained with the beta-fit, including statistical and systematic errors.


MD Lennart ; Hardell
email: lennart.hardell@orebroll.se

Michael ; <none> Carlberg

Hansson Mild

MSc Michael Carlberg

PhD Kjell Hansson Mild

Brain tumour risk in relation to mobile telephone use: results of the Interphone international case-control study

Keywords: Glioma, Mobile phone, Cordless

Re-analysis of risk for glioma in relation to mobile telephone use: comparison with the results of the

Interphone international case-control study L Hardell, Michael Carlberg, Kjell Hansson Mild

The long awaited Interphone study on use of mobile phones and the risk of brain tumour was recently published. 1 It was coordinated by International Agency for Research on Cancer (IARC) and included 16 research centres from 13 countries. Results for cases aged 30-59 years of age diagnosed during study periods of 2-4 years between 2000-2004 were presented.

The results were scheduled to be published in years 5 to 6 (2005-2006) 2 but for unclear and not published reasons they have been delayed for many years.

So far the overall results were published for glioma and meningioma, but the final findings for acoustic neuroma and tumours of the parotid gland are still to be presented.

Other than the Interphone, our research group is the only one that has published results for brain tumour risk and long-term use of mobile phones. In contrast to Interphone, we also included use of cordless phones. Radiofrequency emissions from a cordless phone are in the same magnitude as from a digital mobile phone, as discussed in our publications and recently shown also by Redmayne et al. 3 Moreover cordless phones are used for longer calls. Including such use in the 'unexposed' group as in the Interphone study would bias the odds ratio (OR) towards unity.

The Interphone publication has an extremely meager discussion of their findings in relation to current knowledge from other publications. Our results of a consistent pattern of an association between long-term use of wireless phones and ipsilateral glioma [4][5][6] are dismissed in two sentences stating that 'However, the methods of these studies have been questionned.'

with reference to another publication by some members of the Interphone group. [START_REF] Ahlblom | Epidemiologic evidence on mobile phones and tumor risk: a review[END_REF] No stringent discussion of pros and cons in our studies are presented and these ad hoc statements are made without a thorough review. [START_REF] Ahlblom | Epidemiologic evidence on mobile phones and tumor risk: a review[END_REF] This is in contrast to a balanced commentary in the

F o r R e v i e w O n l y
3 same issue of Epidemiology 8 and other independent authors who concluded that our studies have less bias than the Interphone studies. [START_REF] Myung | Mobile phone use and risk of tumors: a metaanalysis[END_REF] We have previously compared study methods and results in our investigations with those in the Interphone group. [START_REF] Hardell | Methodological aspects of epidemiological studies on the use of mobile phones and their association with brain tumors[END_REF] The research budget for Interphone totalled over 19 million euro (€) and a substanial part, 5.5 million €, came from industry. [START_REF]Interphone study reports on mobile phone use and brain cancer risk[END_REF] Additional funding was provided by industry in some countries. Furthermore, according to the study protocol "Other parties may also be involved in the Study Group as observers or consultants. These may include representatives of industry, other concerned organisations.." In addition, "representatives of industry and other concerned organisations… shall be informed shortly (maximum of seven days) before publication," that is before the scientific community and the laymen have access to the study results. 2 Due to the lack of information and any discussion of the Interphone findings in relation to our results it is pertinent to use the same criteria as in Interphone for our case-control studies on glioma. 4 Our inclusion period was 1997-2003 and we give results for all glioma for the same age group, 30-59 years as in Interphone, (Table 1) and glioma located in the temporal lobe (Table 2). Overall results are also presented for our studies as well as inclusion of the youngest subjects 20-29 years, and in one analysis including use of cordless phone among the unexposed.

In Appendix 2 in the Interphone analysis was restricted to ever users with lowest category of use as reference. There might be a 'healthy mobile phone user' effect among the controls that participated, 1 similar to a 'healthy worker effect' in occupational studies. Thus, the analysis in Appendix 2 would be justified to correct for the lower prevalence of mobile phone use among controls that refused to participate than among included controls in Interphone. indicating that excluding such use, as in Interphone, would also bias the risk towards unity.

Table 2 gives the results for glioma in the temporal lobe. Similarly as for overall findings risk estimates were lower in our studies when we restricted the age group to 30-59 years and considered use of cordless phone as no expsosure. No results were given in Appendix 2 for glioma in the temporal lobe.

As has been pointed out elsewhere a probable explanation for the different results in our studies compared with Interphone is bias in the Interphone study. [START_REF] Myung | Mobile phone use and risk of tumors: a metaanalysis[END_REF] This is also discussed in a commentary to the Interphone article. [START_REF] Saracci | Commentary: Call me on my mobile phone…or better not?-a look at the INTERPHONE study results[END_REF] Thus, of 50 ORs in Table 2 in the article only 3 ORs were above 1. For no association ORs would vary randomly above and below 1, and not even The definition of exposure, at least one call per week for 6 months, seems to be vague and arbitary chosen. Taking the fact that 13 countries with 16 study centres were included must have entailed many interviewers, especially since vast geographical areas needed to be covered in many countries. It is not explained how these interviews were performed in e.g.

Sweden with large sparsely populated areas, or from what areas controls were recruited, e.g.

excluding some geographical areas with low population.

The participation rate was only 64 % for glioma cases and 53 % for controls, i.e. much lower than in the studies from the Hardell group, 90 % of cases with malignant brain tumor and 89 % of the controls. 4 Furthermore, we used a self-administered questionnaire that was supplemented over the phone. This was done without knowledge if it was a case or a control.

Low participation rate may create selection bias and not blinding as to case or control status may give observational bias, especially in a study with such vague definition of cut-off for exposure. Especially worrying as to observational bias are bed-side interviews of such a mentally ill patient group as with brain tumour. They may even have been newly operated before the interview. In fact patients scored significantly lower than controls due to recalling of words (aphasia), problems with writing and drawing due to paralysis in the Danish part of Interphone. [START_REF] Christensen | Cellular telephones and risk for brain tumors: a population-based, incident case-control study[END_REF] It is unclear why younger cases were excluded from the final We urge Interphone to fill in the gaps in our Tables 1 and2, so as to make full comparison with our data possible. Currently we present results on the association of use of wireless phones and malignant brain tumours among deceased cases, that were excluded from our study, using deceased controls. These results confirm our previous findings of an increased risk for malignant brain tumour among mobile phone users. Due to the lack of information and any discussion of the Interphone findings in relation to our results it is pertinent to use the same criteria as in Interphone for our case-control studies on glioma. 4 Our inclusion period was 1997-2003 and we give results for all glioma for the same age group, 30-59 years as in Interphone, (Table 1) and glioma located in the temporal lobe (Table 2). Overall results are also presented for our studies as well as inclusion of the youngest subjects 20-29 years and in one analysis including use of cordless phone among the unexposed. We have also re-analysed our material with the same cumulative exposure time as in the Interphone study, i.e. >1640 h, since we before had >2000 h.

In Appendix 2 in the Interphone paper analysis was restricted to ever users with lowest category of use as reference in each category. There might be a 'healthy mobile phone user' effect among the controls that participated, 1 similar to a 'healthy worker effect' in occupational studies. Thus, the analysis in Appendix 2 would be justified to correct for the As can be seen in Table 1 our results in the same age group as in Interphone, 30-59 years, are similar as in Appendix 2 for latency >10 years and cumulative use > 1640 h. Unfortunately

Interphone did not give results for laterality analysis in Appendix 2.

Interestingly our results for cumulative use in the age group 30-59 years are similar to Interphone results. Furthermore, in both studies highest ORs were found for ipsilateral use.

We found higher risks if the age group 20-29 years was included. This is in agreement with our previous publication showing highest risk for persons that started use of mobile or cordless phone before the age of 20 years. 5 Thus excluding that age group from the final Interphone seems to have biased the risk towards unity. We examined the results if we considered use of cordless phone as no exposure to microwaves, which yielded lower ORs indicating that excluding such use, as in Interphone, would also bias the risk towards unity. We urge Interphone to fill in the gaps in our Tables 1 and2, so as to make full comparison with our data possible. Currently we have presented results on the association of use of wireless phones and malignant brain tumours among deceased cases, that were excluded from our study, using deceased controls. These results confirm our previous findings of an increased risk for malignant brain tumour among mobile phone users.

  Re-analysis of risk for glioma in relation to mobile telephone use: comparison with the results of theInterphone international case-control study

5 the

 5 Interphone authors favour the idea that mobile phone use would protect against brain tumours.

  mobile phone use among controls that refused to participate than among included controls in Interphone.1

  Norway 19-29 and UK 18-29, and the age groups are unclear for the countries that have not published individual results.[START_REF]Interphone Study Results[END_REF] There are several other methodological issues in Interphone that would be pertinent to discuss, e.g. how was use of mobile phone in a car with external antenna judged. Several factors may explain the seemingly discrepancy between our results and those in Interphone.

	included the age group 20-29 years, These include in Interphone e.g. proxy interviews among cases (13 % versus 1% among
	r o F controls), restricting age group to 30-59 years, including use of cordless phone among the
	R
	e v
	i e
	w
	O n l
	y
	6

Interphone report, especially since our results indicate highest risk in the youngest age group.

6

Thus, Denmark and Sweden unexposed, vague definition of exposure categories, low participation rates for cases and controls, selection bias of controls, bedside interviews of cases, not blinding as to case or controls status and a multitude of research centres and interviewers with potential for observational bias.

Table 1 .

 1 Odds ratio (OR) and 95 % confidence interval (CI) for glioma in Interphone compared with the Hardell group. Numbers of cases (Ca) and controls (Co) are given. N.R. = not reported. All glioma. Note that > 10 y latency was used in the Hardell group studies and contralateral was defined as < 50% use on tumour side.

	15

Table 2 .

 2 Odds ratio (OR) and 95 % confidence interval (CI) for glioma in Interphone compared with the Hardell group. Numbers of cases (Ca) and controls (Co) are given. N.R. = not reported. Glioma, temporal lobe. Note that > 10 y latency was used in the Hardell group studies and contralateral was defined as < 50% use on tumour side.The long awaited Interphone study on use of mobile phones and the risk of brain tumour was recently published.1 It was coordinated by International Agency for Research on Cancer (IARC) and included 16 research centres from 13 countries. Results for cases aged 30-59 years of age diagnosed during study periods of 2-4 years between 2000-2004 were presented.Our research group has published results for brain tumour risk and long-term use of mobile phones. In contrast to Interphone, we also included use of cordless phones. Radiofrequency emissions from a cordless phone are in the same magnitude as from a digital mobile phone, as discussed in our publications and recently shown also by Redmayne et al.2 Moreover cordless phones are used for longer calls. Including such use in the 'unexposed' group as in the Interphone study would bias the odds ratio (OR) towards unity. We have previously compared study methods and results in our investigations with those in the Interphone group.3

		Hardell,	Hardell,	Hardell,	Hardell,	Interphone,	Interphone,
		20-80	20-59	30-59	30-59, cordless	30-59	30-59,
		(all)			among		appendix 2
					unexposed
	Latency > 10 y	(28/99)	(15/74)	(14/74)	(14/74)	(94/69)	N.R.
		2.26	1.74	1.48	1.40	1.36
		1.32-3.86	0.85-3.56	0.71-3.10	0.70-2.81	0.88-2.11
	Latency > 10 y, ipsilateral	(18/45)	(10/30)	(9/30)	(9/30)	N.R.	N.R.
		2.49	1.94	1.73	1.69
		1.29-4.81	0.81-4.63	0.70-4.26	0.71-4.02
	Latency > 10 y,	(9/29)	(4/24)	(4/24)	(4/24)	N.R.	N.R.
	contralateral	2.08	1.35	1.28	1.21
		0.89-4.87	0.41-4.49	0.38-4.28	0.37-3.90
	Cumulative use > 1640 h	(14/43)	(9/37)	(7/37)	(7/37)	(78/47)	N.R.
		2.44	1.96	1.53	1.46	1.87
		1.21-4.95	0.82-4.66	0.60-3.94	0.59-3.63	1.09-3.22
	Cumulative use > 1640 h,	(11/21)	(7/18)	(5/18)	(5/18)	N.R.	N.R.
	ipsilateral	3.08	2.18	1.68	1.82
		1.32-7.19	0.77-6.24	0.52-5.41	0.59-5.60
	Cumulative use > 1640 h,	(2/12)	(1/11)	(1/11)	(1/11)	N.R.	N.R.
	contralateral	1.04	0.72	0.72	0.64
		0.22-5.00	0.08-6.11	0.08-6.12	0.08-5.33

Table 2

 2 gives the results for glioma in the temporal lobe. Similarly as for overall findings risk estimates were lower in our studies when we restricted the age group to 30-59 years and considered use of cordless phone as no exposure. No results were given in Appendix 2 for glioma in the temporal lobe. supplemented over the phone. This was done without knowledge if it was a case or a control.Low participation rate may create selection bias and not blinding as to case or control status may give observational bias, especially in a study with such vague definition of cut-off for exposure. Especially worrying as to observational bias are bed-side interviews of such a mentally ill patient group with brain tumour. They may even have been newly operated before the interview. In fact patients scored significantly lower than controls due to recalling of words (aphasia), problems with writing and drawing due to paralysis in the Danish part of Interphone.6 It is unclear why younger cases were excluded from the final Interphone report, especially since our results indicate highest risk in the youngest age group.5 Thus, Denmark and Sweden included the age group 20-29 years, Norway 19-29 and UK 18-29, and the age groups are unclear for the countries that have not published individual results.[START_REF] Ahlblom | Epidemiologic evidence on mobile phones and tumor risk: a review[END_REF]

	The interview rate was only 64 % for glioma cases and 53 % for controls, i.e. much lower
	than in the studies from the Hardell group, 90 % of cases with malignant brain tumour and 89

Table 1 .

 1 Odds ratio (OR) and 95 % confidence interval (CI) for glioma in Interphone compared with the Hardell group. Numbers of cases (Ca) and controls (Co) are given. N.R. = not reported. All glioma. Note that > 10 y latency were used in the Hardell group studies and contralateral was defined as < 50% use of tumour side.

	8

Table 2 .

 2 Odds ratio (OR) and 95 % confidence interval (CI) for glioma in Interphone compared with the Hardell group. Numbers of cases (Ca) and controls (Co) are given. N.R. = not reported. Glioma, temporal lobe. Note that > 10 y latency were used in the Hardell group studies and contralateral was defined as < 50% use of tumour side.

		Hardell,	Hardell,	Hardell,	Hardell,	Interphone,	Interphone,
		20-80	20-59	30-59	30-59, cordless	30-59	30-59,
		(all)			among		appendix 2
					unexposed
	Latency > 10 y	(28/99)	(15/74)	(14/74)	(14/74)	(94/69)	N.R.
		2.26	1.74	1.48	1.40	1.36
		1.32-3.86	0.85-3.56	0.71-3.10	0.70-2.81	0.88-2.11
	Latency > 10 y, ipsilateral	(18/45)	(10/30)	(9/30)	(9/30)	N.R.	N.R.
		2.49	1.94	1.73	1.69
		1.29-4.81	0.81-4.63	0.70-4.26	0.71-4.02
	Latency > 10 y,	(9/29)	(4/24)	(4/24)	(4/24)	N.R.	N.R.
	contralateral	2.08	1.35	1.28	1.21
		0.89-4.87	0.41-4.49	0.38-4.28	0.37-3.90
	Cumulative use > 1640 h	(14/43)	(9/37)	(7/37)	(7/37)	(78/47)	N.R.
		2.44	1.96	1.53	1.46	1.87
		1.21-4.95	0.82-4.66	0.60-3.94	0.59-3.63	1.09-3.22
	Cumulative use > 1640 h,	(11/21)	(7/18)	(5/18)	(5/18)	N.R.	N.R.
	ipsilateral	3.08	2.18	1.68	1.82
		1.32-7.19	0.77-6.24	0.52-5.41	0.59-5.60
	Cumulative use > 1640 h,	(2/12)	(1/11)	(1/11)	(1/11)	N.R.	N.R.
	contralateral	1.04	0.72	0.72	0.64
		0.22-5.00	0.08-6.11	0.08-6.12	0.08-5.33