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Optimization of culture conditions for a synthetic gene expression in Escherichia coli using response surface methodology: The case of human interferon beta Luz M.T. Paz Maldonado a , Vı ´ctor E. Balderas Herna ´ndez a , Emilio Medina Rivero a , Ana P. Barba de la Rosa a , Jose ´ L. Flores Flores b , Leandro G. Ordon ˜ez Acevedo a , Antonio De Leo ´n Rodrı ´guez a, * a Division of Molecular Biology, Institute for Scientific and Technological Research of San Luis Potosi, Apartado Postal 3-74, Tangamanga, 78231 San Luis Potosi, S.L.P., Mexico b Division of Environmental Engineering and Natural Resources, Institute for Scientific and Technological Research of San Luis Potosi, San Luis Potosi, S.L.P., Mexico Received 25 August 2006; received in revised form 30 September 2006; accepted 13 October 2006 Abstract A human interferon beta (hINF-b) synthetic gene was optimized and expressed in Escherichia coli BL21-SI using a vector with the T7 promoter. To determine the best culture conditions such as culture medium, temperature, cell density and inducer concentration, we used the response surface methodology and a Box-Behnken design to get the highest hINF-b production. The maximum hINF-b production of 61 mg l 1 was attained using minimum medium and the following predicted optimal conditions: temperature of 32.5 8C, cell density of 0.64, and inducer concentration of 0.30 M NaCl. This is the first report showing the successful performance of the BL21-SI system in a minimum medium. The response surface methodology is effective for the optimization of recombinant protein production using synthetic genes. # 2006 Elsevier B.V. All rights reserved. Keywords: Codon bias; E. coli BL21-SI; Multiple sclerosis; Response surface methodology (RSM); Synthetic gene; Yeast extract 1. Introduction Escherichia coli is the most used host for the over- expression of recombinant proteins. Weak expression of foreign genes has been attributed to the difference of codon usage between eukaryotic organisms and those preferred by E. coli (Jonasson et al., 2002). There are strategies to overcome the problem of codon bias, such as commercial E. coli strains containing copies of tRNA genes, which are rare in E. coli but frequently used in other organisms (Sørensen and Mortensen, 2005), however, no E. coli strains described contain all ‘‘rare’’ tRNA genes. On the other hands, the rapid degradation of mRNA transcribed from foreign cDNA causes poor expression in heterologous systems and the replacement of rare codons in the target gene improves the protein expression (De Rocher et al., 1998; Makrides, 1996). However, culture conditions such as inducer concentration, cell density (induction time), and temperature also affect the recombinant proteins production (Yildir et al., 1998; Neubauer et al., 1992; Donovan et al., 1996, 2000; De Leo ´n et al., 2003, 2004). Human interferon b (hINF-b) is a glycoprotein involved in antiviral, antiproliferative and immunoregulatory processes. The recombinant hINF-b has been approved for the treatment of multiple sclerosis, arthritis, genital condylomata acuminata and malignant melanoma therapy (Hong et al., 2002; Tak et al., 1999; Bornstein et al., 1997; Czarnieckt et al., 1984) and for in vitro studies (Huang et al., 2001). In this work, we assessed the production of hINF-b using a synthetic gene optimized for its expression in E. coli BL21-SI (Bhandari and Gowrishankar, 1997) (a T7 system inducible with NaCl) in minimum medium. The effect of yeast extract and culture conditions such as temperature, cell density and NaCl concentration was evaluated using the response surface methodology (RSM). www.elsevier.com/locate/geneanabioeng Biomolecular Engineering 24 (2007) 217–222 * Corresponding author. Tel.: +52 444 8342000; fax: +52 444 8342010. E-mail address: [email protected] (A. De Leo ´n Rodrı ´guez). 1389-0344/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.bioeng.2006.10.001

2006. Optimization of Culture Conditions for a Synthetic Gene Expression in E Coli Using Response Surface Methodology, The Case of Human Interferon Beta

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Page 1: 2006. Optimization of Culture Conditions for a Synthetic Gene Expression in E Coli Using Response Surface Methodology, The Case of Human Interferon Beta

Optimization of culture conditions for a synthetic gene expression

in Escherichia coli using response surface methodology:

The case of human interferon beta

Luz M.T. Paz Maldonado a, Vıctor E. Balderas Hernandez a, Emilio Medina Rivero a,Ana P. Barba de la Rosa a, Jose L. Flores Flores b, Leandro G. Ordonez Acevedo a,

Antonio De Leon Rodrıguez a,*a Division of Molecular Biology, Institute for Scientific and Technological Research of San Luis Potosi, Apartado Postal 3-74,

Tangamanga, 78231 San Luis Potosi, S.L.P., Mexicob Division of Environmental Engineering and Natural Resources, Institute for Scientific and Technological Research of San Luis Potosi,

San Luis Potosi, S.L.P., Mexico

Received 25 August 2006; received in revised form 30 September 2006; accepted 13 October 2006

Abstract

A human interferon beta (hINF-b) synthetic gene was optimized and expressed in Escherichia coli BL21-SI using a vector with the T7

promoter. To determine the best culture conditions such as culture medium, temperature, cell density and inducer concentration, we used the

response surface methodology and a Box-Behnken design to get the highest hINF-b production. The maximum hINF-b production of 61 mg l�1

was attained using minimum medium and the following predicted optimal conditions: temperature of 32.5 8C, cell density of 0.64, and inducer

concentration of 0.30 M NaCl. This is the first report showing the successful performance of the BL21-SI system in a minimum medium. The

response surface methodology is effective for the optimization of recombinant protein production using synthetic genes.

# 2006 Elsevier B.V. All rights reserved.

Keywords: Codon bias; E. coli BL21-SI; Multiple sclerosis; Response surface methodology (RSM); Synthetic gene; Yeast extract

www.elsevier.com/locate/geneanabioeng

Biomolecular Engineering 24 (2007) 217–222

1. Introduction

Escherichia coli is the most used host for the over-

expression of recombinant proteins. Weak expression of foreign

genes has been attributed to the difference of codon usage

between eukaryotic organisms and those preferred by E. coli

(Jonasson et al., 2002). There are strategies to overcome the

problem of codon bias, such as commercial E. coli strains

containing copies of tRNA genes, which are rare in E. coli but

frequently used in other organisms (Sørensen and Mortensen,

2005), however, no E. coli strains described contain all ‘‘rare’’

tRNA genes. On the other hands, the rapid degradation of

mRNA transcribed from foreign cDNA causes poor expression

in heterologous systems and the replacement of rare codons in

the target gene improves the protein expression (De Rocher

* Corresponding author. Tel.: +52 444 8342000; fax: +52 444 8342010.

E-mail address: [email protected] (A. De Leon Rodrıguez).

1389-0344/$ – see front matter # 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.bioeng.2006.10.001

et al., 1998; Makrides, 1996). However, culture conditions such

as inducer concentration, cell density (induction time), and

temperature also affect the recombinant proteins production

(Yildir et al., 1998; Neubauer et al., 1992; Donovan et al., 1996,

2000; De Leon et al., 2003, 2004).

Human interferon b (hINF-b) is a glycoprotein involved in

antiviral, antiproliferative and immunoregulatory processes.

The recombinant hINF-b has been approved for the treatment

of multiple sclerosis, arthritis, genital condylomata acuminata

and malignant melanoma therapy (Hong et al., 2002; Tak

et al., 1999; Bornstein et al., 1997; Czarnieckt et al., 1984)

and for in vitro studies (Huang et al., 2001). In this work, we

assessed the production of hINF-b using a synthetic gene

optimized for its expression in E. coli BL21-SI (Bhandari and

Gowrishankar, 1997) (a T7 system inducible with NaCl) in

minimum medium. The effect of yeast extract and culture

conditions such as temperature, cell density and NaCl

concentration was evaluated using the response surface

methodology (RSM).

Page 2: 2006. Optimization of Culture Conditions for a Synthetic Gene Expression in E Coli Using Response Surface Methodology, The Case of Human Interferon Beta

L.M.T.P. Maldonado et al. / Biomolecular Engineering 24 (2007) 217–222218

2. Materials and methods

2.1. Bacterial strains and plasmids

The pCR4-585 vector containing the optimized synthetic hINF-b gene was

purchased from Entelechon GmbH (Regensburg, Germany). The NdeI and

BamHI sites were added to hINF-b synthetic gene by PCR using pCR4-585 as

template and the primers sense 50-CATATGAGCTATAACCTG-30 and anti-

sense 50-GGATCCTTAATTACGCAG-30. The NdeI–hINF-b–BamHI amplified

fragment was cloned in a pET12a (Novagen, Darmstadt, Germany) vector to

construct pTPM13, then E. coli BL21-SI (GIBCO, Darmstadt, Germany) was

transformed by heat-shock method with the pTPM13 plasmid and transforming

clones were selected on LBON medium (Luria-Bertani salt-free) with

100 mg l�1 ampicillin.

2.2. Media and culture conditions

The minimum medium contains per liter: 5.0 g glucose, 3.5 g (NH4)2HPO4,

3.5 g KH2PO4, 1.0 g MgSO4, 40 mg thiamine and 100 mg ampicillin. The pH

was adjusted to 7.4 with NaOH prior to sterilization (20 min at 121 8C). The

supplemented medium consists of minimum medium plus 5 g l�1 of yeast

extract (Difco Laboratories, Franklin Lakes, NJ, USA). For all experiments,

pre-inocula were grown in supplemented medium overnight at 37 8C and

shaken at 250 rpm. Batch cultures were carried out in 500 ml Erlenmeyer

flasks with 100 ml of minimum medium or supplemented medium inoculated at

a cell density of 0.20 at 620 nm, and shaken at 250 rpm. Each experiment was

performed under different conditions of temperature, cell density and inducer

concentration as described in experimental design (Table 1).

2.3. Experimental design and optimization by RSM

To study the effect of three independent variables on the production of hINF-b

in E. coli BL21-SI/pTPM13, we constructed a random experimental design via

Box-Behnken strategy (Montgomery, 1997). The independent variables were

temperature (factor A), cell density at 620 nm (factor B) and inducer concentra-

tion (factor C). Each variable was divided into three levels and 12 treatments were

made in accordance to Box-Behnken factorial design (Table 1). Three additional

experiments were included in order to analyze the effect of non-adjustable data.

The production of hINF-b was tested using both minimum medium and supple-

mented medium via the Box-Behnken design. The analysis of RSM and analysis

of variance (ANOVA) was done using MinitabTM v 14.0 software (Minitab Inc.,

Pennsylvania, USA). The significance of each coefficient (linear or quadratic) was

Table 1

Box-Behnken experimental design with the values of the independent variables temp

the results for the production of hINF-b using supplemented medium (1) and min

Experiment Factor A (8C) Factor B (Abs) Factor C (M)

1 28.0 0.6 0.45

2 32.5 1.0 0.45

3 32.5 0.2 0.15

4 28.0 0.6 0.15

5 28.0 0.2 0.30

6 37.0 0.6 0.45

7 32.5 1.0 0.15

8 37.0 0.6 0.15

9 28.0 1.0 0.30

10 32.5 0.6 0.30

11 37.0 1.0 0.30

12 37.0 0.2 0.30

13 32.5 0.2 0.45

14 32.5 0.6 0.30

15 32.5 0.6 0.30

a Supplemented medium (1).b Minimum medium (2).

determined with the Student’s t-test, at 0.05 probability level. The optimal values

were obtained solving the regression equation by the Newton–Raphson method

and analyzing the response surface contour.

2.4. Analytical methods

Cell density was measured at 620 nm in a Varian Cary Bio-50 spectro-

photometer (Varian Inc., Palo Alto, CA, USA). Glucose concentration was

determined by the dinitro-salicilic acid (DNS) method for reducing sugars,

using glucose as a standard (Miller, 1959). Protein concentration was deter-

mined by the method of Lowry et al. (1951), using bovine serum albumin

(BioRad, Hercules, CA, USA) as the standard. Cell samples of 2 ml were

collected, centrifuged at 5000 � g for 10 min, resuspended in PBS (0.1 M pH

7.8) and lysed by sonication. Proteins then were separated in a 15% sodium

dodecyl sulphate polyacrylamide gel electrophoresis (15% SDS-PAGE) using a

Miniprotean III System (BioRad). Proteins were stained with Coomassie Blue

R-250 (BioRad). For Western blot, proteins were transferred from gel onto a

nitrocellulose membrane (Amersham Biosciences, Piscataway, NJ, USA) using

a Semi-Dry Transblot (BioRad). The membrane was blocked with Svelty milk

(3%, w/v in PBS). The membrane was incubated with the rabbit anti-hINF-b

polyclonal antibody (PBL Biomedical Lab., Piscataway, NJ, USA), followed by

goat anti-rabbit IgG antibody conjugated to alkaline phosphatase (BioRad), and

visualized with p-nitro blue tetrazolium chloride and 5-bromo-4-chloro-3-

indolyl-phosphate (NBT/BCIP, Amersham Biosciences). hINF-b concentration

was measured by densitometry using the Quantity OneTM v 4.5 software

(BioRad). Recombinant non-glycosilated hINF-b (PBL Biomedical Lab.)

was used as the standard.

3. Results and discussion

3.1. Design of hINF-b synthetic gene

We designed a synthetic hINF-b gene guided by the

preferred codons to be expressed in E. coli. The resultant

optimized gene had 77.25% of identity with respect to the wild-

type gene (Fig. 1). A summary of codon preference in E. coli

based on the Ikemura classification (Ikemura, 1981) and codon

usage in the wild-type and the optimized synthetic hINF-b gene

is shown in Table 2. The most significant changes were for

arginine, leucine, glycine and proline codons. Previous reports

erature (factor A), cell density (factor B), inducer concentration (factor C), and

imum medium (2), respectively

Production of hINF-b (mg l�1)

Observeda Predicteda Observedb Predictedb

7 8 18 18

12 10 22 22

8 9 10 11

19 15 19 19

4 6 3 2

7 11 20 20

12 15 19 19

11 10 17 17

7 8 15 15

18 18 60 61

10 8 11 12

4 3 5 5

13 10 10 10

18 18 61 61

17 18 61 61

Page 3: 2006. Optimization of Culture Conditions for a Synthetic Gene Expression in E Coli Using Response Surface Methodology, The Case of Human Interferon Beta

Fig. 1. Alignment of nucleotide sequence of wild-type and the optimized synthetic hINF-b gene used in this work.

L.M.T.P. Maldonado et al. / Biomolecular Engineering 24 (2007) 217–222 219

showed that expression of mammalian genes in E. coli

increased after codon-optimization (Kane, 1995; Hale and

Thompson, 1998; Li et al., 2002, 2003).

3.2. Kinetics of hINF-b production

A typical batch culture of E. coli BL21-SI/pTPM13 in

supplemented medium is shown in Fig. 2 (experiment 8 from

the Box-Behnken design). Cell density increased to a maximum

of 3.9, and thereafter it remained constant (Fig. 2A). During this

period, glucose was consumed and cell growth ceased upon

glucose depletion (Fig. 2B). The hINF-b concentration

increased from 0 to 11 mg l�1 after induction with 0.15 M

NaCl (Fig. 2C). Cultures maintained under different conditions

showed a similar trend to those in Fig. 2, although the

parameters measured, their maximum concentrations, and

times to reach them were different in each case. Fig. 3A shows

Table 2

Summary of codon preference in E. coli based on Ikemura classification (Ikemura, 1

Aminoacid Expected codon preference in E. coli Codon usage i

Arg CGY AGA, AGG, C

Leu CTG CTG, TTG, CT

Gly GGY GGG, GGA, G

Pro CCR CCT

Thr ACY ACA, ACC, A

Phe TTC TTC, TTT

Ile ATY, ATC ATT, ATC, AT

Val GTR, GTT GTT, GTC, GT

Ser NR TCT, TCA, AG

Ala GCT, GCR GCC, GCT, G

Tyr TAC TAC, TAT

His NR CAT, CAC

Gln CAG CAG, CAA

Asn AAC AAC, AAT

Lys AAA AAG, AAA

Asp NR GAC, GAT

Glu GAA GAG, GAA

Cys NR TGT, TGC

Y: pyrimidine, R: purine, NR: not reported.

the protein patterns obtained from experiment 10. The identity

of the hINF-b was confirmed by Western blot using

recombinant hINF-b as the standard (Fig. 3B). The hINF-b

produced led the formation of cytoplasmic inclusion bodies,

then studies for recovering and re-folding are further

recommended as reported for others recombinant proteins

produced in E. coli (Jin et al., 2006). There are several reports

on the production of recombinant proteins using salt induction

systems in LBON (Bhandari and Gowrishankar, 1997; Bell

et al., 2002; Bouley et al., 2000), however, to our knowledge,

there are no previous reports using minimum medium for the

expression of proteins using E. coli BL21-SI.

3.3. Optimization of hINF-b production

The Box-Behnken design, the experimental and predicted

results for hINF-b production in minimum medium and

981) and codon usage in the wild-type and the optimized synthetic hINF-b gene

n wild-type hINF-b gene Codon usage in the synthetic hINF-b gene

GA CGT, CGC

T CTG

GT, GGC GGT, GGC, GGA

CCA

CT ACC, ACG, ACT

TTT, TTC

A ATT, ATC

G GTT, GTC, GTG

T, AGC TCT, TCC, AGC, TCA, AGT

CA GCC, GCG, GCA, GCT

TAT, TAC

CAT, CAC

CAG

AAC, AAT

AAA

GAT, GAC

GAA, GAG

TGT, TGC

Page 4: 2006. Optimization of Culture Conditions for a Synthetic Gene Expression in E Coli Using Response Surface Methodology, The Case of Human Interferon Beta

Table 3

Estimated regression coefficients of independent variables temperature (A), cell

density (B) and inducer concentration (C) for hINF-b production using sup-

plemented medium

Term Coefa S.E. Coefb t ratioc P-valued

Constant �264.221 2.133 6.281 0.002

A 17.446 2.001 �0.593 0.579

B 38.333 1.664 2.967 0.031

C �70.741 2.001 �0.219 0.836

A2 �0.288 2.021 �2.886 0.034

B2 0.417 0.505 �2.762 0.04

C2 2.963 2.021 �0.412 0.697

AB 0.417 0.971 0.386 0.715

AC 2.963 1.942 1.03 0.35

BC �34.896 0.971 �0.644 0.548

a Coef: estimated coefficient.b S.E. Coef: standard error coefficient.c t ratio: t-Student distribution value.d P-value: probability distribution value. P-value less than 0.05 indicates that

the term was significant. The correlation coefficient (R2) was 0.79 and the

standard error was 3.884.

Fig. 2. Growth kinetics of E. coli BL21-SI/pTPM13 in supplemented medium

for the experiment 8. (A) Cell density [*] (Abs); (B) glucose concentration [&]

(g l�1); (C) hINF-b concentration [~] (mg l�1). Arrow shows induction time

with NaCl.

L.M.T.P. Maldonado et al. / Biomolecular Engineering 24 (2007) 217–222220

supplemented medium are summarized in Table 1. The cultures

in minimum medium showed a higher hINF-b concentration

than those cultures in supplemented medium under the same

operational conditions. The highest hINF-b production was

attained in minimum medium for the experiment 10. For the

cultures using supplemented medium, the significant factors

were B, A2 and B2 (Table 3), whereas for cultures in minimum

medium the significant factors were B, A2, B2, C2, AB and AC

interaction (Table 4). To estimate the optimal region of hINF-b

production in minimum medium or supplemented medium,

second-order models were fitted to the hINF-b observed results

Fig. 3. Protein patterns and Western blot analysis for hINF-b obtained in E. coli

BL21-SI/pTPM13 cultures from the experiment 10. (A) Typical protein patterns

in minimum medium. Lane 1, protein ladder (Invitrogen); lane 2, culture before

induction; lanes 3–7, total cell proteins of five samples after induction. (B)

Western blot for samples described above. Lane 1, standard hINF-b (PBL

Biomedical Lab); lanes 2–6, five samples after induction.

(data from Table 1) and the response surface graphs are shown

in Fig. 4.

For cultures in supplemented medium the model is described

by Eq. (1), where the variables are specified in their original

units as follows:

Yðsupplemented mediumÞ

¼ �264:22þ 17:45Aþ 38:33B� 70:74C � 0:288A2

� 34:90B2 � 37:04C2 þ 0:42ABþ 2:96AC � 20:83BC

(1)

where Y is the response variable (hINF-b production), and A, B

and C are the independent variables (temperature, cell density

and inducer concentration, respectively). The standard error of

the model was 3.884 and according to the R2 value, the

predictors included in the model explain 79.0% of the variance

in hINF-b production. For the set of experiments in supple-

mented medium, the maximum hINF-b concentration of

19 mg l�1was attained when temperature, cell density and

Table 4

Estimated regression coefficients of independent variables temperature (A), cell

density (B) and inducer concentration (C) for hINF-b production using mini-

mum medium

Term Coef S.E. Coef t ratio aP-value

Constant �1354.582 0.382 108.454 0

A 78.508 0.358 2.442 0.059

B 243.333 0.298 77.945 0

C 420.741 0.358 0.174 0.868

A2 �1.208 0.362 �67.601 0

B2 �173.177 0.09 �76.584 0

C2 12.5 0.362 �48.944 0

AB �0.833 0.174 �4.315 0.008

AC 1.481 0.348 2.877 0.035

BC �173.177 0.174 2.158 0.083

For abbreviations, see Table 3.a P-value less than 0.05 indicates that the term was significant. The correla-

tion coefficient (R2) was 0.999 and the standard error was 0.695.

Page 5: 2006. Optimization of Culture Conditions for a Synthetic Gene Expression in E Coli Using Response Surface Methodology, The Case of Human Interferon Beta

Fig. 4. Response surface plot of hINF-b concentration as a function of

temperature and cell density. (A) Cultures in supplemented medium induced

with 0.15 M NaCl. (B) Cultures in minimum medium induced with 0.30 M

NaCl.

L.M.T.P. Maldonado et al. / Biomolecular Engineering 24 (2007) 217–222 221

inducer concentration were 31.6 8C, 0.69 and 0.15 M, respec-

tively.

The mathematical model representing the hINF-b produc-

tion in minimum medium in the experimental region studied is

explained by Eq. (2):

Yðminimum mediumÞ

¼ �1354:58þ 78:51Aþ 243:33Bþ 420:74C � 1:20A2

� 173:18B2 � 787:04C2 � 0:83ABþ 1:48AC þ 12:5BC

(2)

The standard error was 0.695 and the correlation coefficient

(R2) was 99.9%. These values indicate a good fit between the

model and the experimental data, and can explain the majority

of variance in the hINF-b production in minimum medium. In

this case, the maximum concentration of hINF-b (61 mg l�1)

was attained at temperature, cell density and inducer

concentration of 32.5 8C, 0.64 and 0.30 M, respectively. These

operational conditions are the optimal values predicted to

improve the hINF-b production. The culture conditions

suggested by the provider for E. coli BL21-SI are: LBON

medium, 37 8C, 0.6 and 0.3 M NaCl (Donahue and Bebee,

1999), using those the hINF-b production was 12 mg l�1 (data

non-shown), whereas using a minimum medium and the

optimal conditions proposed by the RSM, the amount of hINF-

b increased five-fold. Goeddel et al. (1980) reported a

maximum hINF-b production of 0.2 mg l�1 using the wild-

type gene cloned in E. coli and using minimum medium with

casaminoacids, while we produced 95 and 305 times more

hINF-b in supplemented medium and minimum medium,

respectively. Skoko et al. (2003) reported a maximum hINF-b

production of 12 mg l�1 in Pichia pastoris cultures. Afore-

mentioned, we attained the highest hINF-b production using

minimum medium. Ling (2005) reported that recombinant

protein ZZT2 production by E. coli was higher using an

aminoacid free medium than cultures supplemented with

aminoacids. Ignatova et al. (2003) reported that the penicillin

acylase production increased 1.7-fold in M9 minimal medium

compared to attained in complex LB or M9 plus yeast extract.

Shin et al. (1997) reported that the addition of yeast extract onto

the culture medium enhanced the production of human

proinsulin in E. coli cultures. We therefore strongly suggest

assaying the use of aminoacids or yeast extract to design the

culture medium for the production of recombinant proteins in

each expression system. RSM has been used previously for the

optimization of secondary metabolite production such as xylitol

by Candida guilliermondii (Silva and Roberto, 2001), xylanase

by Bacillus circulans (Bocchini et al., 2002) and recombinant

endochitinase by E. coli (De Leon et al., 2004). Our work is the

first report showing the optimization of recombinant protein

production using synthetic genes.

Acknowledgements

Financial support of National Council of Science and

Technology of Mexico (CONACyT) Grant J39639-Q and

CONACyT-FOMIX Grant FMSLP-2002-4100. Luz M.T. Paz-

Maldonado is grateful for scholarship CONACyT No. 172257.

We thank Dr. P. Johnson for English corrections.

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