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Temperature dependence of mean square displacement by IN13: a comparison between trehalose and sucrose water mixtures
Chemical Physics 292 (2003) 247–251 www.elsevier.com/locate/chemphys
Temperature dependence of mean square displacement by IN13: a comparison between trehalose and sucrose water mixtures S. Magaz u a,*, F. Migliardo a, C. Mondelli b, G. Romeo a b
a Dipartimento di Fisica and INFM, Universit a di Messina, P.O. Box 55, I-98166 Messina, Italy INFM-Operative Group Grenoble CRG IN13 and Institut Laue–Langevin, 38042 Grenoble Cedex 9, France
Received 3 October 2002; in final form 6 February 2003
Abstract An analysis in terms of elastic scans of the neutron intensity in mixtures of homologues disaccharides (i.e., trehalose and sucrose)/D2 O as a function of temperature has been carried out. The study provides an effective way for characterizing the dynamical behavior, furnishing a set of parameters characterizing the ‘‘flexibility’’ and the ‘‘rigidity’’ that justifies the better cryptobiotic effect of trehalose in respect to sucrose. Elastic scans make evident a non-Gaussian behavior of the intensity profiles which is more marked for sucrose, with a dynamical transition at T 253 K and T 250 K for trehalose=D2 O and sucrose=D2 O mixtures, respectively. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years many progresses have been made in cryobiology, the important research field that studies mechanisms and consequences for organisms living at any temperature below the physiological range. The reason that induces the research activity in this direction is the understanding of the tools used by nature to adapt organisms to the stresses of low temperatures, such as freeze-drying, supercooling, cryosurgery, frost-
*
Corresponding author. Tel.: +39-90-391-478; fax: +39-90395-004. E-mail address: [email protected] (S. Magazu`).
bite and cryopreservation [1–3]. Trehalose has been found to be the most common sugar in many species, that survive to low temperature by means of natural cryoprotective agents [2–5]. These multiple effects of trehalose suggest manifold promising applications [6,7]. Also other disaccharides of the same homologues series ðC12 H22 O11 Þ, such as maltose and sucrose, show similar action on biological structures, but trehalose has peculiar properties that make it the most extraordinary bioprotectant. It is well-known that molecular dynamics plays a fundamental role in many aspects of biological activity. The timescales of the motions involved cover several orders of magnitude: from the femtosecond for electronic rearrangements, via the
0301-0104/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00101-0
248
S. Magazu et al. / Chemical Physics 292 (2003) 247–251
picosecond-to-nanosecond for thermal fluctuations, the millisecond of conformational changes involved in biostructures functional kinematics, to the seconds and minutes of protein kinesis and cell division [8]. Since the typical energies of the thermal molecular motions arising from H-bonding, electrostatic and van der Waals interactions are of the order of a few kcal/mol and atomic thermal [9], and since fluctuations are of the order of 1 A wavelength have an energy close neutrons with 1 A to 1 kcal/mol, neutron scattering has revealed itself particularly useful to study thermal molecular motions [8,10]. Experiments focused on the solvent properties by several spectroscopic techniques [11–17] indicate that the structural and the dynamical properties of water, even at low concentration, result drastically perturbed by disaccharides, and in particular by trehalose, and that a preferred trehalose–water interaction takes place. More specifically ultrasonic velocity [11] and viscosity measurements [12] evidence that, in respect to the other disaccharides, the trehalose–water system is characterized in all the investigated concentration range, by both the highest value of the solute– solvent interaction strength and of hydration number. Neutron diffraction [13], INS [14], Raman [15] and FTIR results [16] confirm a remarkable destructuring effect of disaccharides on water. On the other hand QENS results [17] on disaccharides solutions clearly indicate that also the water dynamics is strongly affected by the presence of disaccharides and by trehalose in particular. In this contribution we show results on trehalose and sucrose=D2 O mixtures in a wide temperature range across the glass transition which allow to characterize the systems ‘‘flexibility’’ and the ‘‘rigidity’’.
2. Experimental Neutron scattering experiments on IN13 at the ILL facility (Grenoble, France) [18] provide information on the motions of the sample hydrogens and 0.1 ns given in a space-time window of 1 A by its scattering vector modulus, Q, range and energy resolution and allow to characterize both
flexibility (obtained from the fluctuation amplitudes) and rigidity (obtained from how fluctuations vary with temperature and expressed as a mean environmental force constant). Furthermore the wide Q-range enables to emphasize the nonGaussian Q dependence of the elastic intensity. Ultrapure powdered trehalose and sucrose, and D2 O, purchased from Aldrich–Chemie were used to prepare solutions at a weight fraction corresponding to 19 water molecules for each disaccharide molecule. At such a concentration value the glass transition temperature, as determined by differential scanning calorimetry is T 253 K and T 250 K for trehalose=D2 O and sucrose=D2 O mixtures, respectively [16]. Neutron diffraction [13], ultrasonic [11] and viscosity measurements [12] clearly indicate that the disaccharides in water solution are strongly bonded to more than 22 water molecules at room temperature (with a difference from disaccharide to disaccharide: trehalose bonds a higher number of water molecules) and that this hydration number abruptly increases by lowering temperature. Measurements were carried out across the glass transition temperatures in a temperature range of 18–309 K. The samples were continuously heated from 18 to 309 K over a period of 24 h. The incident wavelength was ; the investigated Q-range was 0:28– 2.23 A 1 ; the elastic energy resolution (FWHM) 4:27 A was 8 leV. Raw data were corrected for cell scattering and detector response and normalized 1 . to unity at Q ¼ 0 A
3. Results and discussion As it is well-known [8], in incoherent neutron scattering experiments the function measured is the incoherent dynamic structure factor Sinc ðQ; xÞ, i.e., Fourier transform of the incoherent intermediate scattering function IðQ; tÞ IðQ; tÞ ¼
N X
xa h exp ½iQra ðtÞ exp ½ iQra ð0Þi;
ð1Þ
a¼1
where xa is the fraction of particles following the same dynamics in the potential Va ðrÞ, and ra ðtÞ the position vector of the particle a at time t.
S. Magazu et al. / Chemical Physics 292 (2003) 247–251
The incoherent dynamic structure factor Sinc ðQ; xÞ is composed by two contributions: an el elastic contribution Sinc ðQÞ ¼ Sinc ðQ; x ¼ 0Þ ¼ IðQ; 1ÞdðxÞ and a quasielastic contribution that involves energies hx > 0. The mean square displacement, hu2 i, which takes into account fluctuations of all particles in the investigated system is given by el d ln Sinc ðQÞ hu2 i ¼ 3 dQ2 Q¼0 ¼
N X xa ra2 ½1 Ca ðsÞ
249
(a)
ð2Þ
a¼1
with s resolution time of the experiment and Ca ðsÞ stationary position relaxation function. Nonetheless, for a given experiment Ca ðsÞ is a constant that rescales the observed mean square displacement, and hence Ca ðsÞ ¼ 0 can be assumed [8]. In Figs. 1(a) and (b), we show the elastically scattered intensity of trehalose and sucrose water mixtures at different temperature values. The most interesting aspect of the presented data is the non-Gaussian behavior of the intensity profiles, which is more marked for sucrose indicating a softer structure. The simplest way to account for the non-Gaussian elastic intensity and to extract numerical parameters is to consider jumps between two energetically asymmmetric sites. Following the double well potential model suggested by Doster et al. [10], in which the H atoms are able to perform jumps between two discrete sites of different energies, the expression of the integrated intensity as a function of Q is [10] Iel ðQÞ ¼ SðQ; x ¼ 0Þ
2
sinðQdÞ 2 ¼ A exp Q u ; 1 2p1 p2 Qd ð3Þ where p1 and p2 are the probabilities to find the scattering particles (hydrogens in our case) on the sites 1 (ground state) and 2 (excited state), and d is the distance between the two potential minima. The first term describes the Gaussian contribution to the mean square displacement and the term in brackets denotes the elastic incoherent structure factor of the two-state model. The mean square displacements have been evaluated from the one-
(b)
Fig. 1. Logarithm of scattering intensities as a function of Q2 at some temperature values for (a) trehalose and (b) sucrose=D2 O mixtures across their glass transition temperature. The continuous lines are the fit results by Eq. (3).
parameter fit furnished by Eq. (2) and employed for the fit of the intensity profiles with Eq. (3). The continuous lines in Figs. 1(a) and (b) are the fit result. From the fitting procedure the values obtained for p1 (always higher for trehalose than su and dsucrose 1:1 A ) crose) and d (dtrehalose 0:9 A confirm that in the case of trehalose/water mixture we are in the presence of a more hindered dynamics in respect to the case of sucrose/water mixture and hence of a more rigid structure on a nanoscopic scale. In Figs. 2(a) and (b), we show the temperature dependence of the derived mean square displacements for trehalose and sucrose mixtures, respectively. Below the dynamical transition the mean
250
S. Magazu et al. / Chemical Physics 292 (2003) 247–251
(a)
hki ¼ 0:00138=ðdhu2 i=dT Þ is applied. Although calculating force constants following this procedure is not a straightforward process, nevertheless an order of magnitude analysis is worthwhile also because in the present work the attention is focused on a comparison between the behavior of the two disaccharides. We obtain the values of hki ¼ 0:08 N=m and hki ¼ 0:03 N=m for trehalose and sucrose mixtures, respectively.
4. Conclusions (b)
Fig. 2. Temperature dependence of the mean square displacement for (a) trehalose and (b) sucrose=D2 O mixtures.
In this work we show neutron scattering findings on trehalose/water and sucrose/water mixtures. Elastic scans make evident a non-Gaussian behavior of the intensity profiles which is more marked for sucrose, with a dynamical transition at T 253 K and T 250 K for trehalose/water and sucrose/water mixtures, respectively, marking a cross-over in molecular fluctuations between harmonic and non-harmonic dynamical regimes. These findings evidence a higher ‘‘rigidity’’ of trehalose=D2 O in respect to sucrose=D2 O which is confirmed by new IN13 data on protonated hydrated disaccharides [21].
Acknowledgements
square displacement behavior can be fitted within the framework of the harmonic approximation
2 hhmi hhmi coth Du ðT Þ ¼ ; ð4Þ 2K KB T
The authors gratefully acknowledge the Institut Laue–Langevin ILL (Grenoble, France) for dedicated runs at IN13 spectrometer.
where K and hmi are, respectively, the average force field constant and the average frequency of a set of oscillators considered as an Einstein solid. After being trapped in harmonic potential wells at low temperatures, protons beyond the dynamical transition have sufficient thermal energy to jump between different wells (sites 1 and 2). Because a force constant is not defined for an anharmonic motions, an operational approach suggested by Zaccai [19,20], in which the ‘‘resilience’’ of an anharmonic environment is quantified by a pseudo-force constant hki calculated from the derivative of the scan at T according to
References [1] A. Hirsh, Cryobiology 24 (1987) 214. [2] K.B. Storey, J.M. Storey, Annu. Rev. Physiol. 54 (1992) 619. [3] R.E. Lee Jr., J.P. Costanzo, E.C. Davidson, J.R. Layne Jr., J. Therm. Biol. 17 (1992) 263. [4] L.K. Miller, Comp. Biochem. Physiol. 59A (1978) 327. [5] R. Zentella, J.O. Mascorro-Gallardo, P. Van Dijck, J. Folch-Mallol, B.V. Bonini, C. Vaeck, R. Gaxiola, A.A. Covarrubias, J. Nieto-Sotelo, J.M. Thevelein, G. Iturriaga, Plant Physiol. 119 (1999) 1473. [6] K. Yoshinaga, H. Yoshioka, H. Kurosaki, M. Hirasawa, M. Uritani, K. Hasegawa, Biosci. Biotech. Biochem. 61 (1997) 160.
S. Magazu et al. / Chemical Physics 292 (2003) 247–251 [7] N. Saita, N. Fujiwara, I. Yano, K. Soejima, K. Kobayashi, Infect. Immun. 68 (2000) 5991. [8] D.J. Bicout, G. Zaccai, Biophys. J. 80 (2001) 1115. [9] T.E. Creighton, Curr. Opin. Struct. Biol. 1 (1991) 5. [10] W. Doster, S. Cusack, W. Petry, Nature 337 (1989) 754. [11] S. Magaz u, P. Migliardo, A.M. Musolino, M.T. Sciortino, J. Phys. Chem. B 101 (1997) 2348. [12] C. Branca, S. Magaz u, G. Maisano, F. Migliardo, P. Migliardo, G. Romeo, J. Phys. Chem. B 105 (2001) 10140. [13] C. Branca, S. Magaz u, G. Maisano, F. Migliardo, A.K. Soper, Appl. Phys. A 74 (2002) 450. [14] C. Branca, S. Magaz u, F. Migliardo, Rec. Res. Develop. Phys. Chem. 6 (2002) 35.
251
[15] C. Branca, S. Magaz u, G. Maisano, P. Migliardo, J. Chem. Phys. 111 (1999) 281. [16] C. Branca, A. Faraone, S. Magaz u, G. Maisano, F. Migliardo, P. Migliardo, V. Villari, Rec. Res. Develop. Phys. Chem. 3 (1999) 361. [17] S. Magaz u, V. Villari, P. Migliardo, G. Maisano, M.T.F. Telling, J. Phys. Chem. B 105 (2001) 1851. [18] J.C. Smith, Q. Rev. Biophys. 24 (1991) 227. [19] G. Zaccai, Science 288 (2000) 1604. [20] L. Cordone, M. Ferrand, E. Vitrano, G. Zaccai, Biophys. J. 76 (1999) 1043. [21] S. Magaz u, F. Migliardo, C. Mondelli, in preparation.
Temperature dependence of mean square displacement by IN13: a comparison between trehalose and sucrose water mixtures S. Magaz u a,*, F. Migliardo a, C. Mondelli b, G. Romeo a b
a Dipartimento di Fisica and INFM, Universit a di Messina, P.O. Box 55, I-98166 Messina, Italy INFM-Operative Group Grenoble CRG IN13 and Institut Laue–Langevin, 38042 Grenoble Cedex 9, France
Received 3 October 2002; in final form 6 February 2003
Abstract An analysis in terms of elastic scans of the neutron intensity in mixtures of homologues disaccharides (i.e., trehalose and sucrose)/D2 O as a function of temperature has been carried out. The study provides an effective way for characterizing the dynamical behavior, furnishing a set of parameters characterizing the ‘‘flexibility’’ and the ‘‘rigidity’’ that justifies the better cryptobiotic effect of trehalose in respect to sucrose. Elastic scans make evident a non-Gaussian behavior of the intensity profiles which is more marked for sucrose, with a dynamical transition at T 253 K and T 250 K for trehalose=D2 O and sucrose=D2 O mixtures, respectively. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction In recent years many progresses have been made in cryobiology, the important research field that studies mechanisms and consequences for organisms living at any temperature below the physiological range. The reason that induces the research activity in this direction is the understanding of the tools used by nature to adapt organisms to the stresses of low temperatures, such as freeze-drying, supercooling, cryosurgery, frost-
*
Corresponding author. Tel.: +39-90-391-478; fax: +39-90395-004. E-mail address: [email protected] (S. Magazu`).
bite and cryopreservation [1–3]. Trehalose has been found to be the most common sugar in many species, that survive to low temperature by means of natural cryoprotective agents [2–5]. These multiple effects of trehalose suggest manifold promising applications [6,7]. Also other disaccharides of the same homologues series ðC12 H22 O11 Þ, such as maltose and sucrose, show similar action on biological structures, but trehalose has peculiar properties that make it the most extraordinary bioprotectant. It is well-known that molecular dynamics plays a fundamental role in many aspects of biological activity. The timescales of the motions involved cover several orders of magnitude: from the femtosecond for electronic rearrangements, via the
0301-0104/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00101-0
248
S. Magazu et al. / Chemical Physics 292 (2003) 247–251
picosecond-to-nanosecond for thermal fluctuations, the millisecond of conformational changes involved in biostructures functional kinematics, to the seconds and minutes of protein kinesis and cell division [8]. Since the typical energies of the thermal molecular motions arising from H-bonding, electrostatic and van der Waals interactions are of the order of a few kcal/mol and atomic thermal [9], and since fluctuations are of the order of 1 A wavelength have an energy close neutrons with 1 A to 1 kcal/mol, neutron scattering has revealed itself particularly useful to study thermal molecular motions [8,10]. Experiments focused on the solvent properties by several spectroscopic techniques [11–17] indicate that the structural and the dynamical properties of water, even at low concentration, result drastically perturbed by disaccharides, and in particular by trehalose, and that a preferred trehalose–water interaction takes place. More specifically ultrasonic velocity [11] and viscosity measurements [12] evidence that, in respect to the other disaccharides, the trehalose–water system is characterized in all the investigated concentration range, by both the highest value of the solute– solvent interaction strength and of hydration number. Neutron diffraction [13], INS [14], Raman [15] and FTIR results [16] confirm a remarkable destructuring effect of disaccharides on water. On the other hand QENS results [17] on disaccharides solutions clearly indicate that also the water dynamics is strongly affected by the presence of disaccharides and by trehalose in particular. In this contribution we show results on trehalose and sucrose=D2 O mixtures in a wide temperature range across the glass transition which allow to characterize the systems ‘‘flexibility’’ and the ‘‘rigidity’’.
2. Experimental Neutron scattering experiments on IN13 at the ILL facility (Grenoble, France) [18] provide information on the motions of the sample hydrogens and 0.1 ns given in a space-time window of 1 A by its scattering vector modulus, Q, range and energy resolution and allow to characterize both
flexibility (obtained from the fluctuation amplitudes) and rigidity (obtained from how fluctuations vary with temperature and expressed as a mean environmental force constant). Furthermore the wide Q-range enables to emphasize the nonGaussian Q dependence of the elastic intensity. Ultrapure powdered trehalose and sucrose, and D2 O, purchased from Aldrich–Chemie were used to prepare solutions at a weight fraction corresponding to 19 water molecules for each disaccharide molecule. At such a concentration value the glass transition temperature, as determined by differential scanning calorimetry is T 253 K and T 250 K for trehalose=D2 O and sucrose=D2 O mixtures, respectively [16]. Neutron diffraction [13], ultrasonic [11] and viscosity measurements [12] clearly indicate that the disaccharides in water solution are strongly bonded to more than 22 water molecules at room temperature (with a difference from disaccharide to disaccharide: trehalose bonds a higher number of water molecules) and that this hydration number abruptly increases by lowering temperature. Measurements were carried out across the glass transition temperatures in a temperature range of 18–309 K. The samples were continuously heated from 18 to 309 K over a period of 24 h. The incident wavelength was ; the investigated Q-range was 0:28– 2.23 A 1 ; the elastic energy resolution (FWHM) 4:27 A was 8 leV. Raw data were corrected for cell scattering and detector response and normalized 1 . to unity at Q ¼ 0 A
3. Results and discussion As it is well-known [8], in incoherent neutron scattering experiments the function measured is the incoherent dynamic structure factor Sinc ðQ; xÞ, i.e., Fourier transform of the incoherent intermediate scattering function IðQ; tÞ IðQ; tÞ ¼
N X
xa h exp ½iQra ðtÞ exp ½ iQra ð0Þi;
ð1Þ
a¼1
where xa is the fraction of particles following the same dynamics in the potential Va ðrÞ, and ra ðtÞ the position vector of the particle a at time t.
S. Magazu et al. / Chemical Physics 292 (2003) 247–251
The incoherent dynamic structure factor Sinc ðQ; xÞ is composed by two contributions: an el elastic contribution Sinc ðQÞ ¼ Sinc ðQ; x ¼ 0Þ ¼ IðQ; 1ÞdðxÞ and a quasielastic contribution that involves energies hx > 0. The mean square displacement, hu2 i, which takes into account fluctuations of all particles in the investigated system is given by el d ln Sinc ðQÞ hu2 i ¼ 3 dQ2 Q¼0 ¼
N X xa ra2 ½1 Ca ðsÞ
249
(a)
ð2Þ
a¼1
with s resolution time of the experiment and Ca ðsÞ stationary position relaxation function. Nonetheless, for a given experiment Ca ðsÞ is a constant that rescales the observed mean square displacement, and hence Ca ðsÞ ¼ 0 can be assumed [8]. In Figs. 1(a) and (b), we show the elastically scattered intensity of trehalose and sucrose water mixtures at different temperature values. The most interesting aspect of the presented data is the non-Gaussian behavior of the intensity profiles, which is more marked for sucrose indicating a softer structure. The simplest way to account for the non-Gaussian elastic intensity and to extract numerical parameters is to consider jumps between two energetically asymmmetric sites. Following the double well potential model suggested by Doster et al. [10], in which the H atoms are able to perform jumps between two discrete sites of different energies, the expression of the integrated intensity as a function of Q is [10] Iel ðQÞ ¼ SðQ; x ¼ 0Þ
2
sinðQdÞ 2 ¼ A exp Q u ; 1 2p1 p2 Qd ð3Þ where p1 and p2 are the probabilities to find the scattering particles (hydrogens in our case) on the sites 1 (ground state) and 2 (excited state), and d is the distance between the two potential minima. The first term describes the Gaussian contribution to the mean square displacement and the term in brackets denotes the elastic incoherent structure factor of the two-state model. The mean square displacements have been evaluated from the one-
(b)
Fig. 1. Logarithm of scattering intensities as a function of Q2 at some temperature values for (a) trehalose and (b) sucrose=D2 O mixtures across their glass transition temperature. The continuous lines are the fit results by Eq. (3).
parameter fit furnished by Eq. (2) and employed for the fit of the intensity profiles with Eq. (3). The continuous lines in Figs. 1(a) and (b) are the fit result. From the fitting procedure the values obtained for p1 (always higher for trehalose than su and dsucrose 1:1 A ) crose) and d (dtrehalose 0:9 A confirm that in the case of trehalose/water mixture we are in the presence of a more hindered dynamics in respect to the case of sucrose/water mixture and hence of a more rigid structure on a nanoscopic scale. In Figs. 2(a) and (b), we show the temperature dependence of the derived mean square displacements for trehalose and sucrose mixtures, respectively. Below the dynamical transition the mean
250
S. Magazu et al. / Chemical Physics 292 (2003) 247–251
(a)
hki ¼ 0:00138=ðdhu2 i=dT Þ is applied. Although calculating force constants following this procedure is not a straightforward process, nevertheless an order of magnitude analysis is worthwhile also because in the present work the attention is focused on a comparison between the behavior of the two disaccharides. We obtain the values of hki ¼ 0:08 N=m and hki ¼ 0:03 N=m for trehalose and sucrose mixtures, respectively.
4. Conclusions (b)
Fig. 2. Temperature dependence of the mean square displacement for (a) trehalose and (b) sucrose=D2 O mixtures.
In this work we show neutron scattering findings on trehalose/water and sucrose/water mixtures. Elastic scans make evident a non-Gaussian behavior of the intensity profiles which is more marked for sucrose, with a dynamical transition at T 253 K and T 250 K for trehalose/water and sucrose/water mixtures, respectively, marking a cross-over in molecular fluctuations between harmonic and non-harmonic dynamical regimes. These findings evidence a higher ‘‘rigidity’’ of trehalose=D2 O in respect to sucrose=D2 O which is confirmed by new IN13 data on protonated hydrated disaccharides [21].
Acknowledgements
square displacement behavior can be fitted within the framework of the harmonic approximation
2 hhmi hhmi coth Du ðT Þ ¼ ; ð4Þ 2K KB T
The authors gratefully acknowledge the Institut Laue–Langevin ILL (Grenoble, France) for dedicated runs at IN13 spectrometer.
where K and hmi are, respectively, the average force field constant and the average frequency of a set of oscillators considered as an Einstein solid. After being trapped in harmonic potential wells at low temperatures, protons beyond the dynamical transition have sufficient thermal energy to jump between different wells (sites 1 and 2). Because a force constant is not defined for an anharmonic motions, an operational approach suggested by Zaccai [19,20], in which the ‘‘resilience’’ of an anharmonic environment is quantified by a pseudo-force constant hki calculated from the derivative of the scan at T according to
References [1] A. Hirsh, Cryobiology 24 (1987) 214. [2] K.B. Storey, J.M. Storey, Annu. Rev. Physiol. 54 (1992) 619. [3] R.E. Lee Jr., J.P. Costanzo, E.C. Davidson, J.R. Layne Jr., J. Therm. Biol. 17 (1992) 263. [4] L.K. Miller, Comp. Biochem. Physiol. 59A (1978) 327. [5] R. Zentella, J.O. Mascorro-Gallardo, P. Van Dijck, J. Folch-Mallol, B.V. Bonini, C. Vaeck, R. Gaxiola, A.A. Covarrubias, J. Nieto-Sotelo, J.M. Thevelein, G. Iturriaga, Plant Physiol. 119 (1999) 1473. [6] K. Yoshinaga, H. Yoshioka, H. Kurosaki, M. Hirasawa, M. Uritani, K. Hasegawa, Biosci. Biotech. Biochem. 61 (1997) 160.
S. Magazu et al. / Chemical Physics 292 (2003) 247–251 [7] N. Saita, N. Fujiwara, I. Yano, K. Soejima, K. Kobayashi, Infect. Immun. 68 (2000) 5991. [8] D.J. Bicout, G. Zaccai, Biophys. J. 80 (2001) 1115. [9] T.E. Creighton, Curr. Opin. Struct. Biol. 1 (1991) 5. [10] W. Doster, S. Cusack, W. Petry, Nature 337 (1989) 754. [11] S. Magaz u, P. Migliardo, A.M. Musolino, M.T. Sciortino, J. Phys. Chem. B 101 (1997) 2348. [12] C. Branca, S. Magaz u, G. Maisano, F. Migliardo, P. Migliardo, G. Romeo, J. Phys. Chem. B 105 (2001) 10140. [13] C. Branca, S. Magaz u, G. Maisano, F. Migliardo, A.K. Soper, Appl. Phys. A 74 (2002) 450. [14] C. Branca, S. Magaz u, F. Migliardo, Rec. Res. Develop. Phys. Chem. 6 (2002) 35.
251
[15] C. Branca, S. Magaz u, G. Maisano, P. Migliardo, J. Chem. Phys. 111 (1999) 281. [16] C. Branca, A. Faraone, S. Magaz u, G. Maisano, F. Migliardo, P. Migliardo, V. Villari, Rec. Res. Develop. Phys. Chem. 3 (1999) 361. [17] S. Magaz u, V. Villari, P. Migliardo, G. Maisano, M.T.F. Telling, J. Phys. Chem. B 105 (2001) 1851. [18] J.C. Smith, Q. Rev. Biophys. 24 (1991) 227. [19] G. Zaccai, Science 288 (2000) 1604. [20] L. Cordone, M. Ferrand, E. Vitrano, G. Zaccai, Biophys. J. 76 (1999) 1043. [21] S. Magaz u, F. Migliardo, C. Mondelli, in preparation.