Distribution of conformational states as common source of g-and A-strain in the ESR spectra of proteins and glasses

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Submitted on 1 Jan 1990

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Distribution of conformational states as common source

of g-and A-strain in the ESR spectra of proteins and

glasses

Salvatore Cannistraro

To cite this version:

Distribution of conformational states

as common source

of

g-and

A-strain in the ESR

_spectra

of

_proteins

and

_glasses

Salvatore Cannistraro

Gruppo

di Biofisica

_{Molecolare, Dipartimento}

di Fisica

dell’Università,

I-U6100

_{Perugia, Italy}

(Reçu

le 9 mars _1989, révisé le 9 août 1989,

accepté

le 15

septembre

1989)

Résumé. 2014

On décrit

_quelques

faits

_{expérimentaux supplémentaires}

concernant la similitude structurale et

_dynamique

entre

_protéines

et verres, à

_partir

de

_l’analyse

de _spectres ESR de

quelques protéines

contenant du cuivre et de verres

_dopés

au _{Cu++ formé par de l’eau} et un

deuxième _composant

_(NaOH,

_DMSO,

_alcools),

obtenus à différentes

_{températures.}

Tous les

spectres obtenus à des

températures

inférieures à environ 210 K montrent des

déformations g

et

A

_{significatives qui}

consistent en un

_{élargissement}

_progressif

et une réduction d’intensité des

lignes hyperfines

du cuivre,

quand

l’ordre de mI, augmente

(le

spin

nucléaire du cuivre est

I =

3/2).

Ces faits _sont

pris

en _compte dans un modèle

_{théorique qui}

attribue la distribution aléatoire des

_champs

_électriques

autour des ions de cuivre à une distribution des

_énergies

de

conformation aussi bien pour les

protéines

que pour les matériaux

amorphes.

Abstract. 2014 Additional

experimental

evidence on the structural and

_{dynamical similarity}

between

proteins

and

_glasses

is

_provided

_by

the

_analysis

conducted on the ESR _spectra, at different

temperatures, of some _copper

_proteins

and of some

_Cu++-doped

_glasses

formed

_by

water and a

second _component

_(NaOH,

_DMSO,

_alcohols).

All the _spectra taken at _temperatures below ~ 210 K

display

_a

significant

_{g- and A-strain that consists in a}

progressive

broadening

and decrese in the

_intensity

_{of the copper}

_hyperfine

lines as the order of mI increases

(I

= 3/2 is the Cu nuclear

spin).

These

_spectral

features are taken into account

_{by using}

a theoretical model which attributes the random distribution of the electric

_ligand

_{fields around the copper ions} to a distribution of the

conformational substate

_energies

both in the

_proteins

and in the

_amorphous

materials. Classification

Physics

Abstracts 76.30 - 61.40 - 87.15

Introduction.

There is

_mounting

evidence that biomolecules and

_{glasses display profound analogies}

in their

structure and

_dynamics

_[1-9].

At low

_temperatures

_amorphous

solids exhibit characteristic

anomalies in their

_thermal,

acoustic and dielectric

_properties.

These anomalies are attributed

to

_low-energy

excitations which are

_generally

described as two level

_tunnelling

_systems

_(TLS)

[10].

In a

_simple

_microscopic

_model,

these excitations are

_thought

to arise from the

_possibility

that in an

_amorphous

_{network small groups of} atoms can

_undergo

local

_{rearrangements}

visualized

_by

a transition between two wells of a double well

_potential.

On the other

_hand,

biomolecules have been shown to exist in very many

different,

thermally

accessible,

configurational

states

_(substates)

that are believed to

_play

an

_important

dynamical

role connected with their

_{functionality.}

On

_cooling

below - 200 K the various

132

molecules freeze into different

substates,

each characterized

_by

a

_slightly

different _energy, transitions _{among these substates}

_being

absent. In that context, the characteristics of

_glasses

and

_{spin glasses}

find a

_{correspondence}

in biomolecules : below a critical

_temperature

there exist a

_large

number of _energy

_valleys

_separated

_by

_effectively

_{infinitely high}

barriers,

the

system

is

_non-ergodic

and

_properties

_{vary from}

_valley

to

_valley

_(substate

to

_substate).

The substates possess a hierarchical structure and relaxation is

_sequential

and

_{non-exponential}

in time as

_suggested

for

_glasses

_(see

Refs.

_{[2, 8]}

and Refs.

_therein).

In

_particular,

it has been

suggested

that the

_glass-like

states in

_proteins

could be due to local

arrangements

of certain

atoms or _{groups of} atoms

_(for

_example,

_{rearrangements}

of

_hydrogen

bonds and rotations of

methyl

or similar

_{groups) [3,}

4,

9]

and that

_hydration

water could

_play

a crucial role in the

dynamics

of conformational transitions

_{[1, 4, 7].}

More

_experimental

evidence on the

_similarity

between

_proteins

and

_glasses

is

_provided,

in the

_present

_paper,

_by

the

_analysis

conducted on the Electron

_Spin

Resonance

_(ESR)

_spectra,

at different

_temperature,

of some _copper

_proteins

and of some

65CU2 + -doped

_glasses

formed

by

water and a second

component

(NaOH,

DMSO,

alcohols) [11].

All the

_spectra

taken at

_temperatures

below 210 K

_display

a

significiant

_{g- and A-strain that}

consists in a

_{progressive broadening}

and decrease in the

_intensity

of _{the copper}

_hyperfine

lines

as the order of ml increases

(1

= 3/2 is the Cu nuclear

spin) [12, 13].

These

spectral

features have been almost

_{perfectly reproduced by using}

a theoretical model that attributes the

random distribution of the electric

_ligand

_{fields around the copper}

ions,

which is

_responsible

for the statistical modulation of

the g

and A

values,

to a distribution of the conformational

substate

_energies

both in the

_proteins

and in the

_amorphous

materials.

Materials and methods.

Plastocyanin

(PC)

was

_prepared

from

_spinach

leaves as described in reference

[14]

Azurin

(Az),

from Pseudomonas

_Aeruginosa,

was

_purchased

from

_Sigma

Chem. Co. and used

without further

_{purification. 65Cu++}

was

_purchased

from Oak

_Ridge

Labs,

digested

in HCI

and diluted in

_phosphate

buffer. All the other chemical used were of

_analytical

_reagent

_grade.

65Cu’ ’ -doped amorphous

systems

and related ESR

_samples

were

_prepared

with

_procedures

similar to those

_reported

in reference

_[15].

ESR

_{protein samples}

were

_{prepared according}

to

procedures reported

in reference

_[16].

ESR

_spectra

were recorded

_by

an X-band Varian E109

_{spectrometer,}

_equipped

with a

variable

_temperature

control. To calculate the

_experimental

_g-values,

a

_magnetic

field

calibration was

_performed

with a

_Magnion

Precision NMR Gaussmeter mod.

_G-502,

the

microwave

_frequency

_being

measured with a Marconi 2440 counter. ESR data

_acquisition

was

carried out on an HP 86A

_personal

_computer

_through

a home made interface connected to an

IEEE 488 bus

_[17].

To run simulation and best-fit programs, the same

_{microcomputer}

was

switched to an

_intelligent

terminal of the main frame

_computer

_(a

Prime

_550-1),

_through

an

RS-232C serial interface and an HP terminal emulator.

The

_chi-square

test was used to evaluate the

_goodness

of fits

_utilizing

the

_{expression :}

where

_Iexp(Hi)

is the derivative of the

_{expérimental}

ESR

_absorption

_spectrum

_sampled

at 200

Results and discussion.

Figures

la and 2a show the ESR

_spectra

_arising

_{from frozen aqueous} solutions of two well-known

_{metallo-proteins,}

PC and AZ

_{respectively.}

Each of these two

_proteins

contains one

single

atom _{of copper,}

_which,

under its oxidized form

_CU++,

endows the

_protein

with

paramagnetic properties

[18].

Actually,

their

_spectrum,

taken at 77

_K,

_displays

the character-istic features of a

_powder-like

ESR

_spectrum

of Cu++ ions with

_{low gl}

and

_Ap

values

interpretable

in terms of the

_{following spin}

Hamiltonian :

where

_f3

is the Bohr

_{magneton, gl}

and

_AI

are,

respectively,

the g

value and the

_hyperfine

component

parallel

to the molecular

_symmetry

axis,

g_L

and A_L

are,

respectively,

the g

value

and

_hyperfine

_component

_{perpendicular}

to the molecular

_symmetry

axis,

the S’s

_(S

=

1/2 )

_are the electron

_spin

_components

and l’s

_(I

=

3/2)

are the nuclear

_spin

_components

of the ion.

Fig. 1.

Fig.

2.

Fig.

1. -

Experimental

(a)

and

_{computer-simulated (b)}

ESR _spectrum of PC

_(0.3

mM in water,

pH

7).

The low-field _part

_{(gl region)}

of the spectra is shown at fivefold

_gain.

The

_experimental

spectrum was

recorded at 77 K with the

_{following settings :}

_{microwave power level : 20} mW ;

magnetic

field sweep

rate : 2 000 G in 8 min ; time constant : 0.5 s ; modulation

amplitude :

5 G. The

_computed

_spectrum was

generated through equation

(17)

with the

_following

_{parameters : gl = 2.251 ; gi} = 2.047 ;

Fig.

2. -

Experimental

(a)

and

_{computer-simulated (b)}

ESR spectrum of Az

_(0.2

mM in water,

pH

7).

The low-field part

(91

region)

of the _spectra is shown at fivefold

_gain.

_Experimental

temperature and

settings

are as in

_Fig.

1. Simulated best

_fitting

spectrum was obtained with : g, = 2.275 ;

134

From the

_{hyperfine coupling}

between S and

I,

four lines centered

_{at gll}

and

_separated

_by

All

(related

to _mI = -

3/2, - 1/2, 1/2,

3/2)

and four lines centered at _g1 and

separated

by

A1

could be

_expected.

Qualitatively,

a similar

_spectrum

is also to be

_expected

for Cu++ ions dissolved in

amorphous

matrices as obtained

_{by adding}

suitable amounts of

_NaOH,

DMSO and alcohols

to

_H20

and

_by

_rapidly

_freezing

the mixture below the

_glass

transition

_{[15]. Actually,}

this is the

case

_and,

as

_examples,

in

figures

3a and

_4a,

we show the ESR

_spectra

of

65Cu+

+

_-doped

solutions of

_H20-DMSO

and

_{D20-NaOD, respectively,}

recorded at 77 K after the

_glass

matrices were formed

(isotopically

enriched copper ions and deuterated chemical

_compounds

were used to

_{improve spectral}

_resolution).

We would like to draw attention to a common feature shared

_by

the

_spectra

shown in the four

_figures.

As

_already

observed for some

_particular

cases

[14, 15],

all the

_spectra

of

figures

1-4

show,

in

_{the gp region}

of the

_spectrum

_(this

_part

is

_reproduced

in the insets of the

Fig. 3.

Fig. 4.

Fig.

3.

_{- Experimental}

_(a)

and

_{computer-simulated}

_(b)

ESR spectrum

65Cu+ +

(0.1 mM)

in

water-DMSO

_(1:1,

in

_vol).

The low-field _part

_(gl

_region)

of the _spectra is

shown 1 at

fivefold

_gain.

The

experimental

spectrum was recorded at 77 K with the

_{following settings :}

_{microwave power level :} 12 mW ;

magnetic

field sweep rate : 2 000 G in 8 _{min ;} time constant : 0.5 s ; modulation

amplitude :

5 G. The

_computed

spectrum was

_generated

_{through equation}

₍₁₇₎

with the

_following

parameters :

Fig.

4. ESR _spectrum from

_{65Cu2 + doped}

_{(0.01 mM)}

_NAOD-D20

in the

_{amorphous phase}

_(a)

and its

parallel

part

at a tenfold

_gain

_{(b). Spectrum (c)}

is the best fit of all the

_experimental

spectrum

(fitting

pararneters : gl = 2.271 ;

g1 = 2.031 ;

AI =

197.6

G ;

A1

= 40.0

G ; u 91

= 0.0062 G ; 0-Al = 4.1 G ;

01R

= 2.5 G ;

p =

1). Only

the

g-parallel

_part

(where

the strain effects _are

mostly

seen)

of the simulated

spectrum is shown to _{compare it} to the related _part od the

_experimental

spectrum at

_{high gain.}

The

experimental

spectrum was recorded at 77 K, the other _spectrometer

_{settings being :}

microwave

frequency :

9.133

_{GHz ;}

_{microwave power ; 10} mW ;

_magnetic

field sweep rate : 2 000 G in 8 min ; time

Fig.

at a

_higher

_gain),

a

_{progressive braodening}

and

_decreasing

in

intensity

of the

hyperfine

lines as _{mI increases. Such} an effect can be

immediately

observed in the case of

_amorphous

systems

(Figs.

3,

4)

since the

_hyperfine

lines are

_spaced

to a

_higher

extent than those

_arising

from the

_{metallo-proteins.}

In the ESR

_pattern

of the latter

_{systems, however,}

a closer

inspection

reveals a similar behaviour

_{[14, 19].}

Moreover,

an

_irregular

_spacing

between

_pairs

of

_adjacent

_hyperfine

lines in

_{the gl}

_region

is found

_{[12, 13].}

_Spectral

anomalies of this kind

have been

named,

in a

_general

_{way, g- and A-strain}

_[12,

_{13, 20,}

_21].

In the course of

_previous

works

_{[12, 13],}

we have shown

that,

under these

conditions,

a

_computer

simulation of the

experimental

ESR

spectra

is

_{indispensable}

if a reliable extraction of the

_spin

hamiltonian

parameters

is to be achieved. For sake of

_{completeness,}

it should be recalled that

the g

strain effect in some classes of iron

_{metalloproteins}

has been described in the literature with the aid

of two different

_{approaches :}

one

_taking

into account a statistical fluctuation of some

_spin

hamiltonian

_parameters

_{(statistical model) [21-24]}

and the other

_expressing

_{the g}

values in terms of the related

_physical

_parameters

_{(physical model) [25, 26].}

In the

_present

_paper we would

_mainly

like to

_point

out that these features are

_present,

with

striking similarity,

in the ESR

_spectra

of both

_{copper-proteins}

and of

_{Cu++-doped glassy}

systems.

In this

_connection,

we have moreover

_attempted

to relate these common anomalous

spectral

features to the

_microscopic,

structural and

_{dynamical, properties}

of both

_glassy

and frozen

_protein

_systems.

Both

_proteins

and

_glassy

_systems

can be considered as

_{microscopically}

disordered

_systems.

This fact

_originates

from fluctuations of local structure in

_glasses

_[10]

_{and from the presence of}

a static ensemble of frozen conformational states, to which

_{correspond randomly}

oriented or

positioned

side groups

(see

Introduction

_section),

in the frozen

_protein

solutions. As a

consequence, we can

_imagine

that the Cu++

_complexes

are deformed

_{(as regarding}

their bond

_length

and

_angles)

in a

_slightly

_{different way}

_according

to the microenvironmental fluctuations

_that,

_very

_probably,

follow a random distribution. The statistical distribution of

the atomic coordinates that can

_{be, then,}

_envisaged

for the copper ion

_ligands

will result in a

distribution of strains at the metal sites

_[21].

In the framework of the

_crystal

field

_theory

for the

3d9

Cu++ ions

_[27],

such a

_physical

situation could be described

_by

a distribution of the

crystal

field

_splittings

_(a)

of the

d9

levels of the Cu++ ions both in the

_protein

and in the

glassy

systems.

In other

_words,

it seems reasonable to

_imagine

that _{the copper}

ions,

present

either as

_dopant

in the

_amorphous

matrices or as intrinsic constituents in the

_proteins,

could

sense the energy distribution

_{corresponding}

to the existence of a

_multiplicity

of

con-formational states as a statistical modulation of their

_crystal

field

_strengths

_(in

this

_respect,

an

Angular Overlap

Model calculation has

_provided

a

_{quantitative relationship}

between

thé n

bond

_angle

distribution

_[28]

and the

_{corresponding crystal}

_{field energy distribution for} Az

_[29]).

The

_quite

realistic

_assumption

of a distribution

of

the conformational

_energies

for the

glasses

and for the frozen solutions of

_proteins

of the

type

[2, 3] :

leads then to a Gaussian distribution of the

_crystal

field

_{splittings a}

_(viewed,

for

_example,

as

136

If one now takes into account the Kivelson and Neiman formulas

_[30],

written in a more

compact

way :

where :

and

P, k

and À have their usual

_meaning

_[30],

it can be

_easily

shown

_that,

for small fluctuations in d

_(i.e.

_for

_{1 (,à -,ào)/,àol «}

₁₎

the

_{following expressions}

hold :

where :

In the derivation of

_equation

_(6),

the fluctuation in the

_parameters

_g1 and

_{A-L ,}

as

_resulting

from the fluctuation in

à,

has been

_neglected.

Such an

_{approximation}

can be made for two

reasons : the first is related to the fact

that,

for these

_complexes,

the strain effects are

_mostly

seen in the

_{g-parallel region}

_(a

similar

_{approximation}

is made

_by

other authors

_[20]),

the second is based on the check that the inclusion in the model of the fluctuations in

91. and

_{A_L}

resulted in

_only

a _{very small}

_change

in the

_computed

_spectra

_[12].

The

_following

distributions

_{for 91}

and

_AI

will result from

_{equations (4)}

and

_{(6) :}

with :

The effect of

_introducing

the distributions of these

_spin

Hamiltonian

_parameters

will be that

of

_creating

a distribution in the resonant field

_positions,

_Ho,

which are obtained

by

solving

to the second order the

_spin

Hamiltonian

_appearing

in

_equation

_{(2) [12, 13].}

For small

_changes

in these

_parameters,

_{8 ga}

and

_8AI,

the

_following

fluctuation in

_Ho

will result :

The next

_step

is that of

_conceiving

a theoretical

_model,

_encompassing

the above mentioned

distributions

_{in 91}

and

_{A~ ,}

and of

_finding

whether the

_subsequently

_computer

_synthesized

spectra

are able to

_provide

a best fit to the

_experimental

_spectra

_arising

from all the different

systems

investigated.

axial

_symmetry,

but in the absence of

_strain,

can be

_{performed by}

the

_{following expression}

([13]

and Refs.

_{therein) :}

where

_{S (v,H)}

_{expresses the} net

_absorption

of microwave

_radiation,

the normalization constant,

N,

takes account all the instrumental

_{parameters ;}

_gf

_represents

the

orientation-dependent

ESR transition

_{probability ;}

_{f[(v -}

_{v0)2, UR]}

is the Gaussian

_lineshape,

whose

peak-to-peak

halfwidth is

_{a R}

_(R

stands for residual linewidth that is

_mainly

determined

_by

the unresolved

_coupling

of electron

_spin

to

_{ligand nuclei) ;}

_Po are the resonant

_frequencies

corresponding

to the resonant field values at which the

_hyperfine

lines are situated

(we

consider here

_frequency

_{swept spectra,}

see Ref.

[13]) ;

_finally

the

_integral

over 0 takes into account the random orientation of the molecular

_symmetry

_{axis of the copper}

_complexes.

To

_take,

_now, into account the above mentioned fluctuations in _gN and

_{All, equation}

₍₁₀₎

should be

_integrated

over the distributed values of these two

_{parameters ;}

then we have

F (gl , A~)

is taken as a bivariate normal

_density

function which describes the Gaussian distribution

_{of gl}

and

_Ap

in terms of the

_respective

variances,

_{(u 91}

)’

and

(u AI

)2,

and of the correlation coefficient

_p(-lp+l).

By

integrating equation

(11),

we see that the ESR

_spectrum,

_{in the presence of}

_strain,

can

then be

_{synthesized by}

an

_expression

of the

_type

_{[13] :}

where u Tv

can be cast into the form :

and

From

_{equation (14), a Il S}

can be

_expressed

as a _power

_expansion

of _ml and H as follows :

Equations

(13)

and

₍₁₅₎

_{indicate that the presence of strain effects results in} an

ml-dependent

contribution,

expressed

by aj,

to the total

_{linewidth, uT@ (which}

is

_actually

observed in the

_experimental

_spectra).

It should be remarked that

_{expression (15),}

_analitically

derived in the

_present

case, has been sometimes introduced as an

_empirical

expression

in the

fit of the copper

complex

spectra

(see

Refs.

_reported

in

_[12,

13,

20].

Moreover,

such an

138

Finally,

to

_compute

the field

_swept

ESR

_spectra

that are

_usually

recorded at a fixed

frequency

vc and

displayed

as the first derivative of the

_absorption,

it is necessary to

differentiate

_equation

_(12),

taken at the

_frequency

_vc, with

_respect

to H

_{[13] :}

This model

_function,

which is non linear in the

_parameters

_{p, has been used} to fit all the

experimental

spectra

obtained. The set of

_parameters

_{p, with}

_respect

to which

_expression

_[1]

was

_minimized,

is : _{gll, g 1. ,}

_{All , A 1.’}

the residual

_{linewidth o- vgl}

,

0 A,

and p.

Pattern b of each

_figure

shows the simulated ESR

_spectrum

that best fits the

_{corresponding}

experimental

spectrum

(pattern a).

As can be seen, the

agreement

between each two related

spectra

is very

good ;

the

_goodness

of the fits has been checked with the

_chi-square

method and values

_ranging

from 260 to 320 were obtained for

_{X 2.}

The

_fitting

_parameters

are

_reported

in the

_legend

of each

_figure.

In this

connection,

from

_{equation (8)}

it is

_expected

that the ratio

O’A,lo-g,

were about

P,

i.e. about 0.036 cmw.

However,

while such a value is

reasonably

approached

in the simulated

spectra

of

_figures

3 and 4 and in

_agreement

with the values

reported

in reference

_[20],

a value about five fold

_higher

is obtained in the case of the two

proteins.

Such a

_{discrepancy might}

be attributed either to the lower resolution achieved in the

spectra

of these

_systems

or to different microenvironment sensed

_by

_{the copper ions. We}

believe,

however,

that this

_aspect

could be an

_{interesting point}

to take into consideration for further refinement of the model.

Nevertheless the results obtained

confirm,

in our

_opinion,

the

_{newly emerging picture}

that

glasses

and

_proteins

_{have many} features in common. Their

_properties

are characteristic for the presence of disorder on a

_microscopic

scale. Such a disorder reflects the fact that both

systems

possess an immense

_{configurational}

_{space and similar}

_probability

distributions of conformational states results for

_glasses

and

_proteins.

We

have,

additionally,

submitted all the

systems

studied to a careful ESR

_analysis

as a

function of the

_temperature

_(in

_{the range from 240 down} to 4

_K)

to ascertain if a critical

temperature

for the onset of the

_spectral

strain exists and/or if the latter shows some sort of

dependence

on the

_temperature

itself.

We found that the strain effects in the ESR

_spectra

arise below 200 K for the

metallo-protein

solutions and below the

_glass

transition

_temperature

_(situated

_{in the range from 160} to 200 K

_[15])

for the various

_amorphous

_systems

_{investigated.}

_{Incidentally,}

for some of the

latter

_systems,

_{that also possess} a

_{polycrystalline phase,}

we observed that the strain effects were

_completely

removed when the matrices switched to that

_phase,

as a _consequence of the

stress

_relieving

_[15].

For

_protein

_aqueous

solutions,

the

_temperature

of 200 K

_corresponds

to the

_freezing

of the

conformational substates

_{[2, 8]}

which,

very

probably,

is

_consequent

on the

_freezing

of the

hydration

water

_[1,

_4,

_7].

For the

_amorphous

_systems

the

_glass

transition

_corresponds

to the

dynamical

arrest of the structure in a metastable state in which the

_transport

_properties

are

drastically

reduced

_[10].

Moreover,

no

_significant

_changes

were observed as the

_temperature

was lowered

progressively

down to 4 K.

_According

to our

_model,

the

_temperature

_independence

of the

spectral

strain is indicative of the fact that the distributions

_{in gp and A~}

do not

_change

with the

_temperature

below a critical value. Such a value

_corresponds

to the onset of

_dynamical

restrictions in our

_systems,

in

_particular

to the

_suppression

_{of transitions among the} conformational substates in

_{proteins [8]}

and to the frozen-in of all the atomic motions in the

Finally,

we would

_point

out

_that,

_owing

to its

_{high sensitivity}

in

_detecting

microenvironmen-tal fluctuations around

_{paramagnetic probes,}

ESR

_spectroscopy

can be a

_rewarding

tool to

study

the structural and

_dynamical

_properties

of these disordered

systems

especially

as

regards

the energy distribution of their

substrates,

the _{related energy barriers and their}

_phase

transitions.

Acknowledgments.

This work has been

supported by

CNR and MPI

_grants.

Very

useful discussions with Drs. P. Marzola and G.

_Giugliarelli

are

_{acknowledged.}

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