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A study of the structure of highly concentrated phases of DNA by X-ray diffraction

Denys Durand, J. Doucet, F. Livolant

To cite this version:

Denys Durand, J. Doucet, F. Livolant. A study of the structure of highly concentrated phases of DNA by X-ray diffraction. Journal de Physique II, EDP Sciences, 1992, 2 (9), pp.1769-1783.

�10.1051/jp2:1992233�. �jpa-00247765�

Classification

Physics

Abstracts

61.10 64.70 87.15

A study of the structure of highly concentrated phases of DNA

by X-ray diffraction

D. Durand (1.

~),

J. Doucet (1, 3) and F. Livolant

(4)

(1) L-U-R-E-, Laboratoire CNRS-CEA-MEN, Bit. 209D, Universit6 Paris-Sud, 91405

Orsay

Cedex, France

(2) Laboratoire L£on Brillouin

(CEA-CNRS),

CE

Saclay,

91191 Gif-sur-Yvette Cedex, France (3) Laboratoire de

Physique

des Solides, Bit. 510, Universit6 Paris-Sud, 91405

Orsay

Cedex,

France

(4) Centre de

Biologie

Cellulaire (CNRS), 67 _rue Maurice

Giinsbourg,

94205

Ivry-sur-Seine

Cedex, France

(Received18 March 1992, accepted in

final form

5 June 1992)

R4sum4. L'ADN donne _en solution _aqueuse concentr6e

plusieurs phases

cristallines

liquides

et cristallines.

Quand

la concentration _en ADN augmente, on observe la

s6quence

de

phases

suivante _:

isotrope

_-

cholest6rique

_- colonnaire

hexagonale

-

phases

cristallines. Le but de _ce travail £tart d'obtenir _par diffraction des rayons X, des informations structurales sur les

phases

tr~s concentr6es _en

particulier

sur les

phases

cristallines form6es par des

fragments

d'ADN de

500A

_de

longueur.

Nous _avons montr£ que dans la

phase hexagonale

ordonn6e h 2

dimensions, _un orate

longitudinal

entre mot£cules d'ADN voisines s'installe progressivement, et donne lieu h _une

phase hexagonale

ordonn6e h 3 dimensions.

Quand

la concentration _en ADN cr&t _{encore, on} observe _une transition discontinue _{vers une}

phase

de sym6trie

orthorhombique.

Les

pararn~tres

structuraux

caract6ristiques

de _ces diff6rentes

phases

ont 6t£ d6termin6s. Un r£sultat

important

_{est que} le nombre de nuc16otides par ^tour d'h61ice d6croit continoment,

quand

la concentration en ADN augmente,

depuis

10,3 _± 0,1 h la transition

cholest6rique

-

hexagonale, jusqu'h

9±0,1 _pour les dchantillons les

plus

concentr6s par ailleurs, la conformation des

mo16cules d'ADN semble _ne subir _aucun

changement

et reste de type B.

Abstract In aqueous solution, _pure DNA forms

multiple liquid crystalline

and

crystalline phases

whose nature

depends

_on the

polymer

concentration. The

following phase

_sequence is

observed when the DNA concentration increases _:

isotropic

- cholesteric

- columnar

hexag-

onal _-

crystalline phases.

The aim of this work is to obtain structural information about the

highly

concentrated

phases

formed

by 500A long

DNA molecules in

particular

about the

crystalline phases by

_means of

X-ray

diffraction. We show that in the two-dimensional (2D) ordered

hexagonal phase

a

longitudinal

order

progressively

_appears between

neighbouring

DNA helices

leading

continuously to a three-dimensional (3D) ordered hexagonal

phase.

For

higher

concentrations the

specimens undergo

a discontinuous transition towards _an orthorhombic

phase.

The characteristic structural parameters ^{of these different}

phases

have been determined. An

important

result is that the number of nucleotides per helix rum decreases

continuously,

when the DNA concentration increases, from 10.3 ± 0.I at the cholesteric

-

hexagonal

transition down _to 9 _± 0.I without _any apparent

change

of the B conformation of the molecules.

1770 JOURNAL DE PHYSIQUE ^{II N° 9}

1. Introduction.

It has been well established for _some time that in aqueous

solution,

DNA _can form like

numerous

polymers highly

ordered

liquid crystalline phases [1-18]

above _a critical

concentration

depending

on the

length

of the DNA molecules and

nearly

insensitive _to the

supporting electrolyte

concentration

[18].

For

instance,

the critical DNA concentration is about 160

mg/ml

for 500

A long

DNA

fragments

in

physiological

salt conditions

[I1, 12, 18].

The _nature of the different

liquid crystalline phases depends

_on the DNA concentration and the

following phase

_sequence is observed _:

cholesteric

germs columnar

isotropic

_{- or}

- cholesteric

-

hexagonal

phase precholesteric phase phase

organization (for

details _see Refs.

[17, 18]).

In the columnar

hixagonal phase [14, 19]

the DNA molecules _are

unidirectionally aligned

and form _a

hexagonal

network in the

plane perpendicular

to their axis. The order is

only

two- dimensional _: the columns of molecules _are able _to slide

against

each other, and each molecule

is free to rotate around its axis. For

higher

DNA concentrations _more ordered _{structures are}

observed

[14].

Studies of the concentrated

phases

of DNA in vitro _are of interest since the local

concentration of DNA in vivo _can also be

quite large

it _can reach values up ^to 800

mg/ml

_as

estimated

by Kellenberger

et al.

[20]

and

liquid crystal

formation may

possibly play

_some

role in

packaging

DNA in certain systems. ^Various works have evidenced that condensed chromatin _can present ^the same geometry as DNA molecules in

liquid crystals (for

a review

see Ref.

[17]).

For

example,

_a cholesteric

organization

_can be

recognized

in

Dinoflagellate

chromosomes

[21, 22],

in bacterial nucleoids

[23]

and in

special

kinds of mitochondria

[24].

A

hexagonal packing

of DNA molecules is also observed in _some virus

capsids [25, 26].

Studies of DNA

liquid crystals

are also of intrinsic interest in _terms of

liquid crystalline properties

of

polyelectrolytes [27].

DNA is _a

good example

of _a linear

polyelectrolyte,

even of

rigid

rodlike _ones when the DNA

fragments

_are

sufficiently

short

[28-30].

Little information is available about the behaviour of such macromolecules. A strong

polyelectrolyte,

like

DNA,

is surrounded

by

a counterion

layer

which determines the effective

polymer

dimensions

[31].

Thus it is

expected

that the

ordering properties

of DNA will be

strongly

influenced

by

the

polyionic

character of this

system.

Until _{now, a} lot of

experiments espec1ally polarizing

and electron

microscopy

studies

were

performed

on the

liquid crystalline phases

of

DNA,

but much less is known about the structural features _at the molecular scale of these

phases

_as well _as of the _more concentrated

phases.

The aim of the

present

^{work is} to obtain structural information about the very

highly

concentrated

phases

of DNA in

particular

the

crystalline phases

in order to get a better

insight

into the nature and geometry ^{of the} intermolecular interactions. The

appropriate technique

for such _a

study

is

X-ray

diffraction. The results obtained for the

crystalline phases

will be

compared

to those

given by X-ray

measurements on DNA fibers.

2. Material and methods.

2.I DNA PREPARATION. DNA

fragments

with _{a most}

probable length

of 500

A ₍₁₄₆

_base

pairs)

were isolated from nucleosome _cores obtained

by digestion

of calf

thymus

chromatin

with micrococcal nuclease after removal of Hl histones

(for

_a detailed

description

of the

procedure

used to isolate and characterize the DNA

fragments,

see Ref.

[ll]).

Concentrated solutions of DNA

(m

200

mg/ml)

were

prepared

in two

types

^{of saline buffers} :

1)

0.25 M

ammonium _acetate, 10mM sodium

cacodylate

and 0.5mM EDTA

(pH =7); 2)

0.25MNaCl,

0.5mM EDTA and 10mM sodium

cacodylate.

In such conditions the

organization

of the DNA molecules is cholesteric the transition to the columnar

hexagonal phase

_occurs after slow

evaporation

of the _water.

Specimens

of the cholesteric

phase

and of the columnar

hexagonal phase

were introduced into

quartz capillaries

of I _mm diameter. In the latter _case the DNA

fragments

were

flow-aligned

with their axis oriented

parallel

to the

capillary

axis. The _more concentrated

phases

_were obtained

by evaporation

of the _water.

2.2 METHOD.

X-ray

diffraction

experiments

_were

performed using

_a

synchrotron

source

(station D43)

at LURE

(Univ. Paris-Sud).

The

X-ray

beam _was monochromatized

by

_a bent

germanium crystal

^which selected _a

wavelength

of 405

A. X-ray

diffraction

pattems

^{of the}

specimens

_were obtained _on films with the

sample-film

distance fixed at

100,

125 _or 250 _mm.

3. Results and discussion.

X-ray

diffraction

pattems

were recorded at constant temperature

(20 °C)

for _a

great

number of different DNA concentrations from the cholesteric

phase

_up to the _more concentrated state

(typically

about 055

mg/ml

for DNA in ammonium acetate buffer and 840

mg/ml

for DNA in Nacl

solution).

Results _are very similar for the two types ^{of buffer. For}

clarity, only

the characteristic parameters

corresponding

to the ammonium acetate salt will be

given

below.

The

phase

_{sequence as} a function of the concentration is the

following

_:

cholesteric

-

hexagonal

- orthorhombic

3.I THE CHOLESTERIC PHASE. The _texture of the

samples

in the cholestedc

phase

_was

controlled

optically

with _a

polarizing microscope. Typical

_«

fingerprint

_»

_pattems [8, 16, 17]

were observed between crossed circular

polarizers,

with _a cholesteric

pitch

of the order of 2 _~Lm.

For this

phase

the

X-ray

diffraction

pattems

are characterized

by

_a broad and very intense

ring

in the inner part

(Fig. I).

Its diameter increases when the _{water content} is lowered. At

larger

diffraction

angles,

several broad and much less intense

rings

are visible.

They

are

characteristic of the

pseudo-periodicity

of the DNA _structure

along

the helix axis which is due to base

pair stacking [32].

The most intense of these

rings corresponds

to _a

spacing

of 3.36

A

and represents the

periodicity

of the base

pairs.

In the small

angle region,

_{one can} deduce from such a pattem ^{the variation of the scattered}

intensity, I(s),

as a function of _s, where

s =

2 sin 9/A, 2 9

being

the

scattering angle

and A the

wavelength

of the

X-rays. Figure

2 shows the I

(s)

_curves obtained for _two different concentrations in the cholesteric

phase. They

are characterized

by

_an intense

peak appreciably

broader than the

experimental

resolution. A concentration increase _moves the

position

of the maximum of the scattered

intensity

towards

higher

s-values

simultaneously

the width of the

peak

decreases. The value of the maximum

seems to vary very

slowly

with the concentration but _no

quantitative

results _can be obtained

with _our apparatus.

Finally, preliminary experiments

have shown that the behaviour of I

(s)

is very sensitive to the salt concentration _: at fixed DNA concentration a decrease of the

salt concentration results in _a

narrowing

of the

peak.

From the

position (s~ )

of the maximum off

(s)

one can deduce _an

approximate

value of the

mean interhelices

distance,

_a~,

using

the formula _a~

=

I.117/~,

which is _an extension of the

Bragg

law suitable for such _a

liquid crystalline phase (after

Ref.

[33]).

With

increasing

DNA concentration a~ is found to decrease from about 49

A

_{to 32}

A.

1772 JOURNAL DE

PHYSIQUE

II N° 9

*

Fig.

I. Pattem of the cholesteric

phase

recorded at

wavelength

1.405

A.

_The

very strong

ring

in the inner part ^{indicates the existence of} a

short-range

order with _{a mean} interhelices distance a~ » 35.5

A.

_{The most extemal}

ring

represents ^the

periodicity

of the base

pairs

_(d~~

= 3.36

A).

lsl

la-u-) 3

~

- FWHM

0 0.025 0.050 o.075 o-loo

s

k~l

Fig.

2. Scattered

intensity profile

I(s) _{as a} function of s ₌ 2 sin 9/A, obtained

using

_a microden- sitometer in the cholesteric

phase

for two values

Cl

(- -) and

C~(--)

of the DNA concentration, with

C~~C

j. The horizontal bar represents the instrumental resolution

during

this

experiment

; FWHM (full width at half

maximum)

= 0.0012

A-I

_{The maximum at about 0.075}

A-I

_{is due to the DNA}

molecular conformation and is not due to intermolecular interactions like the mean

peak

around 0.025

A-1

The broad

peak

described above is

thought

to reflect _a local ordered arrangement ^{of the} DNA molecules

superimposed

_on the cholesteric order. Robinson et al.

[34]

have observed _a similar

peak

in concentrated solutions of PBLG

~poly-~Gbenzyl-L-glutamate)

and

proposed

that _a local

hexagonal

order

perpendicular

to the molecular axis is present ^{in the} cholesteric

phase.

A

single peak

is also observed in the

scattering

of semi-dilute solutions of

highly charged synthetic [35, 36]

and

biological [37, 38] polyelectrolytes,

and

especially

in

isotropic

solutions of short DNA

fragments (150-160

base

pairs) [30, 39].

For flexible chains _no definite

interpretation

of this

scattering peak

has yet ^been

given

in _terms of intermolecular solution

structure

[40].

It _seems,

however,

that for _« rodlike _»

polyelectrolytes,

^such as DNA

[30]

_or chondroitin sulfate

[38],

there _are indications of _some local

hexagonal alignment

of molecules in the

isotropic phase responsible

for this

scattering peak.

Other

experiments

_{are now necessary} to

completely

elucidate the nature and the

origin

of the

short-range

order observed in this cholesteric

phase.

In

particular,

_a

quantitative study

of

I(s)

_as a function of DNA

concentration,

salt concentration and counterion

type

must be undertaken.

3.2 CHOLESTERIC

- HEXAGONAL TRANSITION. -When the content of water is

decreased,

the

X-ray

small

angle

diffraction

pattems change suddenly

_{: a very}

strong

^and narrow

ring (with

a width

equal

to the instrumental resolution

width)

_appears

superimposed

_on the broad

ring specific

of the cholesteric

phase.

This indicates _a discontinuous transition from the cholesteric to the two-dimensional

hexagonal phase (the justification

for such _a structure will be

given

ⁱⁿ Sect. 3.3.

I).

The diameter of this _narrow

ring provides

the value of the

parameter

^of

the

hexagonal long-range

lateral order:

a~=2/(s/);

at the transition _one finds:

a~ = 31.5

A.

_{In the}

high angle region

the

ring corresponding

to _a

spacing

^{of 3.36}

^A

^remains

unchanged.

Direct measurements of the DNA concentration in _our

samples

have not been

performed, mostly

because of

experimental

difficulties. However, it is

possible

to evaluate it in the

hexagonal

and _more concentrated

phases-

from the

parameters

^{of the} two-dimensional latice

perpendicular

to the axis of the molecules. The concentration C defined _{as :}

C

=

weight

of

DNA/volume

of solution

is

given by

: C

=

MDNA/"h (~)

where

M~~~

is the molecular

weight

of _a base

pair (b.p.),

_« the _area of the unit cell of the two-dimensional lattice and h the axial translation per residue

(commonly

called _« rise

»).

Equation (I)

allows _{us to} obtain _an

approximate

value of the DNA concentration at the cholesteric

-

hexagonal

transition _:

C~

= 380

mg/ml.

Finally,

_we would like _{to stress an}

experimental

observation. When the critical _concen- tration

C~

is

approached,

the

X-ray

pattems ^{of the} cholesteric

phase

^of some

specimens undergo

modifications _: reinforcements appear

simultaneously

on the

ring corresponding

to the

spacing

between two

b.p.

ⁱⁿ the direction of the

capillary,

and the

perpendicular

to this direction on the

ring

in the small

angle region.

It indicates

that, by approaching

the transition towards the

hexagonal phase,

the DNA molecules

align spontaneously

with the cholesteric

pitch

axis

perpendicular

to the

capillary.

Other

experiments

_are

required

to

clarify

this

point.

3.3 THE _{HEXAGONAL PHASES.} All the results

presented

below _concem oriented

specimens

with the DNA molecules

parallel

to the

capillary

axis _: either the

samples

have been

introduced in the

capillary

after transition to the

hexagonal phase

and then

flow-aligned,

_or

they aligned spontaneously

in the

capillary

in the cholesteric state and retain their orientation

during

the transition to the

hexagonal phase.

3.3.1 2D-ordered

phase. Figure

3a shows _a

X-ray

pattem characteristic of the columnar

hexagonal phase just

after the transition. Such _a pattem ^{has been}

previously

described in reference

[14].

The

sharp

arc, with _a strong

equatorial reinforcement,

reveals the

long-range periodic

lateral arrangement ^{of the} DNA molecules. Another very weak reflection is

observed in the

equatorial region (not

visible _on this

picture)

_: the ratio of the

spacings

of both

previous

reflections is I _:

/

_{in unit}

s

(s

=

2 sin

9/A).

When the DNA concentration

increases,

two new weak

equatorial

_{arcs appear} in the ratios I _:

/

_{and I}

:

/

_{with the}

_strong

reflection. The existence of these three weak reflections with

spacing

ratios 1:

/:

1774 JOURNAL DE PHYSIQUE II N° 9

Fig.

3. -a) Pattem of the 2D-ordered

hexagonal phase (Cm395mg/ml)

recorded at

wavelength

A

= 1.405

A.

_{This pattem is} characteristic of DNA in the B form with _a strong meridional _arc at 3.36

A

in its outer part. ^{One observes in the inner} part :I) The

typical

crosslike

intensity

distribution suggesting

a helical _structure. ii) A strong

equatorial

reinforcement of the

sharp

_arc

revealing

the hexagonal lateral order with interhelix distances of 30.9

A.

_{b) Simulation of} the inner part ^{of the}

previous

_pattem

using

the atomic coordinates

given by

Chandrasekaran and Amott [34] for the B form of calf

thymus

DNA and

taking

into account the disorientation of the helices axis with respect to the

capillary

axis.

/

:

/

~gests

^a two-dimensional

hexagonal

lattice. We have checked that the absence of

the _{« :} 4

»

reflection,

which is

normally

observed for such _a

lattice,

is due to its very weak molecular _structure factor. It is recalled that _at the cholesteric

-

hexagonal transition,

the

parameter

_a~ of the

hexagonal

lattice is found to be

equal

to 31.5

A

_then

a decrease of a~ is observed when the water content is lowered.

The inner part ^of

figure

3a also

displays regions

of strong

intensity forming

_{a cross pattem.}

Such features _are characteristic of the helical structure of the DNA molecule _: the scattered

intensity

is located _on

layers corresponding

to the helix

pitch periodicity

P

[41].

Just after the cholesteric

-

hexagonal

transition _no

Bragg

reflections _are observed _on these

layers,

which is indicative of the absence of

longitudinal

order between

neighboring

DNA molecules.

Finally,

a

strong

^diffuse arc near the

meridian,

located at 3.36

A,

is

present

^{in the} outer part ^{of the} pattem. ^This arc is

usually

observed for DNA chains in the B conformation and reveals the

step-like

structure of the helix with _a rise of h

= 3.36

A

_{and the base}

pairs nearly perpendicular

to the helix axis.

It is

possible

to simulate

numerically

such _a

pattem using

the atomic coordinates

given by

Chandrasekaran and Amott

[42]

for the B conformation of calf

thymus

DNA

(the

same

coordinates have been used for the other simulations of the B conformation

presented

in this

paper).

The result is illustrated in

figure

3b where _we have taken into _account the disorientation of the helices axis with

respect

to the

capillary

axis. In

fact,

the DNA molecules

are not

rigorously parallel

to the

capillary

and we have shown that _a

good description

of the diffuse _arcs observed in

figure

3a is obtained if _{we assume a} Gaussian distribution of

orientation with _a standard deviation of 10°. The main interest of the

comparison

between the

experimental (Fig. 3a)

and simulated

(Fig. 3b) pattems

^{results from the fact that the}

simulations include two

parameters:

^{the interhelix distance} _a~ ^{and the helix}

pitch

P,

and in

particular

allows the determination of P in this

liquid crystalline hexagonal phase.

Just after the transition from cholesteric to

hexagonal,

P is found to be

equal

to 34.6 _± 0.3

A

which

corresponds

to 10.3 ±1 nudeotides per helix tum. This

point

will be discussed in details in section 4,1.

3.3.2 Evolution towards the 3D-ordered

phase.-At increasing

DNA

concentration,

the

inner part ^{of the}

X-ray

_pattems

changes

and becomes _more structured. The diffuse

intensity

observed

along

the first

layer

condenses

progressively

into _a

sharp

_arc

(Fig.4a)

which becomes _more intense with

decreasing

water content. This

Bragg

reflection is observable when the

hexagonal parameter

a~ becomes smaller than about

29.5A.

_For

_higher

_DNA

concentrations the _same type ^of

sharp

_{arc occurs}

along

the second

layer

and

finally along

the third _one

(Fig. 4b).

We _can conclude that a

longitudinal

^order

progressively

_appears ^between

neighbouring

DNA helices

leading continuously

to a 3D-ordered structure. The three-

dimensional lattice _seems to be well established when the intermolecular distance has reached

a value close _to 25.5

A.

'

~ ~$

-

-~ ~~

~6

,~~

~~-'

' _'

~ ~-

~~-

,

"Ii'

1776 JOURNAL DE PHYSIQUE II N° 9

Fig.

5. Freeze-fracture-etch electron microscopy of the concentrated

phase

of DNA

prepared

in 0.25 M ammonium acetate, 0.5 mM EDTA and 10 mM sodium cacodylate (pH 7). The samples, with 109b

glycerine

added, _were

deposited

onto copper ^{discs and} allowed to concentrate to _a thick

consistency. Samples

_were then

quickly

frozen in

liquid

freon 22 and

immediately

transferred into

liquid nitrogen.

Fractures _were made at 110 °C under _a 2 _x 10T~ _{ton vacuum,} etched at 100 °C for 3 _mn,

platinum-carbon

shadowed _{at an}

angle

of 45° and carbon coated (BaJzers BAF 400 T). After

washing

in distilled _water,

replicas

_were observed in _a 201

Philips

electron

microscope

at 40 kV

accelerating voltage

(x 50 000).

number of domains with different orientations of the molecules

increases, giving

rise _to crinkled

paper-like

textures

(Fig. 5).

3.3.3 Structure

of

the

3D-hexagonal phase.

All the

X-ray

_pattems obtained after the

emergence of the

longitudinal

order fit _a

hexagonal

lattice. The

Bragg

reflections _can be

unambiguously

indexed

taking

_a

hexagonal

unit cell with three molecules located at

(0, 0, 0), (1/3, 2/3, z)

and

(2/3, 1/3, z). Figure

6a shows the arrangement ^{of the molecules in the unit} cell. Molecules mi are at the _same

height

molecules m~ and m~ are

displaced

relative to the molecules mi

by

the fraction _z or z of the helix

pitch, P,

in the _c direction of the helix axis

[43].

The parameter

A~

^of the unit cell is

equal

to a~

/

_where

a~ represents the intermolecular distance _;

A~

decreases with the _content of _water. It is also

possible

to deduce from the

X-ray pattems

the value of the helix

periodicity along

the

c-axis,

I.e. the helix

pitch

P. Like

A~,

^P decreases with the water content. More details about this

point

_are

given

in section 4.I. One remarks that the space lattice used _to index the

Bragg

reflections is defined from the three vectors _a, b and _c, where _a and b _are related _to the two-dimensional

hexagonal

lattice and _c is

parallel

_to the helix axis with

(c

= P. If the number of residues per ^tum is not

integral

there is _no translation

periodicity along

the _c direction and _c is not

truly

_a lattice

parameter.

^In this context additional

Bragg

reflections should

theoretically

_appear outside the main

layers corresponding

to the helix

periodicity

P.

However,

_no such reflections _are

mj

' I

a

I

, a

Jlfj

'

ml

_,

a) b)

Fig. I. Arrangement

of the molecules in the unit cell _:

projection

down the helix axis. a)

Hexagonal packing

(a

= b

=

A

~)

; molecules m~ and m~ are

displaced

relative to the molecules mi

by

^the fraction

z or z of the helix

pitch

in the direction

perpendicular

to the

diagram,

with _z

» 1/6. b) Orthorhombic

packing

_; both molecules mj and m2 of the unit cell have _a relative

displacement

z'- 0.30 in the

direction of the helix axis.

observed in _our

X-ray

_pattems, and _we have checked that the calculation of their

intensity

in the B forms

yields negligeable intensity

values.

Consequently

it is

acceptable

to consider the

DNA helix _as continuous and to define the unit cell from the

(a, b, c)

vectors.

The value of _{z can} be deduced from the

comparison

between observed and calculated

intensities of the

Braggs

reflections. We find that _z is close to

1/6

and remains

nearly unchanged

when the DNA concentration increases. Such _a

hexagonal

arrangement ^{of three} molecules with _z =1/6 is also found in DNA fibers in the B conformation with various counterions

(Li, Na,

K _or

Rb)

at a

high

relative

humidity (r.h.

_~ 90 fb

about) [44, 45].

For

example,

in NaDNA fibers _at 92 fb r.h. the

parameter A~

is found to be of the order of 45

A,

which

yields

_an intermolecular distance _a~ »26

A

_{similar to those observed in}

our 3D-

ordered

phase (cf.

Sect.

3.3.2).

However,

the

analogy

^between DNA fibers and concentrated

phases

is not

complete

: in this range of interhelix distances the fibers _are often not

fully crystalline (so

called

«

semicrystalline »)

and

present

a

high degree

of disorder

[46].

For

instance,

various authors

[45, 47, 48]

have noted the presence of

strong

continuous streaks

along

the

layer

lines

superimposed

_on the

crystalline

reflections which _are sometimes very weak. This indicates

large

random

displacements

of the molecules from

regular positions along

the _c direction

(these displacements

_can reach values of the order of

c).

In other _cases

[44], only

the

Bragg

reflections _on the first and third

layer

lines _are

completely

absent and

replaced by

diffuse

scattering.

This _means that the molecules tend to be

randomly

translated

by

±1/2 _c in the direction of the helices.

Finally,

_some fibers _are formed of such small

crystallites

that diffraction

broadening

of reflections _occurs. We have _never observed such behaviour _; for a~ w 25.5

A,

_the

_Bragg

reflections _are

always sharp

and well

defined,

at least for the three

first

layer

lines. Three

points

must be

emphasized

_:

I)

The width of the

Bragg

reflections

(equal

to the instrumental resolution width

FWHM

=

0.0025

A-I) _implies

_{that the domains of the}

crystalline phase

are greater ^than

400A.

1778 JOURNAL DE

PHYSIQUE

II N° 9

it)

The absence of

Bragg

reflections _on the fifth

layer

line and the _{outer ones}

(the

fourth

layer

is

always missing

for

B-DNA)

indicates that the

longitudinal

order is not

perfect

and that

the molecules exhibit small

displacements

from their average

positions.

The

amplitude

Az of these

displacements

_can be estimated

by introducing

in the

Bragg intensity analysis

an

« extra _»

Debye-Waller

factor :

exp(- Bs)/2)

where s~ is the component ^{of the}

scattering

vector s

along

the c-axis and B

=

8 ar

~(Az)~/3.

The value of B

m

300,

which accounts for _our

pattems,

leads to Az

m 3.4

A,

I.e.

m

(1/10)

_c.

iii) Only

_one other kind of disorder is

present

ⁱⁿ our concentrated

phases.

The

intensity analysis

of the

Bragg

reflections show that the two

following arrangements

of the molecules

(0, 0, 0) (1/3, 2/3, z) (2/3, 1/3, z)

and

(0, 0, 0) (1/3, 2/3, z) (2/3, 1/3, z)

are

equiprobable,

and each unit cell _can

independently adopt

^{either of them.}

Finally,

^it can be

suggested

that the

higher degree

^{of order in the}

phases

studied here with respect to the conventional fibers is related _to the short

length

of the DNA

fragments (m

500

A)

_{used in}

our

study. However,

it is also

possible

^that these different behaviours _are

due to the differences between the

preparation methods;

in

particular,

the fibers _are

generally

submitted _{to a} mechanical _stress

[49].

3.4 THE ORTHORHOMBIC PHASE. When the intermolecular distance reaches _a value close

to 23.7

A _(C

m 670

mg/ml),

new

sharp

_{arcs appear} in the inner part ^{of the}

X-ray

_patterns

superimposed

on the first set of

Bragg

reflections characteristic of the

hexagonal phase.

These

new

Bragg

reflections cannot be indexed in _a

hexagonal

lattice.

By increasing

the DNA

concentration,

their

intensity

increases with _a simultaneous

vanishing

of the first _set of reflections

(Fig. 7).

This behaviour indicates _a discontinuous transition from the 3D-

hexagonal phase

to another

crystalline phase

^{of different} symmetry.

Fig. 7. Pattem of the orthorhombic phase (C

- 775

mg/ml)

recorded _at wavelength A ₌ 1.405 A. _The indexation of the Bragg reflections leads _to the determination of the

crystallographic

parameters _;

a = 23.60

A.

_b

= 35.65

A

_and

c = 32. 83

A.

The new

Bragg

reflections _can be indexed

unambiguously

ⁱⁿ an orthorhombic lattice with two molecules _per unit cell located at

(0, 0, 0)

and

(1/2, 1/2, z').

The arrangement ^{of the} molecules in the orthorhombic unit cell is shown in

figure

6b. The

longitudinal distance, z', separating

the _two molecules of the unit cell is found _to be close to 0.30 from the

Bragg

intensity analysis

and _{seems to} be insensitive _to the DNA concentration. Similar values

(z'

= 1/3 _or z'

=

IN)

have been obtained in LiDNA fibers in B conformation at low relative

humidity (r.h.

« 90

fb) [45].

Just after the

hexagonal

_- orthorhombic transition

(C

m 690

mg/ml),

the parameters ^{of the} orthorhombic lattice _{are a}

=

24.09

A,

_b

=

39.33

A

_and

c ₌ 33.50

A.

_{When the DNA}

concentration

rises,

the three parameters ^decrease

regularly

down _{to a=}

20.77A,

b ₌ 29.72

A

_and

c = 30.20

A

_{measured for the driest}

specimens (C

_m 055

mg/ml)

obtained

by complete evaporation

of the water at room

humidity.

^The distorsion from the

hexagonal

lattice- which

corresponds

to bla

=

/-

_{increases when the DNA} concentration rises _;

bla decreases down to 1.43 for the driest

samples.

Finally

_one must remark in

figure

7 that the outer

part

of the

X-ray pattems

is still

unchanged

with

just

_one diffuse _arc located _at 3.36

A.

_{As mentioned above}

_(Sect.

_3.3.

_I)

_such

a

scattering diagram

is characteristic of DNA in B conformation with _a rise h

=

3.36

A

_and

indicates that the tilt between base

pair

and helix axis remains small _{even as} the DNA concentration is

greatly

increased.

We have summarized the main results in table I which

gives

the

phase

_{sequence as a}

function of the DNA concentration

together

with the structural parameters ^{of the different}

phases

for the ammonium acetate salt. Parameters for the Nacl salt _are very similar.

Table I.

Sequence ofthe different liquid crystalline

and

crystalline phases

with characteristic parameters ^determined

for

the ammonium acetate

buffer.

Isotropic

Cholesteric

Hexagonal

Orthorhombic

2D

progressive

3D

longitudinal ordering

C(mg/ml) (*)

380 670 1055

mean interhelices intermolecular distance a~ lattice parameters

distance a~

49

A

₃₂

A

_31.5

A

₂₉

A

_23.7

A

a = 24.09

A

a ₌ 20.77

A

b

= 39.33

A

_b

= 29.72

A

helix

pitch

P

A

_30.2

A

(*) The value of the critical concentration at the

isotropic

- cholesteric transition is taken from Strzelecka et al. [ll, 12, 18]. The others C values _are calculated from

equation

(1).

4. Discussion.

4.I HELICAL _PiTCH. -The first comment _concems the variation of the number of

nucleotides per helix _tum.

In the 2D-ordered

hexagonal phase

the

pitch

value P is deduced from the

position

of the three first diffuse

layer

lines corrected for disorientation effects. This correction is

performed

1780 JOURNAL DE

PHYSIQUE

II N° 9

by comparing experimental pattems

with simulated _ones. For the 3D-ordered

phases,

P is

directly

obtained from the

Bragg

reflection

positions (P

_=c,

«pseudo»

lattice

parameter along

the direction of the

helices,

_see Sect.

3.33).

Figure

8 shows the variation of

P(j£where

^the concentration C is estimated

by

the formula: C

=

M~~~/«h

with _«

=

al

_{3/2 in the}

_{hexagonal phase}

_and

« = ab/2 in the

orthorhombic _one.

By increasing

the DNA

concentration,

the helix

pitch

P _seems to decrease

regularly,

within the measurement accuracy

(w0.3A),

from 34.6

A

_at the choles- teric-

hexagonal

transition down _to 30.2

A

_{for the driest}

specimens.

Since the axial translation per residue h remains constant at all concentrations

(h

=

3.36

A),

it follows that the number

of

nucleotides _per helix turn, n =

P/h,

decreases

continuously JFom

10.3 _± 0.I down _to 9.0 _± 0. I

bp/tum

when the water evaporates. ^{The DNA helix is}

slightly

underwound

by

0.3

bp/tum

in the

2D-hexagonal (liquid crystalline) phase

_as

compared

to the structure

generally

found in fibers

(10 bp/tum)

and

progressively

coils with

decreasing

water content. It

is worth

noting

that the number of residues per tum

depends solely

_on the number of

H~O

molecules and _seems insensitive to the

type

^of structure 2D-ordered

hexagonal,

3D- ordered

hexagonal

_or orthorhombic. The value found for _n in dilute

(isotropic)

solution is about 10.5

bp/tum [50, 51],

I.e.

slightly higher

than the value measured in the

hexagonal

columnar

phase.

p(A)

_Hexagonal Ofihothombic n

35 34

,

' j~

33

,,

, ,

3~ ,,

, ,

~~

,,

, ,

~~

,, 9

800

C(mg/ml)

Fig.

8. Variation of the helix

pitch

P (or the number of nucleotides per helix tum, n) as a function of the DNA concentration C in the

hexagonal

and orthorhombic

phases.

C is calculated from the

expression

_: C

=

M~~~/«d~~,

^where « is the _area of the unit cell in the

plane perpendicular

to the helix axis and

d~~(=

^3.36

A)

the distance between _two base

pairs.

The full line _{acts as a} visual

guide.

4.2 CONFORMATION. The second

point

_concems the conformation of the DNA molecules.

It is obvious that _our

X-ray _pattems

do not exhibit _a sufficient number of

Bragg

reflections to allow _a

complete

structural

analysis

of the DNA molecule. It is

possible

however _to simulate the

X-ray

pattems

by using

the atom coordinates

corresponding

to the different

potential

conformations

(A,

B _or

C).

Such simulations show that, _even for the

higher

concentrations

(1055mg/ml

for DNA in ammonium acetate buffer and

840mg/ml

for DNA in Nacl

solution),

the DNA structure in the A and C forms do not account for the observed

X-ray

pattems. ^In

particular,

in their outer part,

just

_one

strong

^diffuse arc at 3.36

A

_{is detected at}

all concentrations. On the other hand the _use of the coordinates of the B form

provides

a

satisfactory description

of _our

pattems.

It is of interest _to evaluate the number of

H~O

molecules per

nucleotide,

_n~, for the driest

specimens.

It is easy ^to show that n~ is

given by

the

following expression

_:

[ ~ ~ Jll~

~ ~

l~~~

~~

~~w~w~~~~

^~~~~~~~ _'llDNA ~~

where

M~~~, M~

and

M~

represent ^{the molecular}

weight

of _a DNA base

pair, H~O

and added

salt, respectively

_{; m~} and m~~~ are the added salt and DNA

molarities, respectively,

of the

initial solution before water

evaporation

_{v~p~~, v~ and v~ are} the

partial specific

volumes. The

value of v~p~~ ⁱⁿ

highly

concentrated solutions is not

accurately

known. From

density

measurements

performed by

Franklin _et al.

[47]

_we have estimated it for the driest

samples

to

about v~p~~

=0.60cm~/g.

_The values of _{v~ are} extracted from reference

[52]. Finally,

equation (2) yields

for the

higher

concentrations _n~

= 5 ± for the ammonium acetate buffer and n~ =

10.5 _± for the Nacl solution.

In

conclusion,

_no

change

of conformation is observed in _our

X-ray _pattems

when the _water

content

decreases,

for the two

types

^{of counterion}

NH(

_or Na+ The DNA helix _seems to

remain in _a B

type form,

_even for the driest

specimens

which contain

only

5 _or

10.SH~O

molecules per nucleotide in the _case of ammonium acetate _or Nacl salts

respectively.

The

comparison

with DNA fibers cannot be

performed

in the _case of the

NH(

counterion because _no

experimental

results _are available for

NH~DNA

fibers.

However,

a lot of studies

performed

_on NaDNA fibers have shown that reduced

humidity

leads to _a transition from the B form to the C _or A form

depending

_on the ionic

strength [41] (for

a review _see Ref.

[32]

p. 368 and Ref.

[53] ).

^It seems that for added salt content,

comparable

to the _one used in _our

specimens (0.4

Nacl per

nucleotide),

the B

- A transition starts from _a relative

humidity

of the order of 90 fb which

corresponds

to about 15

H~O

molecules per nucleotide

[53, 54].

The

mechanical _stress

generally applied

_on fibers is

possibly

the

origin

of this different behaviour of the NaDNA fibers with respect to our concentrated

phases.

5. Conclusion.

Up

to now the

X-ray

structure

investigations

of DNA have been

performed

in order _to

determine the molecular conformations at the atomic scale. Such studies either need

oligonucleotide crystals

or DNA

fibers,

I.e.

samples

with

extremely high

DNA concentrations.

Surprisingly only

little attention has been

paid

to the intemolecular interactions in

spite

of their

possible key

role in _some

biological

_processes.

We have tried to characterize

by X-ray

diffraction the behaviour of

500A _long

_DNA

molecules in aqueous concentrated solutions. It appears

that, by increasing

the DNA

concentration,

the solutions transform from cholesteric

phases

_up to three-dimensional ordered

phases

not

quite

identical _to those

given by

conventional fibers. This transformation is _a

gradual

_one with _a

progressive

emergence of the order between molecules _; cholesteric

ordering

then columnar

hexagonal ordering (I,e.

two-dimensional lateral

order),

followed

by

a

longitudinal ordering

between

neighbouring

DNA molecules which

gives

rise _{to a} three- dimensional order

(hexagonal

and

finally

orthorhombic for the driest

specimens).

During

this transformation the distance between molecules decreases when their _concen- tration increases

simultaneously

the number of base

pairs

per helix tum varies from 10.3 down _to 9 for the most concentrated

phases.

It is remarkable that

during

these

changes

both the overall conformation

(B conformation)

and the rise

(3.36 A)

remain

unchanged.

We have shown that

X-ray

diffraction

experiments performed

_on the various concentrated DNA

phases

lead _to

interesting

and valuable information which _are

quite complementary

_to

those derived from

microscopy

observations.

1782 JOURNAL DE PHYSIQUE II N° 9

Acknowledgments.

We would like to thank Prof. J. P. Benoit for his

helpful advice,

Dr.

G.Jannink,

Dr.

G. Albiser and Prof. S. Premilat for fruitful

discussions,

and W.

Shepard

for

revising

the

English Manuschpt.

This research _was

supported by

_grants from INSERM

(n° 910905)

and from Association pour la Recherche _sur le Cancer

(ARC).

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[43] For _reason of

simplicity

_we have used _an

hexagonal

lattice to describe the 3D-ordered

phase

which

follows the

2D-hexagonal

_one. However, the real

crystallographic

_symmetry is

trigonal

since it is characterized

by

_a 3-fold axis and not

by

_a 6-fold _one (see

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