Con inemen , spa ial co ela ions and lexibili y in he
mel ing ansi ion o DNA
Uni e si y o Bu gos and Ins i u Laue-Lange in
Ad i´an Gonz´alez Rod ´ıguez
Ad iso s: And ew Wildes and San iago Cues a L´opez
Decembe 20, 2017
2
Con en s
1 In oduc ion 5
2 Me hods and heo y 10
2.1 Samplep epa a ion................................ 10
2.1.1 P oduc ion o o ien ed DNA ibe s . . . . . . . . . . . . . . . . . . . 10
2.1.2 Widom-sequence ............................. 15
2.2 Di e en ial scanning calo ime y . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 The modynamical p inciples . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 DSC echnique .............................. 17
2.2.3 Ins umen s................................ 18
2.2.4 Expe imen al p o ocol . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.5 Da aanalysis ............................... 21
2.3 In oduc ion o sca e ing heo y . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Basic p inciples o a sca e ing expe imen . . . . . . . . . . . . . . . 23
1
2.3.2 Sca e ing by a single ixed a om . . . . . . . . . . . . . . . . . . . . 26
2.3.3 Sca e ing om an assembly o a oms . . . . . . . . . . . . . . . . . . 27
2.3.4 Fibe Di ac ion ............................. 28
2.3.5 Small angle sca e ing . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Di ac ionIns umen s.............................. 36
2.4.1 Neu on di ac ome e s . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.2 X- ayde ices ............................... 41
2.5 Da a collec ion and educ ion . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.5.1 Wide angle neu on sca e ing . . . . . . . . . . . . . . . . . . . . . . 45
2.5.2 Small angle neu on sca e ing . . . . . . . . . . . . . . . . . . . . . . 51
2.5.3 Small angle X- ay sca e ing . . . . . . . . . . . . . . . . . . . . . . . 53
3 Li e a u e e iew 54
3.1 P e ious di ac ion s udies in ibe DNA . . . . . . . . . . . . . . . . . . . . 54
3.1.1 Con o ma ion o humidi ied ibe s. A and B o m DNA as seen by
neu onsca e ing ............................ 55
3.1.2 Con o ma ion o DNA ibe s subme ged in e hanol solu ions. The B-
o-A ansi ion .............................. 58
3.1.3 DNA ibe s subme ged in PEG solu ions. The osmo ic p essu e me hod
59
3.2 Con inemen o DNA............................... 60
2
3.3 Mel ing ansi ion................................. 63
3.3.1 E ec o he con inemen o DNA in he mel ing ansi ion . . . . . . 64
3.3.2 E ec o PEG in he mel ing ansi ion . . . . . . . . . . . . . . . . . 66
3.3.3 E ec o e hanol in he mel ing ansi ion . . . . . . . . . . . . . . . 67
3.4 Models o DNA and he mel ing ansi ion . . . . . . . . . . . . . . . . . . . 69
3.4.1 Pey a d-Bishop-Dauxois model . . . . . . . . . . . . . . . . . . . . . 69
3.4.2 K a ky-Po od model . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 S udy o subme ged DNA ibe s 76
4.1 S uc u al cha ac e iza ion wi h X- ays . . . . . . . . . . . . . . . . . . . . . 76
4.2 Room empe a u e s udy wi h neu ons . . . . . . . . . . . . . . . . . . . . . 79
4.2.1 Fibe s subme ged in PEG solu ions . . . . . . . . . . . . . . . . . . . 79
4.2.2 Fibe s subme ged in e hanol solu ions . . . . . . . . . . . . . . . . . . 83
4.3 Mel ing ansi ion s udied by calo ime y . . . . . . . . . . . . . . . . . . . . 93
4.3.1 Fibe s subme ged in PEG solu ions . . . . . . . . . . . . . . . . . . . 93
4.3.2 Fibe s subme ged in e hanol . . . . . . . . . . . . . . . . . . . . . . . 100
4.4 S udy o he mel ing ansi ion wi h neu on sca e ing . . . . . . . . . . . . 105
4.4.1 Fibe s subme ged in PEG . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.2 Fibe s subme ged in e hanol . . . . . . . . . . . . . . . . . . . . . . . 120
5 Widom-601 in es iga ed by SAS 129
3

5.1 Room empe a u e s udy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.2 Tempe a u e-dependen s udy . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.2.1 SANS ................................... 147
5.2.2 SAXS ................................... 152
5.2.3 Discussion................................. 156
6 Conclusions 159
4
Chap e 1
In oduc ion
Deoxy ibonucleic acid (DNA) is a mac omolecule which ca ies he gene ic in o ma ion es-
sen ial o e e y li ing o ganism. I is a biopolyme buil by he epe i ion o monome s
called nucleo ides. Each nucleo ide consis s o a phospha e g oup, a suga g oup and a ni-
ogen base. The phospha e and suga g oups al e na e in sequence and o m a linea chain.
Two o hese chains a e linked by hyd ogen bonds be ween ni ogen bases gene a ing he
amous double helix. Each couple o linked ni ogenous bases is called a base pai .
The mel ing ansi ion ( he mally induced helix- o-coil ansi ion) o DNA is a i s o de
phase ansi ion induced in DNA molecules by hea . In such a p ocess he hyd ogen bonds
be ween base pai s b eak as he empe a u e is inc eased. Local openings o consecu i e base
pai s can occu a a empe a u e below he ansi ion esul ing in zones o open base pai s
(called dena u a ion bubbles) which a e su ounded by closed zones in which he double helix
is in ac . As he empe a u e is aised and mo e base pai s b eak, he open zones expand o
la ge sizes and e en ually he wo s ands o he double helix sepa a e. Fig. 1.1 illus a es
he p ocess.
The mel ing ansi ion o his li e-essen ial molecule has been hea ily s udied o lea n
abou he in amolecula in e ac ions, he impac o he base pai sequence in DNA unwind-
ing and he e ec o he sol en in DNA s abili y [2, 3, 4]. A be e unde s anding o he
5
Figu e 1.1: DNA openings as Tinc eases. Adap ed om [1].
ansi ion could ha e an immedia e impac in applica ions such as high esolu ion mel ing
analysis o polyme ase chain eac ions, which a e widely used in bio-labs a ound he wo ld
[5, 6]. Howe e , he mel ing o DNA i sel is in e es ing o s udy om a heo e ical poin o
iew since i is, essen ially, a phase ansi ion in a one dimensional sys em.
In his hesis, a be e unde s anding o he mel ing ansi ion o DNA and i s e ec s
in he unc ionali y o he molecule is a emp ed by ollowing wo a enues: i) he s udy
o highly o ien ed DNA ibe s wi h wide angle di ac ion echniques and calo ime y. ii)
he in es iga ion o a sho chain, biologically ele an , sequence wi h small angle sca e ing
echniques (SAS).
Highly o ien ed DNA ibe s
Expe imen ally, he ansi ion has been s udied wi h echniques ha ei he p obe he bulk
sample, like calo ime y, UV-Vis abso p ion and ci cula dich oism spec oscopy, o local-
ized poin s on he molecule, like luo escence spec oscopy. The spa ial s uc u e o DNA
molecules is no accessible using hese echniques, and he e o e, he dis ibu ion o open
and closed base pai s du ing he phase ansi ion can no be de e mined. Knowledge o
6
he spa ial co ela ions and how hey e ol e wi h empe a u e is necessa y o a comple e
unde s anding o he ansi ion.
Sca e ing echniques allow o access s uc u al in o ma ion and hus he spa ial co e-
la ions wi hin he molecule. Such in o ma ion is mo e easily accessible when he sample has
long- ange o de , which gi es ise o B agg peaks. DNA ibe s, in which he molecules a e
coaligned and a e close packed, ha e su icien long- ange o de o exhibi B agg peaks in
hei di ac ion pa e ns. By s udying hese peaks, he in o ma ion o in e es is collec ed
in a measu emen which is only weakly pe u bed by sample impe ec ions and incohe en
con ibu ions o he sca e ing.
The mel ing ansi ion o o ien ed DNA ibe s equilib a ed wi h a humid a mosphe e has
been p e iously s udied [7, 8] using neu on sca e ing. The esul s ha e been success ully
modeled wi h he mesoscopic s a is ical-mechanical Pey a d-Bishop-Dauxois (PBD) model
[9]. The e o e, hese wo ks we e able o access he spa ial co ela ions o he molecules
du ing he ansi ion and ein o ce he alidi y o he PBD model, which is al eady widely
used o desc ibe complex DNA dena u a ion cu es. Du ing he analysis, he ques ion o
whe he he con inemen o he DNA molecules in he ibe s has an e ec on he ansi ion
a ose. The es ic ed deg ees o spa ial eedom due o he con inemen o he molecules
could a guably ha e an impac on he in e p e a ion o he esul s since he model does no
accoun o in e molecula in e ac ions.
In o de o es he e ec s o he molecula con inemen , a new expe imen was designed
in which he ibe s we e subme ged in a solu ion wi h a gi en osmo ic p essu e. The osmo ic
p essu e me hod has been epo ed in nume ous a icles [10, 11]. I consis s o subme ging he
DNA ibe s in a saline solu ion wi h a high-molecula -weigh polyme such as polye hylene
glycol (PEG). I he PEG does no pene a e he DNA ibe s, he osmo ic p essu e ac s
analogously o a mechanical and pe meable pis on p e en ing DNA om dissol ing, hus
p ese ing he long- ange o de , while allowing wa e and sal o be exchanged be ween he
ibe s and he solu ion. X- ay di ac ion has p o ed ha ibe s equilib a ed wi h hese kind
o solu ions show a well-de ined in e axial dis ance be ween molecules, which inc eases wi h
7
Figu e 2.3: Pic u e o he inal ilms p oduced by he we spinning appa a us.
Subme ged ibe s
Na−and Li-DNA o ien ed ibe s subme ged in PEG solu ions made wi h 2H2O(hea y
wa e ) and e hanol/2H2Omix u es ha e been in es iga ed in his wo k using calo ime y,
X- ay and neu on sca e ing. Using hea y wa e is an ad an age when in es iga ing samples
wi h neu ons because i minimizes he incohe en sca e ing [12]. 2H2Owas used in he
samples s udied wi h o he echniques o consis ency. Since he chemical p ope ies o hea y
wa e and no mal wa e a e almos iden ical he ange o applica ion o he esul s is no
hinde ed by he use o hea y wa e .
The PEG solu ions we e made by dissol ing he speci ic amoun o PEG in a bu e made
wi h 2H2Owi h 10 mM T is ( is(hyd oxyme hyl)aminome hane), 1 mM EDTA (e hylene-
diamine e aace ic acid). Unless men ioned o he wise he solu ions con ained 0.1M NaCl
o samples made wi h Na-DNA and 0.1M LiCl o samples made wi h Li-DNA. The PEG
solu ions will be iden i ied by he amoun o PEG in weigh pe cen .
The e hanol/wa e mix u es we e p epa ed wi h he same bu e and will be iden i ied
by he amoun o e hanol in olume pe cen . Also, o he sake o simplici y he mix u es
will be add essed as e hanol solu ions. Fo he neu on samples ully deu e a ed e hanol was
used (e hanol-d6), o he o he echniques p o ona ed e hanol was used due o he cos o
14

e hanol-d6.
A speci ic sample o neu on sca e ing consis ed o a numbe o ilms wi h a o al DNA
mass close o 0.6g ha we e conce ina olded and s acked wi h hei axes coaligned. The
dimensions o he inal sample we e app oxima ely 2.5×2.5×0.2cm3. The DNA was placed
in a niobium en elope which in u n was placed inside an aluminum casse e. The niobium is
necessa y since he DNA can eac chemically wi h aluminum a high empe a u es. A ound
0.8ml o a gi en PEG o e hanol solu ion was degassed and placed in he casse e so he DNA
was o ally subme ged. Then he casse e was sc ewed closed and sealed wi h a lead-wi e
gaske .
2.1.2 Widom-sequence
The sho DNA sequence chosen o he small angle sca e ing expe imen s desc ibed in his
documen is he so called Widom-601 sequence. I has g ea a ini y o bind a ound p o ein
his one oc ame s and i is called a s ong posi ioning sequence. I was disco e ed by Lowa y
and Widom [19]. I has 145 base pai s wi h a o al leng h o a ound 485 ˚
A. Fig. 2.4 p esen s
he p ima y s uc u e o he sequence wi h he binding si e highligh ed in ed.
The a i icial DNA needed o he expe imen s was syn hesized by collabo a o s in he
ICCRAM a he uni e si y o Bu gos, Spain (Ma a Ma y Roda, Lo ena Rome o San ac eu),
and in he INMG a he uni e si y o Lyon, F ance (Ramachand an Boopa hi, Dimi a
Angelo ). The exac p o ocol di e ed sligh ly om one lab o ano he bu a gene al summa y
Figu e 2.4: The 145 base-pai sequence co esponding o he NCP-601 nucleosome in es i-
ga ed in [13] also known as Widom-601 sequence. The agmen highligh ed in ed is he
s ong posi ioning elemen cha ac e is ic o his sequence.
15
is p esen ed below.
The s a ing ma e ial was a solu ion o plasmid pGEM-3z/601 pu chased om Addgene,
which con ains he Widom sequence. A polyme ase chain eac ion (PCR) was pe o med
wi h he p ope p ime s in o de o duplica e he Widom sequence. A e enough dupli-
ca ions, he esul was p ocessed wi h a pu i ica ion column ki (Gene Ma ix Basic) o
sepa a ing he Widom sequences om he emanen plasmid. PCR alone is no an op imal
me hod o ob ain he quan i ies o DNA needed o neu on sca e ing (in he o de o he
mg) bu he amoun o widom-DNA ou o he i s PCR allowed o use ano he mul iplica-
ion echnique, called compe en cells. In cell biology, compe ence is de ined as he abili y o
a cell o ake ex acellula DNA and inco po a e i in i s i al cycle, including ep oduc ion.
Thus, o ep oducing a gi en sequence which has been assimila ed by a cell cul u e i is
su icien o allow he cell cul u e o g ow. Cells will no assimila e a sho sequence such
as he Widom-601 in his way bu hey can assimila e and mul iply a plasmid including
he Widom sequence. The e o e he Widom DNA om he i s PCR and pu i ica ion was
used in a liga ion p ocess wi h ligase T4 in which plasmids pGEM/3z-601 we e e o med.
The plasmids we e in oduced in compe en cells DH5α. A e adequa e g owing ime he
plasmids we e ex ac ed om he cells by GeneJET Plasmid Minip ep Ki om The mo
Scien i ic. Finally, epea ing he PCR and column pu i ica ion s a ed abo e and pe o m-
ing u he pu i ica ion using e hanol/chlo o o m/ enol ex ac ion as well as p ecipi a ion
ia cen i uga ion allowed he desi ed quan i ies o Widom-sequence DNA molecules o be
ob ained.
2.2 Di e en ial scanning calo ime y
Di e en ial scanning calo ime y (DSC) is a he mo-analy ical echnique designed o gauge
he change in speci ic hea o a sample as a unc ion o empe a u e. Many he modynamical
quan i ies may be calcula ed om calo ime y da a including ansi ion en halpies, mel ing
empe a u es, speci ic hea and ee ene gy. Apa om he e e ences speci ically highligh ed
16
in he ex , gene al in o ma ion o he elabo a ion o his sec ion has been collec ed om
he book by Hohne [20].
2.2.1 The modynamical p inciples
A gi en con o ma ional o phase ansi ion can be desc ibed by he change in he he -
modynamical p ope ies: in e nal ene gy (∆U), en halpy (∆H), Gibbs ee ene gy (∆G),
Helmhol z ee ene gy (∆F) and en opy (∆S). When he p essu e is cons an he en halpy
is a quan i y equi alen o he o al hea con en o a sys em. The en opy ep esen s he
amoun o ene gy in a sys em which is una ailable o pe o ming wo k. I also is unde s ood
as he deg ee o diso de wi hin he sys em [21, 22].
I he p essu e is kep cons an he di e ence in en halpy and en opy du ing a ansi ion
induced by a change in empe a u e can be calcula ed om he speci ic hea (Cp):
(∆H)p=ZT2
T1
CpdT (2.1)
(∆S)p=ZT2
T1
Cp
TdT (2.2)
Whe e he speci ic hea is de ined as he amoun o hea pe uni mass needed o aise
he empe a u e o he sys em by one deg ee a cons an p essu e.
2.2.2 DSC echnique
The e a e wo ypes o DSC expe imen s: he powe -compensa ed DSC; and he hea lux
DSC which is he echnique o choice o he p esen wo k. In a hea lux di e en ial scanning
calo ime e wo he mally isola ed cells, one o he sample unde s udy and ano he o he
e e ence, a e placed in a u nace connec ed o a hea e . I he empe a u e o he u nace is
aised he empe a u e o he sample and he e e ence cell will di e because hey con ain
17
samples wi h di e en Cp. The di e ence in empe a u e ela es o he di e en ial hea lux
h ough Ke, he hea exchange coe icien o he u nace: ∆P=Ke∆T.Kecan be ob ained
wi h a calib a ion using a ma e ial o well known he mal p ope ies.
The di e en ial hea capaci y o he sample wi h espec o he e e ence can be exp essed
in unc ion o he di e en ial hea lux (de i a ion can be ound in [23]):
∆Cp=−∆P
β−τins
d(∆P)
dT (2.3)
whe e β=dT0
d is he scanning a e o he expe imen (T0is he u nace empe a u e) and
τis he so called he mal ime cons an o he calo ime e [24]. This cons an is ela ed wi h
he he mal lag o he se -up o he ins umen and can be app oxima ed by con olling he
ime i akes o he ins umen o espond o a swi powe change.
Figu e 2.5 is an example o a calo ime y scan p esen ing hea lux (J/s) as a unc ion
o empe a u e du ing a hea ing amp. I he sample does no unde go a physico-chemical
ansi ion in a gi en ange o empe a u es hen he hea lux in o he sample is cons an in
his ange. On he con a y, when a he mal p ocess akes place wi hin he sample he hea
lux changes and he sign o his change depends on whe he he p ocess is exo he mic, like
he c ys alliza ion ansi ion o he igu e, o endo he mic, like he mel ing. In he o me
case hea is p oduced by he sample du ing he ansi ion and so a lowe hea lux is going
in o he sample. The opposi e is ue o he la e case.
2.2.3 Ins umen s
The di e en ial scanning calo ime e used o collec ing he da a o he ibe samples o he
p esen wo k was a Mic oDSC III om Se a am ins umen a ion. I has wo 1 ml olume
Has elloy C (Nickel and Ch omium alloy) cells, he sample cell and he e e ence. The
cells a e placed in highly conduc i e ubes, he mally isola ed om each o he and om he
ou side en i onmen . The mocouples a e ixed o he ubes o empe a u e measu emen .
18
Figu e 2.5: Example o di e en ial scanning calo ime y scan. Th ee di e en ansi ions
can be obse ed: a glass ansi ion, a c ys alliza ion and a mel ing. ep oduced om [25].
Figu e 2.6: Mic oDSC III om Se a am ins umen a ion company. Rep oduced om [27].
Du ing a scan bo h cells a e subjec ed o a empe a u e amp. Cons an ci cula ing oluene
allows o a e y p ecise empe a u e s abili y. The cooling is achie ed h ough an ex e nal
s abiliza ion wa e ba h which was kep a 27 ◦C o all expe imen s. The empe a u es
anged om oom empe a u e o 120 ◦C and he p og ammable scanning a e is 0.001
o 1.2◦C/min. The he mal ime cons an (τins) as p o ided by he manu ac u e is 60 s
[26, 27].
A sample o dissol ed DNA was measu ed in a di e en calo ime e om he es o sam-
ples (a Nano DSC III om Calo ime y Sciences co p.) due o sensi i i y easons. The DNA
concen a ion o he dissol ed sample was 2 mg/ml and he olume o solu ion measu ed
was 0.33 ml. The wo king p inciple o his calo ime e is he same as o he Mic oDSC
III and he me hods used a e iden ical. The sample was measu ed by He ´e Guillou in he
19

Ins i u N´
EEL, G enoble, F ance.
2.2.4 Expe imen al p o ocol
Mos o he calo ime y wo k pe o med o he hesis was on samples o highly o ien ed ibe
Na/Li-DNA subme ged in PEG solu ions o e hanol/2H2Omix u es desc ibed in 2.1.1. Fo
he sake o con enience he liquid in which a gi en ibe sample was subme ged would be
e e ed o simply as solu ion in his sec ion.
In a ypical expe imen he DNA amoun unde s udy was a piece o ilm ha weigh ed
a ound 25 mg when d y. The solu ion used o he expe imen was degassed using ul asound
o 20 min and hen 0.5ml was used o subme ge he DNA. The degassing minimized he
quan i y o bubbles in oduced du ing he p ocess since hey may inc ease he noise o he
signal o gene a e uns able baselines [28]. The DNA was le o equilib a e wi h he aqueous
medium o a ound a week be o e being measu ed.
The scanning a e βwas ixed a 1 ◦C/min o all he expe imen s. Inc easing i o 1.2
◦C/min o dec easing i o 0.5 ◦C/min made no signi ican di e ence in he da a eco ded.
Be o e he DNA sample was measu ed, a ”solu ion e sus solu ion” scan was pe o med
whe e 0.5ml o degassed bu e was place in bo h sample and e e ence cell. The he mal
p og am o hese scans consis ed o successi e cycles o hea ing and cooling om oom
empe a u e o a ound 110 ◦C. The calo ime ic cu e e ol es du ing he i s cycles bu
e en ually s abilized o a cons an alue o a ound ze o. The ins abili y o he cu e in he
i s scans is a well known ins umen al a i ac ela ed o he ac ha he e is a na u al
ins umen al baseline o a pa icula se o scan condi ions which disappea s a e se e al
hea ing cycles [29]. The cu e o he hea ing amp o he las cycle was ep oducible and i
was aken as he e e ence cu e o he DNA sample and used in he da a analysis. Thus,
exac ly he same condi ions o he solu ion-solu ion scan mus be used o he sample in
o de o a oid he eappea ance o his a i ac .
20
A e he e e ence cu e was ob ained he sample (DNA+solu ion) was in oduced in
he sample cell and he DNA mel ing expe imen was launched, wi h he same 0.5ml o
bu e in he e e ence cell. Since app oxima ely he same amoun o bu e (0.5ml) is in
bo h cells, ea u es in he inal cu e could be asc ibed only o he in e nal DNA o he
DNA-bu e in e ac ions.
2.2.5 Da a analysis
The aw ou pu da a o a hea lux DSC de ice is a cu e o di e en ial hea lux in powe
uni s e sus empe a u e (∆P(T)), c. . ig. 2.5. The aim o his subsec ion is o explain how
o use hese da a o calcula e he modynamical quan i ies ha a e ele an o cha ac e ize
a ansi ion. Quan i ies o choice a e he mel ing (o dena u a ion) empe a u e, he wid h
o he ansi ion, and he ac ion o open base pai s. The inal me hodology used o da a
analysis as well as mos o he con en o his sec ion ha e been hea ily based on se e al
wo ks o Cha les H. Spink [29, 30].
The e e ence cu e was sub ac ed om he measu ed ∆P(T). Then ∆P(T) can be
con e ed o ∆C(T) in J/◦C ia eq. 2.3. The di e en ial hea capaci y pe uni mass
(J/g◦C) can be ob ained by:
∆c(T) = ∆C(T)
mDNA
(2.4)
whe e mDNA is he mass o he DNA in he sample cell. The esul ing cu e usually
has a single peak o e a s aigh -line baseline. Tmin and Tmax a e espec i ely he minimun
and maximum empe a u es o he scan. Be o e u he ea men a baseline was de ined
as he connec ion line be ween ∆c(Tmin) and ∆c(Tmax) and hen sub ac ed om he da a.
This cu e could be i ed wi h a Gaussian unc ion and so he ull wid h a hal maximum
(FWHM) could be de e mined. This pa ame e was aken as he wid h o he ansi ion.
The di e en ial hea capaci y allows he calcula ion o he ac ion o base pai s which
21
Figu e 2.7: Example o da a educ ion and analysis pe o med on he calo ime ic cu e o
a sample o Na-DNA subme ged in a PEG solu ion. Le y-axis: ∆cin blue, Gaussian i
o he da a in ed and baseline in g een. Righ y-axis: F ac ion o open base pai s in black.
The mel ing empe a u e is highligh ed.
ha e opened a a gi en empe a u e: SS, whe e SS s ands o single s and. SS(T) was
calcula ed as done in [31] wi h he equa ion:
SS(T) = (∆H)n(T)
∆H(2.5)
Whe e (∆H)n=RT
Tmin ∆Cp(T)dT is called he cumula i e en halpy a empe a u e T.
Once he ac ion o open base pai s is known he ac ion o base pai s which a e closed a
a speci ic empe a u e is calcula ed as:
DS(T) = 1 − SS(T) (2.6)
whe e DS s ands o double s and. The mel ing empe a u e, Tmis he empe a u e a
which hal o he base pai s a e open so i is he empe a u e o which DS = 0.5.
Figu e 2.7 summa izes he da a analysis desc ibed in his sec ion. The igu e shows a
model example o ∆c(T), he i wi h a Gaussian unc ion, he s aigh -line baseline and he
22
calcula ed ac ion o open base pai s.
All he calo ime ic da a p esen ed in he esul chap e s o his wo k a e ob ained by
measu ing h ee iden ical samples and a e aging he esul s. The e o ba s shown a e he
s anda d de ia ion o he h ee measu emen s.
2.3 In oduc ion o sca e ing heo y
The heo e ical and expe imen al desc ip ions in his sec ion will co e only he echniques
used o his wo k. Thus, no inelas ic sca e ing is men ioned, nei he he spin o magne ic
con ibu ions o he sca e ing a e p esen ed. In o ma ion o his sec ion was collec ed om
he books by Si ia [32] and Squi es [33].
2.3.1 Basic p inciples o a sca e ing expe imen
In a sca e ing expe imen mos o he in o ma ion abou he sys em is ex ac ed om he
change o momen um and ene gy o he sca e ed pa icles wi h espec o he inciden
pa icles. The momen um change is desc ibed ma hema ically by:
~
Q=~
ki−~
k (2.7)
whe e ~
Qis he momen um ans e (also called sca e ing ec o ), ~
kiand ~
k a e he ini ial
and inal wa e ec o s o he sca e ed pa icle. The wo k desc ibed in his documen is based
in elas ic sca e ing in which Ei=E , so ki=k =2π
λ, whe e λis he wa eleng h o he
inciden pa icles. The ec o diag am o an elas ic sca e ing e en is shown in ig. 2.8
whe e an incoming pa icle is de lec ed h ough an angle o 2θ. T igonome y hen leads o
he esul :
23
(a) (b)
Figu e 2.11: a) Usual geome y o DNA ibe di ac ion. b) Schema ic o he cons uc ion o
he laye -lines in he X- ay di ac ion pa e n o a linea a ay o poin sca e e s. RL s ands
o eal la ice; ES o Ewald sphe e; CA o cone axis; LP o laye -planes; S o obse a ion
sc een; BS o beam s op and; LL o laye lines. Adap ed om [34].
molecule a e aligned along a egula ci cula helix. The ull gene al heo y o calcula ing
he o m ac o o a helix was published by Coch an, C ick and Vand [37] and is summa ized
wi h he CCV o mula.
This o mula compu es he sca e ing ampli ude o a con inuous helix o adius Rand
pi ch P, o such a sys em he cylind ical coo dina es ~ j= (ρj, ϕj, zj) o iden ical a oms
placed a axial in e als pacan be de ined wi h ela ion o an a bi a y a om aken as he
o igin (R, ϕ0, z0). The s ep-by-s ep de i a ion can be ound a [37] and he o mula is:
A(~
Q) = 2π
P (Q)X
n,m
Jn(Q R)ein(Qϕ−ϕ0+pi/2)e(Qzz0)δ(Qz−n2π
P−m2π
pa
) (2.16)
whe e ~
Q= (Q , Qϕ, Qz) in cylind ical coo dina es and Jn(x) is he cylind ical Bessel
unc ions o in ege o de n.
30

The δ- unc ion in eq. 2.16 makes i clea ha he di ac ion pa e ns will s ill be o ga-
nized in laye lines. The δ- unc ion imposes he selec ion ule:
l
Pa
=n
P+m
pa
(2.17)
Wi h his selec ion ule he δ- unc ion can be ew i en and i can be concluded ha
non-ze o in ensi y will be seen a Qz= 2πl/Pa.
Thus he sca e ing pa e n o a phospho ous helix in a single s and DNA backbone can
be calcula ed wi h eq. 2.16 se ing Pa=P= 10pa= 34 ˚
A−1and R= 10 ˚
A−1. The esul
can be seen in ig. 2.12 ep oduced om [34]. The igu e shows a e y cha ac e is ic c oss
pa e n.
The selec ion ule o his sys em is hen l=n+ 10m. As an, example he selec ion ule
gi es (n= 0, m = 0) (i.e. J0) as leading e m in he di ac ion ampli ude o he equa o ial
line (l= 0). Fo he l= 1,2,3,4,5 he equa ion selec s as leading e ms (1,0), (2,0), (3,0),
(4,0), (5,0). Keeping in mind ha nis he o de o he Bessel unc ion he c oss pa e n o
he i s i e lines can be explained. Mo eo e he same selec ion ule imposes he epea o
he c oss pa e ns along he di ec ion o he axis o he helix e e y en laye -lines. This c ea es
a diamond pa e n in he di ac ion pic u e wi h he in e io o he diamond app oxima ely
emp y o in ensi y. These diamonds a e cha ac e is ic o an helical dis ibu ion o ma e in
he di ac ing objec .
In o de o complemen his heo e ical in oduc ion o ibe di ac ion, wo e y impo -
an esul s will be commen ed. They will allow he main di e ences be ween he seconda y
A and B o m o DNA o be highligh ed, which will be signi ican ly impo an o he dis-
cussion o u u e chap e s.
Fig. 2.13 show di ac ion diag ams o Na-DNA ibe s. The measu emen s we e made
wi h a geome y simila o ha shown in ig. 2.11a. The ibe comp ises a mac oscopic
numbe o long, pa allel DNA molecules, Na+ions and wa e molecules. The ca ions and
31
Figu e 2.12: Simula ed di ac ion pa e n by an a omic phospho us helix. Rep oduced om
[34].
he wa e a e in amo phous s a e and gi e only di use sca e ing. Fig. 2.13a shows he
pa e n classically associa ed wi h he A- o m o DNA, Fig. 2.13b he one associa ed wi h
he B- o m.
A e he disco e y o hese wo o ms o DNA i was p o ed ha he ansi ion be ween
A o B o m is e e sible [39, 40]. In hese wo ks he wa e con en o a sample was modi ied
be ween wo s a es. The d ie s a e o he sample ga e pa e n A and was in e p e ed
as c ys alline, wi h long ange o de , due o he sha p spo s specially close o he cen e .
The we e s a e o he sample ga e pa e n B and due o i s b oade ea u es was called
semyc is alline and was conside ed o ha e less long ange o de due o he diso de ing e ec
o he inc eased amoun o wa e su ounding he molecules.
Bo h pa e ns a e o ganized in egula ly spaced laye -lines as expec ed om long molecules
ha ing a epea ing s uc u al uni ( he base pai ). The d ama ic change o he ea u es be-
ween pa e ns was in e p e ed no only as a change in he long ange a angemen o he
sample bu as a change in he in e nal s uc u e o he DNA molecules. This is why he
DNA is said o adop di e en con o ma ions depending on he en i onmen al condi ions.
The disco e y o A and B o m was ollowed by many o he con o ma ions such as C, D,
Z...[41].
The B- o m is belie ed o be he con o ma ion o ch omosomic DNA in i o and will be
32
(a) (b)
(c)
Figu e 2.13: X- ay ibe di ac ion pa e ns o a) A-DNA, b) Semyc is alline B-DNA. Re-
p oduced om [34] and c) C ys alline B-DNA ep oduced om [38].
33
he ocus o he p esen wo k. I s pa e n is quali a i ely e y simila o ig. 2.13, showing
he helical s uc u e o he molecule. The e lexion o he 10 h laye line o his o m will be
ins umen al in he s udy o he mel ing ansi ion in DNA ib es.
Soon a e he disco e y o he B- o m i was p o en ha his e lexion was ela ed
wi h a nucleo ide epea o 3.4˚
A−1[42]. This e lec ion was modeled as he esul o a
conca ena ion o la nucleo ides (e en hough in eali y he suga and ni ogenous base do
no lie in he same plane) s acked on op o each o he and co alen ly linked o he phospha e
backbone. The bases sca e cohe en ly despi e being i egula in hei chemical composi ion
and geome ical s uc u e because hey beha e like hin sca e ing slabs seen edge-on by he
inciden beam (pe pendicula o he ibe ). In summa y he s acked base pai s ac somewha
like a pa allel sli g a ing o p oduce he la ge 10 h laye e lec ions.
Since he B-pa e n shows en laye -in e als sepa a ing he cen e om his e lexion i
ollows ha in his con o ma ion he pi ch o he DNA is 34 ˚
A−1. The c oss pa e n in he
cen e o he pic u e is he second s onges ea u e, i is, as s a ed abo e, a oo p in o he
helical con o ma ion o he DNA backbone. A las c ucial piece o in o ma ion ha can be
ex ac ed easily om he B-pa e n is he adius o his o m (≈10 ˚
A−1), which is pa en
due o he dis ance be ween he equa o ial e lec ions.
Fig. 2.13c shows a pa e n e y simila o ig. 2.13b bu he blu ed e lec ions a e
subs i u ed wi h sha p poin s and lines which indica es bo h samples a e in he same con o -
ma ion bu he o me has be e c ys alline o de . Because o his, pa e ns like ig. 2.13b
a e usually said o ela e o he ”semic ys alline” B- o m and pa e ns like ig. 2.13c a e
ela ed o he c ys alline B- o m.
The A- o m has 11 nucleo ides pe pi ch wi h an a e age dis ance be ween base pai s o
2.56 ˚
A. The emo al o wa e wi h espec o he B- o m con ac s he molecule along i s
axis and, he base pai s become inclined wi h espec o he ho izon al plane (wi h a il
angle as la ge as 20◦). The e ec o his il is ha mos o he base pai s a e no seen
edge-on by he inciden beam and hus hey no longe ac as a ho izon al sli g a ing. The
base pai s acking no longe gi es a s ong e lexion on he 10 h laye bu wo pai s o smea
34
e lexions appea on he six h, se en h and eigh h laye lines which a e some imes e e eed
o as o -axis B agg peaks.
2.3.5 Small angle sca e ing
When s udying he sca e ing om a conglome a e o a oms, he cha ac e is ics will depend
on he spacial dis ibu ion, numbe and (λ, θ) pa ame e s o he a oms. The spacial dis-
ibu ion weigh ed by he (λ, θ) o each a om can be quan i ied by he so called sca e ing
leng h densi y unc ion, β. The sca e ing leng h densi y a a posi ion ~ in a sys em is gi en
by: β(~ ) = ρ(~ )¯
(λ, θ)(~ ) whe e ρ(~ ) is he local a omic numbe densi y and ¯
(λ, θ)(~ ) is
he mean sca e ing leng h which a ies as a unc ion o a om and iso ope o neu ons and
as he Thomson sca e ing leng h imes he local numbe o elec ons o X- ays [43]. Then
a con inuum gene aliza ion o he disc e e case o eq. 2.14 can be made:
(dσ
dΩ)el ∝N
Vh|ZZZV
β(~
R)ei~
Q•~
Rd3~
R|2iΘ(2.18)
whe e he sys em con ains Npa icles in a olume o Vand he angula b acke s indica e
an ensemble a e age o e all he o ien a ions o he pa icles.
As men ioned p e iously (sec. 2.3.3), he di e en ial c oss sec ion equa es he Fou ie
ans o m o he sca e ing leng h densi y o he sample. A basic p ope y o Fou ie ans-
o ms is he in e se ela ionship be ween leng h scales in eal, ~ , and ecip ocal space, ~
Q.
Thus expe imen s ocusing in small Q anges p o ide low esolu ion s uc u al in o ma ion
bu a e op imal o s udying he con igu a ion o mac omolecules in he mesoscopic scale
(such as sho DNA chains). Equa ion 2.8 demons a es ha low-Q expe imen s should
p io i ize measu emen s a small θs and use la ge λs. Small di ac ion angles a e eached
by ha ing a long ligh -pa h be ween sample and de ec o .
Many small angle sca e ing expe imen s a e pe o med on solu ions so he sample con-
sis s o Nobjec o in e es placed wi hin he sol en . The small angle sca e ing (SAS)
35

expe imen s desc ibed in he p esen wo k we e pe o med on a dilu e solu ion o sho chain
DNA molecules so he objec s o in e es we e Nisola ed molecules iso opically o ien ed
and andomly loca ed wi hin he sample. Unde hese ci cums ances equa ion 2.18 educes
o a one dimensional in eg al:
dσ
dΩ∝Zdmax
0
P( )sin(Q )
Q d (2.19)
whe e dmax is he longes dimension o he sca e ing objec . P( ) is he pai -dis ibu ion
unc ion. I ep esen s he a e age o he shapes o he sca e e s in he solu ion. P( ) is
usually calcula ed by he in e se Fou ie ans o m o he c oss sec ion and i will be essen ial
o he in e p e a ion o he SAS da a in he p esen wo k.
2.4 Di ac ion Ins umen s
In his sec ion an o e iew will be p esen ed abou he ins umen s used o he collec ion
o da a in his wo k.
2.4.1 Neu on di ac ome e s
IN3
IN3 is a h ee-axis spec ome e a he ILL (F ance), i was used o sample cha ac e iza ion.
This echnique p o ides access o he sca e ing unc ion S(Q, w) in a la ge olume o he e-
cip ocal space. Howe e , only elas ic measu emen s we e pe o med. Th ee-axis ins umen s
ha e a mobile o a ional axis a bo h he sample and analyze posi ions. The di ec ion o
he ini ial and inal wa e ec o s wi h espec o he sample is de ined by he angles o each
axis. Any combina ion o kiand k can be selec ed as long as he ec o iangle ~
ki−~
k =~
Q
can close.
36
Figu e 2.14: Scheme o he h ee axis spec ome e IN3 a he ILL. Rep oduced om he
ILL websi e.
Fo he expe imen s p esen ed in his documen a PG(002) monoch oma o was used
deli e ing a λ= 3.3545 ˚
A−1, ano he PG(002) c ys al was used as analyze , 400collima ion
was used be o e and a e he sample posi ion and a PG il e was placed be o e he sample o
il e high o de con amina ion. The measu emen s we e pe o med in ecip ocal ˚
Angs ¨oms
(˚
A−1) wi h an o hogonal co-o dina e sys em.
D16
The di ac ome e D16 a he ILL is used o small angle sca e ing, powde di ac ion and
single c ys al s udies. I uses a py oli ic g aphi e monoch oma o , a be yllium il e , wo se s
o sli s o inciden beam collima ion (one jus a e he monoch oma o and ano he jus
be o e he sample) and a squa e 3He de ec o o a ea 320 ×320 mm2. Fig. 2.15 p esen s a
schema ic o he ins umen . This ins umen was used o he collec ion o ecip ocal space
maps o s uc u ally cha ac e ize he high o ien ed DNA ibe s in PEG and e hanol solu ions
a oom empe a u e. The wa eleng h was se o 4.5 ˚
A and he sca e ing om each sample
was eco ded in wo di e en o ien a ions: wi h he ibe axis pa allel and pe pendicula o
he sca e ing plane. The i s o ien a ion allows o s udy pe iodic o de in he sample along
37
Figu e 2.15: Scheme o he di ac ome e D16 a he ILL. Rep oduced om he ILL websi e.
he ibe axis and he la e o ien a ion gi es in o ma ion abou he la ice spacing o he
sample in he di ec ion pe pendicula o he ibe axis. A cylind ical piece o anadium, o
leng h simila o he sample, was measu ed o e e y de ec o posi ion o accoun o he
e iciency o he de ec o .
D19
D19 is a he mal di ac ome e a he ILL, specially designed o s udying la ge s uc u es
and ibe s. D19 was con igu ed wi h a g aphi e monoch oma o deli e ing an inciden wa e-
leng h o 2.4 ˚
A. The monoch oma o -sample dis ance was 3.18 m. P e-sample collima ion
and beam size we e de ined wi h wo se s o squa ed sli s (12×12 mm2) and a ci cula ape -
u e (diame e o 10 mm). The sli s we e a 1.51 mand 2.49 m om he monoch oma o .
The ci cula ape u e was a 3.1m om he monoch oma o . High-o de B agg con ami-
na ion was elimina ed by using a g aphi e il e . D19 has a 120◦posi ion-sensi i e de ec o
which was ixed h oughou he expe imen . The e was no collima ion be ween sample and
de ec o . Fig. 2.16 p esen s a scheme o he ins umen . A cylind ical piece o anadium,
38
Figu e 2.16: Scheme o he D19 di ac ome e a he ILL. Rep oduced om he ILL websi e.
o leng h simila o he sample, was measu ed o e e y de ec o posi ion o accoun o he
e iciency o he de ec o .
This ins umen was used o s udy he di ac ion pa e n o samples o ibe DNA
subme ged in PEG solu ions and e hanol-d6/2H2Omix u es as a unc ion o empe a u e
h ough he mel ing ansi ion. Recip ocal space maps wi h he ibe axis wi hin he sca -
e ing plane we e collec ed a se e al empe a u es be ween 20 ◦C and 110 ◦C.
The s abiliza ion ime be ween measu emen s when he empe a u e was changed was
15 min. On his ins umen wo di e en sample en i onmen s we e used:
a) Fo he ibe s subme ged in PEG 6000 a 17% (w/w) wo hea e s we e a ached o
opposi e e ices o he squa e casse e. A oom empe a u e he empe a u e s abili y was
a ound 0.2 ◦C bu he mal oscilla ions inc eased wi h empe a u e. Close o he mel ing
empe a u e o his sample (≈95 ◦C) he s abili y was a ound ±1◦C.
b) Fo he e hanol samples he sample en i onmen was a cylind ical aluminum chambe
wi h a low o he malized ai . S abili y o he sample empe a u e du ing he measu emen
was <0.1◦C o e he en i e empe a u e ange.
39
The i s s ep in he analysis was o educe he aw da a o ecip ocal space maps. I was
assumed ha he mos con enien way o p esen ing such maps was by de ining a sys em
o ecip ocal coo dina es wi h e e ence o he sample casse e. Such a e e ence sys em has
been used in p e ious a icles ([31],[45]). As p esen ed in ig. 2.21 he momen um ans e
ec o ~
Qcan be exp essed as ~
Q= ( ~
QH+~
QK+~
QL) whe e ~
QHis pa allel o he axis o he
DNA ibe s, ~
QKis pe pendicula o he axis and o he ace o he casse e, las ly ~
QLis
o hogonal o he p e ious wo.
In o de o p esen he aw da a in e ms o QH,QKand QLeach de ec o image was
i s no malized o moni o and di ided by he anadium da a co esponding o he same
de ec o posi ion (de ec o e iciency co ec ion). In eg a ing o e he heigh o he de ec o
ga e a map o in ensi y as a unc ion o ωand 2θ o each de ec o posi ion, an example
can be seen in ig. 2.22a. In he case o D16 he di e en maps o each de ec o posi ion
we e assembled oge he and in he pa s in which wo maps o e lapped in he 2θ-ωspace
an a e age was aken as he ep esen a i e sca e ed in ensi y ( ig. 2.22b).
The ”ω-2θ” maps in ig. 2.22 p esen a clea ly no na u al dip in he in ensi y whose
posi ion e ol es linea ly wi h 2θ. I is an a i ac due o he sel a enua ion o he sample
when he sca e ing angle o he de lec ed neu ons is so ha hei di ec ion is in he plane
o he casse e. The da a mus be co ec ed o his. In o de o do so he ansmission
ac o o he sample was calcula ed using:
T(ω, 2θ) = 1
AbZxZy
e−µ (x,y,ω,2θ)dxdy ×1
cos ω(2.20)
whe e Tis he ansmission ac o , µis he linea a enua ion coe icien , Abis he a ea
o he inciden beam and is he pa h leng h o a gi en se o neu ons h ough he sample
in unc ion o ω, 2θand (x,y) which is he poin in he sample a which he sca e ing e en
occu ed wi h e e ence o an a bi a y o igin in one o he e ices o he sample ( ig. 2.23).
The aco 1/cos ωwas included o accoun o he oo p in o he beam on he sample as
he sample a a ed. Since he linea a enua ion ac o o he sample is no known, µwas
i s ly app oxima ed by he linea a enua ion ac o o 2H2Oand hem adjus ed sligh ly o
46

(a)
(b)
Figu e 2.21: a) and b) Schema ic o he ecip ocal coo dina e sys em de ined wi h espec
o he DNA ibe axis. ~
QHis pa allel o he ibe axis, ~
QKis pe pendicula o he ibe
axis and o he ace o he casse e, ~
QLis o hogonal o bo h ~
QHand ~
QK.~
QSP is in he
sca e ing plane and i ma ches ~
QHin he longi udinal o ien a ion and ~
QLin he a e sal
o ien a ion.
47
(a) D19 (b) D16
Figu e 2.22: Sca e ed in ensi y as a unc ion o ω(sample o a ion) and 2θ o Na-DNA
subme ged in a PEG 6000 solu ion a as measu ed a oom empe a u e on a) D19 and b)
D16.
he esul o ma ch he a enua ion obse ed in he expe imen al da a.
An example o pa o he calcula ion will be p esen ed he e. The in eg al was di ided
in o di e en cases so ha in each case he ajec o y o he neu ons, , is de ined as a single
unc ion o x,y,ωand 2θ. The simples case assumes ha θ1<0 and θ1< θ2< θmax whe e
θmax =a an(w−Bw
2d), as is highligh ed in ig. 2.23. Unde hese assump ions e e y possible
pa h o he sca e ed neu ons h ough he sample en e s i by he ace A, lea es he sample
by ace Cand he pa h leng h can be desc ibed as:
=d−y
cos θ1
+y
cos θ2
(2.21)
Then Tis compu ed wi h eq. 2.20 wi h he limi s o he in eg a ion in xbeing (w−
Bw)/2< x < (w+Bw)/2 and in ybeing 0 < y < d.
Fig. 2.24 shows an example o he esul o he co ec ion o bo h a single alue o ω
and he comple e ω-2θmap.
The co ec ed in ensi y map was hen ans o m o he QH-QKspace o he da a o
he longi udinal o ien a ion ( ibe axis wi hin sca e ing plane) o he QL-QKspace o
48
Figu e 2.23: Geome y o he calcula ion o he ansmission ac o T.θ1=ω+ ∆θand ∆θ
is an ins umen al o se . wis he wid h o he sample, dis he hickness o he sample. Bw
is wid h o he neu on beam. The cen e o he neu on beam is supposed o go hough he
middle o he sample in he on ace. θmax is a limi o θ2in he example o he calcula ion
o Tand i is desc ibed in he ex .
(a) (b)
Figu e 2.24: a) Example o ω-2θmap a e he sel a enua ion co ec ion. b) In ensi y s. 2θ
o he aw da a (blue), sel -a enua ion co ec ed da a (black) and alue o he ansmission
ac o , T0, ( ed) o a gi en omega alue.
49
Figu e 2.25: Diag am o he sca e ing geome y ela ing he coo dina es ωand 2θ o he
QH-QKspace. In he case o he ans e sal o ien a ion he diag am would be iden ical and
QHwould be eplaced wi h QL.
he ans e sal o ien a ion ( ibe axis no mal o he sca e ing plane). This is done by
ans o ming he ω-2θspace using he equa ions:
QH,L =k(sin ω+ sin(2θ−ω))
QK=k(cos ω−cos(2θ−ω))
(2.22)
whe e k= 2π/λ. These equi alences a e appa en when ollowing he sca e ing geome y
o ig. 2.25.
The inal ecip ocal maps o bo h o ien a ions can be seen in ig. 2.26. The sligh d op
in he in ensi y which is obse able in he uppe le co ne o ig. 2.26a p o es ha he
a enua ion co ec ion is no pe ec . Since such ma ginal de ec is ela i ely a away om
he ea u es o in e es ed s udied in his wo k i can be easonably assumed ha i s e ec in
he in e p e a ion o he da a is negligible.
Be o e in e p e ing he da a o he maps wi h he ibe axis no mal o he sca e ing
plane ( ans e sal o ien a ion) ano he educing s ep was ca ied on. The da a o hese
50
(a) (b)
Figu e 2.26: Recip ocal space map o a DNA sample subme ged in PEG solu ion as mea-
su ed in D16 o bo h o ien a ions: ibe axis in he sca e ing plane (a) and no mal o he
sca e ing plane (b).
maps we e summed o e he sample o a ion angles (ω) and plo ed as a unc ion o he 2θ
o he magni ude o he sca e ing ec o (Q) which a e ela ed h ough ec. 2.8).
Fo he ecip ocal maps collec ed wi h he ibe axis pa allel o he sca e ing plane i was
impo an o ex ac a ep esen a i e da a o a scan along he helix axis, i.e. a scan along
QHwhen QK= 0. To ge his, a na ow QK- ange was chosen cen e ed a QK= 0 (usually
−0.04 < QK<0.04 ˚
A−1) Da a whi hin his ange we e ex ax ed and plo ed agains hei
QH alues, dis ega ding he QK alues.
2.5.2 Small angle neu on sca e ing
The aw SANS pa e ns we e co ec ed o en i onmen al backg ound using a blocked beam
measu emen . De ec s in he sample and e e ence cells we e accoun ed o wi h emp y cell
measu emen s. A e wa ds he in ensi y in absolu e uni s (cm−1) was ob ained by using he
o mula which ela es he expe imen al elas ic signal wi h he di e en ial c oss sec ion:
Iel(~
Q) = I0η(λ)T (λ)∆Ω( dσ
dΩ)el ⊗R(~
Q) (2.23)
51

whe e I0is he inciden lux, ηis he e iciency o he de ec o s, T he ansmission o
he sample, ∆Ω is he solid angle o he de ec o wi h espec o he sample and R(~
Q) is
he ins umen al esolu ion. The expe imen ally de ec ed in ensi y is smea ed wi h espec
o he eal sca e ed in ensi y due o he ini e size o he incoming beam, he wa eleng h
esolu ion and he pixel size o he de ec o . R(~
Q) desc ibes he dis ibu ion o he Q ec o s
a a gi en ins umen con igu a ion and co ec s o his smea ing.
A shee o plexiglass was measu ed in o de o accoun o he de ec o e iciency (η)
since i sca e s iso opically, ansmission o he sample was app oxima ed by a enua ing
he beam and hen measu ing he di ec ansmi ed beam a θ= 0. A moni o be o e
he sample ga e an es ima ion o he inciden lux. A Gaussian unc ion was assumed o
desc ibed he ins umen esolu ion unc ion which has been p o ed easonable in he pas
[46]. The GRASP (G aphical Reduc ion and Analysis SANS p og am) Ma lab code package
was used o applying a ec angula mask o he di ec beam posi ion and hen in eg a e he
da a adially ge ing he inal cu es as in ensi y (cm−1) e sus Q(˚
A).
Then, using he sca e ing c oss sec ion and he GNOM p og am [47] he pai dis i-
bu ion unc ion o each empe a u e was calcula ed. GNOM app oxima es P( ) using he
egula iza ion me hod which is based on minimizing he unc ion:
TG(P) = |I(q)−Zdmax
0
P( )sin(Q )
Q d |2+XΥ(P) (2.24)
whe e Υ(P) is an s abilize con aining a p io i in o ma ion abou he solu ion. I is
no mally assume ha Υ(P) = RdP(R)
d d which equi es P(R) o be a smoo h unc ion. Xis
he egula iza ion pa ame e . The la ge Xis mo e a en ion is paid o he smoo hness o
he inal P( ) and less o i ing he expe imen al da a. The alue o Xis c ucial and he e
is no an accep ed uni e sal e o -p oo me hod o choose he alue.
GNOM sea ch o he op ima Xusing a pe cep ual c i e ia. Wi h his c i e ia he
p og am explo e di e en X alues and es ima es he plausibili y o he solu ion by i s
smoo hness, s abili y wi h espec o X a ia ions and he absence o sys ema ic a ia ions.
52
The pe cep ual c i e ia is epo ed ex ensi ely in he book by Tikhono and A senin [48]
and well summa ized in [49]. The GNOM es ima ions o X a y o di e en SANS cu es
o a sample a di e en empe a u es. The es ima ions all in he ange 0.58 <X<1.2. Fo
consis ency Xwas ixed o 1 o e e y SANS cu e which gi es easonable esul s o all he
da a s udied.
Rega ding he UV-Vis spec oscopy da a eco ded, since in ensi y o he UV-Vis adia ion
h ough he sample was moni o ed a each empe a u e (IS(T)) he abso bance o he sample
can be calcula ed in unc ion o empe a u e as:
A(T) = log10(LS−DS
IS(T)−DS
) (2.25)
whe e LSis he so called ligh measu emen o he in ensi y eco ded when he sample
posi ion is emp y ( ansmi ance o 100%), DSis he da k measu emen o in ensi y eco ded
when he beam is blocked ( ansmi ance o 0%).
2.5.3 Small angle X- ay sca e ing
Fo he SAXS case he educ ion o he da a is almos iden ical. The impo an di e ence is
ha he inal da a was no malized o absolu e uni s using he di ac ion o a glassy ca bon
s anda d as explained in [50].
The calcula ion o he P( ) o SAXS da a was iden ical o he one o SANS.
The con igu a ion o he SAXS ins umen had some ad an ages o e he D22, o exam-
ple he inc eased lux will allowed o pe o m he expe imen wi h a ac ion o he sample
used o neu ons. Howe e , he e we e no in-si u UV-Vis abso ion measu emen s o he
samples s udied by SAXS.
53
Chap e 3
Li e a u e e iew
This chap e p esen s li e a u e esul s which a e ele an o his hesis as well as some o
he models ha will be use o analyze and in e p e he da a.
3.1 P e ious di ac ion s udies in ibe DNA
As desc ibed in he comp ehensi e book by Wa son [51] X- ay di ac ion s udies on DNA
ibe s by Wilkins and Gosling showed ha he DNA molecule can assume a highly pe iodic
s uc u e gi en ha he ibe s a e kep mois . F ankling and Gosling we e he i s o de elop
op imal echniques o con ol he ela i e humidi y o ibe s [52] and hey could ob ain mode
de ined di ac ion pa e ns which hey designa ed A and B. They al eady de ec ed ha
he pa e n o a gi en ibe changes e e sible when he wa e con en o he sample is
modi ied and ha mix u es o A and B pa e ns exi s which co espond o samples wi h a
con o ma ional mix u e.
Wa son and C ick de eloped a wo s anded model [53] which was able o explain he
B di ac ion pa e n and la e a mo e de ailed analysis by Wilkins e al. [54] showed ha
bo h A and B pa e ns could be accoun ed o by he models o wa son and C ick.
54
Since hen, many g oups g ea ly con ibu ed o he o e all knowledge o he cha ac e -
is ics o c ys alline and semic ys aline ibe DNA and hei A and B di ac ion pa e n as
well as he A- o-B ansi ion, a non comple e lis includes: Fulle e al. [55, 41]; F anklin
and Gosling [56]; Lang idge e al. [38]; Fo sy h e al. [57]; Lindsay e al. [58] among o he s.
Se e al comp ehensi e o e iews in he opic can be ound (e.g. [59]), he es o he
sec ion will be ocused in speci ic esul s ha a e specially ele an since hey come om
e y simila expe imen s pe o med on almos iden ical samples wi h espec o he p esen
wo k.
3.1.1 Con o ma ion o humidi ied ibe s. A and B o m DNA as
seen by neu on sca e ing
As desc ibed in sec. 2.3.4 and abo e he di ac ion pa e n o A- o m and B- o m DNA
di e d ama ically and changes in he wa e con en o hyd a ion o he ibe s can igge a
con o ma ional B- o-A ansi ion which is e e sible. The con o ma ion o he DNA unde
s udy mus be aken in o accoun o a co ec in e p e a ion o he sca e ing ea u es.
Valle-O e o e al. [60] s udied ecen ly highly o ien ed we spun ibe s humidi ied a
se e al ela i e humidi ies using neu on sca e ing. They iden i ied he main ea u es which
indica e a gi en sample is in B o m, A o m o a mix u e o bo h con o ma ions.
Fig. 3.1 ep oduced om [60] summa izes hese esul s. The igu e shows selec ed pa s
o he ecip ocal space maps in longi udinal ( ibe axis wi hin he sca e ing plane) o ien a-
ion. The maps ep esen he di ac ed in ensi y in ecip ocal space using he pe pendicula
coo dina e sys em explained in sec. 2.5.1:(QH, QK, QL).
Fig. 3.1a op shows a singula in ense B agg peak cen e ed a (1.87,0,0) ˚
A−1which
is cha ac e is ic o he B- o m. This B agg peak, associa ed wi h a d-spacing ≈3.4˚
A , is
ela ed wi h he long ange o de o he posi ion o he base pai s along he molecula axis
(base pai s acking). This ea u e will be he ocus o he empe a u e dependence s udy by
55
a non andom alignmen o disc e e cha ges on he opposi e molecules.
Exp essions o he h ee componen s can be app oxima ed i he wo molecules a e
assumed o be iden ical al hough hey s ill may o a e a ound i s own axis independen ly.
The whole ma hema ical de i a ion is long and can be ound in [68] (pa C, double helices).
The inal esul s a e:
cyl
16π2ασ0
=1
2κ
K1(κIad)
K1(κRa)K1(κRa)(3.7)
wi h Kn(x) being he modi ied bessel unc ion o he second kind and o de n h.
The sel co ela ion e m:
sel
16π2ασ2
0
=
∞
X
n=1
cos2(nΦs
2)Ω0
n,n(κnIad, κnRa)
κn[K0
n(κnRa)]2(3.8)
whe e κn=p(κ2+ (2π
P)2n2), K0
n(x) = dKn(x)/dx and Φsis he azimu hal hal -wid h o
he mino g oo e (which is ≈0.4π o B-DNA [69]) and Ω0
n,n is so ha :
Ω0
n,m(x, y) =
∞
X
j=−∞ [K0
n−j(x)Kj−m(x) + Kn−j(x)K0
j−m(x)] J0
j(y)
K0
j(y)(3.9)
whe e Jnis he bessel unc ion o he i s kind o de n h and J0
n(x) = dJn(x)/dx.
c oss
16π2ασ2
0
=
∞
X
n=1
(−1)ncos2(nΦn
2) cos[n(Φ1−Φ2)] K1(κnIad)
κn[K0
n(κnRa)]2(3.10)
whe e (Φ1−Φ2) is he ela i e o a ion o he wo iden ical molecules. Fo he calcula ions
o he p esen wo k (Φ1−Φ2) was aking as he op imal ela i e angle which minimizes he
c oss co ela ion ene gy which can be calcula ed as:
62

(Φ1−Φ2) = a ccos κ2
2cos2(Φ
2)[K0
2(κ2Ra)]2K0(κ1Iad)
aκ2
1cos2(φs)[K0
1(κ1)Ra]2K0(κ2Iad)(3.11)
his app oxima ion holds o in e axial dis ances sho e han a c i ical sepa a ion o R∗,
a la ge dis ances he op imal angle is ze o. R∗can be app oxima ed as:
R∗=1
κ2−κ1
ln4 cos2(Φs)[K0
1(κ1Ra)]2κ5/2
cos2(Φs/2)[K0
2(κ2Ra)]2κ5/2
2(3.12)
Fo ces calcula ed wi h his model we e p o en o be consis en wi h expe imen al mea-
su emen s o m Pa segian and cowo ke s [67].
No e ha unde ce ain condi ions his model p edic s an a ac ion o ce be ween DNA
molecules. DNA molecules a e gene ally nega i ely cha ge in solu ion so his may look
un easonable. In a di e en publica ion Ko nyshe and Leikin p o ed ha an a ac i e
esul an o ce can ake place caused by an a ac ion o he phospha es o s ands o one
DNA wi h ca ions adso bed in he g oo es o ano he DNA when DNA is con ined o dense
agg ega es [71].
3.3 Mel ing ansi ion
The mel ing ansi ion is usually cha ac e ized by he mel ing empe a u e, Tm.Tmis de ined
as he empe a u e a which hal o he base pai s in he molecule a e open. I is commonly
used o add essing he s abili y o DNA and o he nucleic acids [72, 73]. In long chain DNA
he mel ing empe a u e depends mainly on he en i onmen al condi ions o he DNA like
hyd a ion le el, ionic s eng h o he medium, he p esence o o he solu es in he su ondings
and also he DNA-DNA in e ac ions.
Ano he ea u e ha helps cha ac e izing he ansi ion is he coope a i i y. The coope -
a i i y o he ansi ion is he endency o he base pai s o open in con iguous segmen s. The
coope a i i y is usually quan i ied by he so called coope a i i y ac o which is he mean
63
numbe o base pai s ha mel as a single he modynamic en i y [74]. In a highly coope a i e
ansi ion, usually shown by sho DNA molecules and specially syn he ic polynucleo ide du-
plexes (poly(dAdT) o poly(dGdC)), mos o he base pai s o he molecule open as a whole
a a single empe a u e. In a less coope a i e ansi ion, asc ibed adi ionally o long na -
u al DNA, many domains in he molecules mel independen ly om each o he a di e en
empe a u es. The coope a i i y depends on he ene gy and en opy changes associa ed wi h
he c ea ion o he open egions be ween helical domains.
The coope a i i y can be accessed expe imen ally since he wid h o he mel ing ansi ion
(which can be measu ed, o example, by calo ime y as explained in sec. 2.2.5) is in e sely
p opo ional o i s coope a i i y. Thus na owe ansi ions a e mo e coope a i e [75].
3.3.1 E ec o he con inemen o DNA in he mel ing ansi ion
A p edic ion o how he in e molecula o ces in dense DNA assemblies a ec he mel ing
ansi ion was published by Che s y and Ko nyshe [69]. They combined he heo y o elec-
os a ic in e ac ions p esen ed in sec. 3.2 (also see [68]) and he wo-s a e one-dimensional
Ising model o DNA mel ing [76].
The model was used o accoun o he di e ence in he ee ene gy o base pai s in closed
(Fc) and open (Fo) s a e. Du ing he mel ing o a single molecule: Fo−Fc= ∆U−T∆S
whe e Tis empe a u e, ∆Uis he hea o mel ing o a base pai and ∆Sis he en opy
di e ence be ween closed and open s a es. ∆S > 0 because open base pai s ha e mo e
deg ees o eedom. A he mel ing empe a u e o his single molecule, Tm0, he numbe o
open (No) and closed (Nc) base pai s is equal so:
s=exp[(Fo−Fc)/(kBTm0)] = 1 (3.13)
whe e kBis he Bol zmann cons an .
This model also includes a coope a i i y ac o σcoop =exp[−Fs/(kBT)] whe e Fsis he
64
ene gy equi ed o c ea e a open egion be ween wo in ac closed egions. Smalle σcop
alues (la ge Fs) co esponds o a mo e coope a i e mel ing.
Che s y and Ko nyshe a gued ha i he o ce be ween DNA molecules is a ac i e
his a ac ion s abilizes he close base pai s, hus i lowe s he ee ene gy in he closed
s a e. The e o e he mel ing empe a u e mus inc easse o eq. 3.13 o s ill hold [69].
Following p e ious s udies in he opic [77, 78] hey modeled he in e ac ion ene gy
be ween pa allel so non-homologous DNA molecules ( o ally independen sequences) as:
E(L) = a0L−La1[1 −l /(2lc)] −a1l2
[1 −el/l ]/(2lc) (3.14)
whe e Lis he leng h o he molecules, lcis he helical cohe en leng h (which has a alue
be ween 300-700 ˚
A o DNA [79, 80]), l =pC /2a1and C is he o sional elas ic modulus
o DNA (usually aken as 3 ×10−18 J˚
A [81]) . a0(Iad) and a1(Iad) a e he elec os a ic
in e ac ion ha monic coe icien s whose exp essions can be ound in he appendix o [69]. As
in p e ious sec ions, Iad is he in e axial dis ance be ween molecules.
Using eq. 3.14 Che s y and Ko nyshe ew o e he ee ene gy o he Ising model as
he sum o he in e ac ion ene gy o he closed agmen s, he ene gy o he closed/open
bounda ies and he ene gy o all he DNA base pai s which allowed hem o ob ain an
exp ession o he ee ene gy as a unc ion o No,Nc,T,Iad and nbwhich is he numbe o
closed/open bounda ies. Minimizing Fwi h espec nand Nh. They de i ed wo coupled
equa ions which mus be ul illed a he mel ing empe a u e in a columna DNA agg ega e:
(N
2nb−1)2=1
σcoop
1−2b/N
2(1 −nb)/N =exp(−1
2
6a(a0−a1)
kBT)
(3.15)
whe e ais he dis ance be ween base pai s (3.4 ˚
A o B o m), nbis he numbe o
closed/open bounda ies and N=Nc+Nois he o al numbe o base pai s.
65
I all he o he pa ame e s a e cons an gi en wo in e axial dis ance: Iad1wi h mel ing
empe a u e Tm1and Iad2wi h mel ing empe a u e Tm2 his model p edic s ha :
Tm2=Tm1
a0(Iad2)−a1(Iad2)
a0(Iad1)−a1(Iad1)(3.16)
3.3.2 E ec o PEG in he mel ing ansi ion
To he bes o ou knowledge he e a e no p e ious s udies on he mel ing o DNA ibe s
subme ged in PEG solu ions. Howe e , he mel ing o DNA dissol ed in many di e en PEG
solu ions was epo ed by di e en g oups (e.g. [82, 83]) and he esul s a e ele an o he
p esen wo k.
When PEG is dissol ed in a DNA-wa e solu ion i dec eases he wa e ac i i y o he
solu ion which in u n dec eases he mel ing empe a u e o DNA because i changes he
wa e s uc u e a ound he DNA molecules [82]. This is belie ed o be he explana ion
o low-molecula weigh PEGs and o he polyme s dec easing he mel ing empe a u e o
DNA dissol ed in solu ion. Howe e , high molecula weigh polyme s inc ease he mel ing
empe a u e o DNA in solu ion. The o igin o such inc ease was said o be he excluded
olume e ec . This assumes ha he olume o he solu ion una ailable o he DNA due o
he PEG p esence s abilizes he molecula con o ma ion which occupies he smalles space,
ha is, he helix molecule [82, 83]. The dec ease o he wa e ac i i y s ill happens o
he long chain polyme s bu i s e ec on he mel ing has been p o en o be e y small in
compa ison o he e ec o he excluded olume [82].
A s ong indica ion ha he excluded olume e ec is aking place is ha he a ia ion
o Tmis changing d ama ically wi h he molecula weigh o he PEG [82, 73], as can be seen
in ig. 3.3.
E en hough i is no pa en , hese esul s o DNA in solu ion a e ele an o he
case o DNA- ibe s subme ged in PEG solu ions. I he PEG pene a es he ibe s hen he
66
Figu e 3.3: Va ia ion o Tmo E.coli DNA in solu ion wi h he mola concen a ion o he
PEG 400 (squa es), 1000 (ci cles), 3400 ( iangles), 8000 (in e se iangles). Rep oduced
om [82].
sample is no much mo e di e en han a e y concen a ion DNA solu ion and he excluded
olume o he PEG will a ec he mel ing ansi ion o he ibe s. On he con a y, i he
PEG emains sepa a ed om he DNA, in he ou side o he ibe s, jus a small ac ion o
he DNA molecules in he sample will be in con ac wi h PEG molecules and he excluded
olume e ec will be negligible.
3.3.3 E ec o e hanol in he mel ing ansi ion
I is known ha inc easing concen a ions o e hanol dec ease he mel ing empe a u e o
DNA in solu ion [84]. The main ac o s explaining his beha io a e he inc eased elec o-
s a ic epulsions among phospha e g oups o he helix due o he lowe ing o he dielec ic
cons an s o he e hanol solu ion as he e hanol concen a ion inc eases, he hyd ophobic
e ec and he dec eased wa e ac i i y [84]. In he case o he ibe s subme ged in e hanol
solu ions he e is no a phase sepa a ion as happens wi h PEG o a high enough molecula
weigh . E hanol is a e y small molecule in compa ison wi h PEG ( he molecula weigh o
e hanol is 46.07 g/mol) and will pene a e he ibe s as easily as he wa e molecules. The e-
67

(a) (b)
Figu e 3.4: Mel ing empe a u e ( illed ci cle) and wid h o he ansi ion (open ci cle) o
ibe subme ged in e hanol solu ions. a)Na-DNA and b)Li-DNA. Rep oduced om [85].
o e he same ac o s which a ec DNA in solu ion will o su e be p esen in he subme ged
ibe samples.
Rupp ech e al. s udied he mel ing ansi ion o e y simila DNA we -spun ibe s
samples subme ged in e hanol/wa e mix u es ([85],[86]). They used a mechanochemical
me hod which can ela e changes in he leng h o he subme ged ibe s s ained by a weigh
wi h con oma ional and he modynamical ansi ions o he DNA [87]. Fig. 3.4 summa izes
hei esul s o Na−and Li-DNA ibe s.
Fo Na-DNA ( ig. 3.4a) Tmdec eases om a ound 60% o 88% e hanol concen a ion
([E OH]) bu he e is a local maximum a a ound 75%. The wid h o he ansi ion dec eases
sligh ly om 60% o 70% and d ops s eeply a a ound 75% [E OH]. These seemingly coupled
changes in he beha io o Tmand he wid h we e ela ed wi h he B- o-A o m ansi ion o
he seconda y s uc u e o he DNA (sec ion 2.3.4). Rupp ech e al. linked he e ec o he
B- o-A ansi ion on Tmand wid h o he s onge in e -helical in e ac ions ha he A- o m
exhibi s wi h espec o he B- o m in agg ega ed DNA [88].
68
Fo [E OH] highe han 90% he changes in Tmand wid h we e ela ed wi h a ansi ion
o P- o m DNA [89], a e y s able and dehyd a ed DNA o m which is no o in e es o
he p esen wo k.
Fo Li-DNA ibe s ( ig. 3.4b) he Tmdec eases mono onically un il a ound 83%. The
wid h s ays cons an om 70% o 75% and hen dec eases s eadily. The aise in Tmand
wid h a e ≈82% is again ela ed wi h he ansi ion o he P- o m. In hese samples a
B- o-C ansi ion was de ec ed a a ound 80% e hanol.
These ansi ions we e also de ec ed by X- ay sca e ing in [61] (B- o-A) and in [62]
(B- o-C) as explained in sec. 3.1.2.
Rupp ec h e al. measu ed samples subme ged in e hanol solu ions in a a he ex ensi e
ange (0.3-3 M) o sal concen a ions (NaCl o Na-DNA ibe s and LiCl o Li-DNA
ibe s). They ound no a iance o he mel ing ansi ion wi h sal concen a ion in his
ange [87].
3.4 Models o DNA and he mel ing ansi ion
3.4.1 Pey a d-Bishop-Dauxois model
The one dimensional Pey a d-Bishop-Dauxois (PBD) model [90], [91] was used o analize
he pa o he neu on da a. The model is able o p edic mel ing cu es o complex DNA
molecules and sol e he dynamical p ope ies associa ed o he o ma ion and s abili y o
he dena u a ion bubbles [92].
A simple e sion o he model desc ibes a DNA molecule as Nbase pai s placed in a
1D diso de ed chain wi h a mean sepa a ion o a, ig. 3.5. The s a e o each base pai is
desc ibed by a single eal a iable, yn, which is he s e ching o he base pai pe pendicula
o he molecula axis wi h espec o i s equilib ium posi ion. yn anges om 0 o +∞. The
Hamil onian o such a sys em is:
69
Figu e 3.5: G aphical ep esen a ion o he PBD model. ynis he s e ching o he n h
base pai , ais he mean dis ance be ween consecu i e base pai s, xnis he local s uc u e
de ia ion o he n h base pai , Wis a po en ial desc ibing in e -pai in e ac ion and Vis a
po en ial accoun ing o he in e ac ions be ween he wo bases wi hin he pai n h.
Hy=
N−1
X
j=1
W(yj, yj+1) +
N
X
j=1
Vj(yj) (3.17)
whe e yj ep esen s he s e ching o he j h base pai caused by he ans e se displace-
men o he bases. W(yj, yj+1) is a po en ial desc ibing he s acking in e ac ion be ween
adjacen bases [93]:
W(yj, yj+1) = 1
2k[1 + ρe−b(yj+yj+1)](yj−yj+1)2(3.18)
whe e kis a coupling cons an , ρis he ela i e s eng h o he nonlinea base s acking
and bis he in e se ange o he nonlinea base s acking. Vjdesc ibes he in a-pai po en ial
in he j h base pai and akes in o accoun he hyd ogen-bonding, elec os a ic in e ac ions
be ween phospha e g oups and sol en e ec s. I is usually aken as a Mo se po en ial:
Vj(yj) = Dj[1 −e−αjyj] (3.19)
wi h Djand αjbeing espec i ely he dep h and in e se ange o he po en ial. Fou
70
di e en pa ame e s we e necessa y o desc ibing he wo kinds o base pai s:DAT ,αAT and
DGC,αGC.
The model can be used o calcula ed he size dis ibu ion o he closed segmen s o DNA
which would be ins umen al o he analysis o he di ac ion da a p esen ed in his wo k.
A de ailed desc ip ion o his calcula ion has been epo ed elsewhe e [7]. He e only main
s eps o he p ocess a e p esen ed.
A quan i a i e de ini ion o a closed base pai is needed o calcula e he size o he closed
egions a a gi en empe a u e (T) . Base pai jis conside ed closed i yj< ycwhe e yc
co esponds o a s e ching well on he pla eau o he Mo se po en ial.
The s a is ical weigh o a gi en con igu a ion o he molecule he malised a empe a u e
Tis[7]:
zT=Zy 1
yl1
dy1···Zy N
ylN
dyN·exp−Hy(y1,··· , yN)/kBT(3.20)
whe e kBis he Bol zmann cons an and yland y de ine he con igu a ion. I yl=−∞
and y =∞ o all j, he molecules explo e he whole con igu a ional space and zT=Z
whe e Zis he pa i ion unc ion. ylj = 0 and y j =ycde ine a con igu a ion in which he
base pai jis closed. I ylj =ycand y j =∞de ine a con igu a ion in which base pai jis
open. The in eg als associa ed wi h all con igu a ions can be easily calcula ed as a se ies o
mono-dimensional in eg las because he model is one-dimensional and es ic ed o nea es
neighbo coupling. [7]
The p obabili y o madjacen base pai s being closed s a ing wi h he si e iis hen:
P(m, i) = zT(y1,··· , yi−1, yi< yc, yi+1 < yc,··· , yi+m−1< yc, yi+m,···)/Z (3.21)
Eq. 3.21 calcula es he s a is ical weigh o con igu a ions whe e es ic ions on he
in eg a ion ange we e imposed o all si es belonging o he closed egion and no es ic ions
71
(a) (b)
(c) (d)
(e) ( )
Figu e 4.1: X- ay di ac ion pho og aphs o DNA ibe s. Fibe s equilib a ed wi h an a -
mosphe e o 75% RH a) Na-DNA and b) Li-DNA. Fibe s subme ged in e hanol solu ions:
c) Na-DNA 60% , d) Na-DNA 70%, e) Li-DNA 20% ) Li-DNA 70%. The momen um
coo dina e sys em is de ined by QH s. QKwhe e QHis pa allel o he molecula axis and
QKis pe pendicula o i . 78

4.2 Room empe a u e s udy wi h neu ons
4.2.1 Fibe s subme ged in PEG solu ions
Fi e samples o Na-DNA subme ged in PEG solu ions we e s udied by neu on sca e ing a
oom empe a u e. The solu ions con ained: PEG 6000 a 17% (w/w) (PEG6K-17%); PEG
6000 a 20% (PEG6K-20%); PEG6K-40%; PEG 8000 a 15% (PEG8K-15%); and PEG 8000
a 20% (PEG8k-20%). As a e e ence, Na-DNA ibe s humidi ied a 92% RH in a 2H2O
a mosphe e we e also measu ed (Na-humid).
The le panels o ig. 4.2 shows he ecip ocal space maps o he Na-humid ibe s.
Fig. 4.2a is he map o he longi udinal o ien a ion ( ibe axis wi hin he sca e ing plane).
Fig. 4.2c is he map o he ans e sal o ien a ion ( ibe axis pe pendicula o he sca e ing
plane). The maps ep esen he di ac ed in ensi y in ecip ocal space using he pe pendic-
ula coo dina e sys em explained in sec. 2.5.1: (QH, QK, QL).
Na- ibe s a his RH a e expec ed o be in he semic is aline B- o m o DNA [98, 60].
Indeed, ig. 4.2a shows a singula in ense B agg peak cen e ed a (1.87,0,0) ˚
A−1( he 10 h
laye B agg peak) which is cha ac e is ic o he B- o m as discussed p e iously (sec. 3.1.1).
The ans e sal ecip ocal map shown in ig 4.2c is quali a i ely iden ical o he esul s
p esen ed in 3.1.1 and also sugges ha he sample is in he B- o m. I shows wo ing-
like ea u es, one s ong and cen e ed a ound Q= 0.5˚
A−1and ano he much weake a
a ound Q= 0.57 ˚
A−1. These e lexions a e ela ed o he semic ys alline packing o he
DNA molecules in he di ec ion pe pendicula o he ibe axis [60, 23].
The ibe s subme ged in PEG solu ions all showed e y simila ea u es and only he da a
o he PEG6k-17% sample a e shown in ig. 4.2b and 4.2d as model examples. The subme ged
samples ha e subs an ially mo e incohe en sca e ing in compa ison o he humid ibe s due
o he p esence o p o ona ed PEG and so he signal- o-noise a ios o he B agg peaks a e
smalle . The ea u es may also be b oade in he sample o a ion angle, sugges ing ha
79
some o ien a ion o he ibe s has been los . Howe e , he esul s a e quali a i ely iden ical
o he humid ibe s. This means ha he ibe s subme ged in PEG solu ions a e also in
he B- o m and mos o he long ange o de o he ibe s is no los du ing he subme sion.
Simila esul s ha e been epo ed p e iously by Wildes e al. [12].
Fig. 4.3 shows he low-Qpa o he ecip ocal space map in longi udinal o ien a ion o
he Na-humid and PEG6K-17% ibe s. The maps a e ea u eless o hese sample excep
o he halo o he di ec beam in he le bo om co ne . This esul is su p ising since
p e ious s udies in e y simila samples concluded ha an addi ional B agg peak in his
egion, cen e ed a (QH, QK) = (0.25,0.3), was ano he e lexion ela ed wi h he B- o m
(sec. 3.1.1 and [60]). This ea u ed has no been de ec ed in hese o o he samples measu ed
in he p esen wo k. This sugges ha he peak a (0.25,0.3) was ela ed wi h some speci ic
c ys alline a angemen o he samples s udied in [60] bu does no seem o be a uni e sal
ea u e o he B- o m o DNA.
The da a o he ans e sal ecip ocal space maps we e used o calcula e he in e axial
dis ance be ween molecules (Iad) o e e y sample and hus o gauge he e ec o he PEG
solu ion on he con inemen o he molecules. The da a o hese maps we e summed o e
he sample o a ion angles o equal Q alues and plo ed as a unc ion o he magni ude o
Q( he sca e ing ec o ). Fig. 4.4 shows he esul s.
The peaks o he subme ged samples a e shi ed o lowe Q alues wi h espec o
hose o he Na-humid ibe s. This sugges an inc ease in he la ice pa ame e s which is
consis en wi h he ibe s swelling when subme ged. B- o m DNA ibe s a e belie ed o ha e
a hexagonal space g oup, as shown o B- o m Na-DNA a 92% RH by Lang idge and Wilson
[38] and o samples subme ged in PEG solu ion by Podgo nik e al. [11]. The wo peaks
can be indexed as he 110 and 200 e lexions espec i ely om he hexagonal la ice. The
d-spacing ela ed wi h a gi en peak is d= 2π/QCwhe e QCis he cen e o he peak and
he ela ion be ween he Mille indices and he la ice pa ame e a, co esponding o he
axis- o-axis dis ance be ween wo molecules, is
80
(a) (b)
(c) (d)
Figu e 4.2: Recip ocal space maps o he Na-DNA ibe s in he longi udinal ( op) and
ans e sal (bo on) o ien a ions. a) and c) a e he maps o ibe s humidi ied o 92% RH.
b) and d) a e maps o ibe s subme ged in a PEG6K-17% solu ion. Da a measu ed in D16.
81
(a) (b)
Figu e 4.3: Low Q-pa o he ecip ocal space maps o he longi udinal o ien a ion o a)
he Na-humid ibe s and b) he ibe s subme ged in PEG6k-17%. Da a measu ed in IN3.
(a) (b)
Figu e 4.4: Sum o he in ensi y o e he sample o a ion angles o he ans e sal ecip ocal
space maps o cons an sca e ing ec o as a unc ion o Q. The cu es ha e been shi ed
e ically o cla i y. Red lines a e he i o he da a. Da a on he le we e measu ed on
D16, da a on he igh on WOMBAT.
82
Sample Iad (˚
A) ∆a
aHu (%)
PEG6k-17% 28.24 ±0.05 14.54 ±0.91
PEG8k-15% 26.92 ±0.06 9.18 ±0.99
PEG8k-20% 26.11 ±0.04 5.90 ±0.81
PEG6k-20% 25.48 ±0.03 3.33 ±0.70
PEG6K-40% 24.08 ±0.03 −2.35 ±0.62
Humid ibe s 24.66 ±0.09 0
Table 4.1: Pe cen age inc ease in he in e molecula spacing o Na-DNA ibe s subme ged
in PEG solu ions Wi h Respec o he Humidi ied Fibe s.
a=d(4
3(h2+kh +k2))1/2(4.1)
The cen e s o he peaks o each sample we e de e mined by i ing wo Gaussian unc-
ions wi h a linea backg ound. The esul s o he i s can be seen in ig. 4.4. The la ice
pa ame e o he Na-humid sample was calcula ed using he a e age a om bo h peaks.
The esul was aHu = 24.66 ±0.09 ˚
A, which is consis en wi h p e ious esul s [38]. The in-
e molecula dis ances o he o he samples we e compu ed analogously and he pe cen age
inc ease in in e molecula dis ance wi h espec o he humidi ied ibe s was calcula ed. Ta-
ble 4.1 shows he alues o he pe cen age inc ease and he in e axial dis ance (Iad) o each
sample. All he samples swelled unde subme sion (Iad inc eased) excep o PEG6K-40% in
which he osmo ic p essu e comp essed he ibe s o Iad sho e han ha o he Na-humid
ibe s.
4.2.2 Fibe s subme ged in e hanol solu ions
Six samples subme ged in deu e a ed e hanol solu ions we e in es iga ed wi h neu ons a
oom empe a u e: Na-DNA in 60% e hanol-d6 ( / ) wi h 0.1M NaCl (Na-60%-0.1); Na-
DNA in 66% wi h 0.1 M NaCl (Na-66%-0.1); Na-DNA in 66% wi h 0.01 M NaCl(Na-66%-
0.01); Li-DNA in 20% (Li-20%); Li-DNA in 60%(Li-60%); and Li-DNA in 80% (Li-80%).
83

All he solu ions o li hium samples had a LiCl concen a ion o 0.1Mand so i has no
been included in he code o he sample. As a e e ence o he li hium samples, Li-DNA
ibe s humidi ied a 75% RH (Li-humid) we e also measu ed.
E hanol mix u es p esen some ad an ages o e polyme solu ions o he s udies o DNA
ibe s using neu on sca e ing: a) hey do no con ain long-chain polyme s which con ibu e
o he sca e ing o he sample and could mask he signal o he DNA. b) ully deu e a ed
e hanol is easily accessible while ully deu e a ed PEG is p ohibi i ely expensi e. Minimizing
he amoun o 1Hin he sample is impo an o neu on sca e ing since i con ibu es o
he incohe en sca e ing and deg ades he peak-signal- o-noise a io.
As shown in sec. 4.1 he Na- ibe s subme ged in e hanol unde go a B- o-A ansi ion
due o he e hanol d as ically educing he wa e ac i i y o he solu ion [61].
Fig. 4.5 shows a longi udinal ecip ocal space map o Na-66%-0.1. I shows o -axis
peaks cha ac e is ic o he A- o m DNA as p esen ed in sec. 3.1.1. This is consis en wi h he
X- ay measu emen s p esen ed in p e ious sec ions and wi h he li e a u e (sec. 4.1 and [61])
which p o ed ha he e hanol-induced B- o-A ansi ion happens a e hanol concen a ions
be ween 60%-70%. I is impo an o no ice ha he 10 h laye peak s ill emains al hough
i is much weake . The supe posi ion o B- and A- o m ea u es indica es ha he sample is
a mix u e o con o ma ions. Mos o he molecules a e in A- o m bu some o hem a e s ill
hyd a ed enough o be in B- o m. I can be said ha he sample has ”B- o m con amina ion”.
As p esen ed in sec. 3.1.1 e idence o con o ma ional mix u es we e p e iously de ec ed using
neu on sca e ing and o he echniques.
The in luence o he sal concen a ion on he amoun o e hanol needed o cause he
A- o-B ansi ion has been p e iously epo ed [58]. Highe sal con en seems o a o he
A- o m. Neu on da a suppo his. Fig. 4.6a shows he high-Qpa o he longi udinal
ecip ocal map o he Na-66%-0.01 sample. The 10 h laye B agg peak is s ong and he o
axis peaks a e weak. Fig. 4.6b show he low-Qpa o he map. A B agg peak appea s a
(QH, QK) = (0.45,0.3) which is usually ela ed wi h A- o m DNA (sec. 3.1.1). These esul s
sugges his sample is composed p edominan ly by B-DNA wi h some A- o m con amina ion
84
Figu e 4.5: Recip ocal space map in longi udinal o ien a ion o he Na-66%-0.1 sample.
Measu ed in IN3.
in opposi ion o he simila sample wi h 0.1M NaCl. The lowe NaCl con en o his
sample seems o inc ease he numbe o molecules which emain in he B- o m.
Fig. 4.6c shows he 10 h laye peak o he Na-60%-0.1 sample. I sugges s ha his
sample is in he B- o m which is consis en wi h he p e ious p esen ed X- ay da a bu
some e y weak o -axis ea u es may be asse ed o exis a (QH, QK) = (1.6,0.5) ˚
A−1and
(1.6,−0.5) ˚
A−1. In addi ion, he low-Qpa o he longi udinal ecip ocal space map (shown
in ig. 4.6d) shows clea ly he A- o m B agg peak men ioned abo e. I seems like he Na-
60%-0.1 sample has some A- o m con amina ion e en hough i was no app eciable in he
X- ay images.
Simila measu emen s p o ed ha Li-DNA ibe s show a pu e B- o m a e hanol concen-
a ions up o 80% (compa e ig. 4.6e and 4.6 wi h sec 3.1.1).
He ea e Li-DNA ibe s subme ged in e hanol will be conside ed o be in a pu e B- o m.
On he con a y, Na-DNA ibe s subme ged in e hanol concen a ions equal o abo e 60%
e hanol in olume would be conside ed o ha e some deg ee o A/B mix u e o con o ma ions.
The e ec o he subme sion o he Na- and Li-DNA samples in e hanol on he in e axial
85
(a) (b)
(c) (d)
(e) ( )
Figu e 4.6: Longi udinal ecip ocal space maps (le :high-Q, igh :low-Q) o : Na-66%-0.01
[(a), and (b)]; Na-60%-0.1 [(c), (d)]; and Li-80% [(e) and ( )]. Measu ed in IN3.
86
dis ance (Iad) was add essed using he same p ocedu e as o he PEG samples. Recip ocal
space maps in he ans e sal o ien a ion we e measu ed and he in ensi y was summed o e
he sample o a ion angles ( o cons an Q) and plo ed as he magni ude o Q.
Fig. 4.7 shows ep esen a i e examples o he ecip ocal space maps collec ed on D16 o
gauge he in e molecula dis ance o he samples subme ged in e hanol solu ions along wi h
he humidi ied Li- ibe s. Fig. 4.7a is iden ical o ig. 3.2a wi h h ee ing-like e lec ions,
one s ong and cen e ed a Q≈0.3˚
A−1and wo weake ones a Q > 0.3˚
A−1. In he maps
o he samples subme ged in e hanol a ea u e can be seen a a ound 0.3˚
A−1which was no
p esen in hei PEG coun e pa s ( ig. 4.4). Fo he Li-DNA ibe s he adial dis ibu ion
o his new ea u e is homogeneous. Fo he Na-DNA ibe s, he e is a guably a spo o
highe in ensi y cen e ed a app oxima ely (QL, QK) = (0.3,0) which is simila o he peak
obse ed in ig. 3.2b, he pa e n o a pu e A- o m sample. This is ano he p oo ha he
Na-DNA ibe s subme ged in e hanol ha e a mix u e o con o ma ions A and B.
The esul o he summa ion o e he o a ion angle o equal Qs o he e hanol samples
can be seen in ig. 4.8.
The da a o he Li- ibe s humidi ied a 75% RH (black in ig. 4.8a) show a leas h ee
clea e lexions a app oxima ely 0.3, 0.58 and 0.68 ˚
A−1. The o he Li-samples show co e-
sponding e lexions. Fo all Li- ibe s he e lexion a 0.3˚
A−1is composed o wo peaks which
a e e y close. This is pa en o he Li-20% sample and i is sugges ed o he es o he
samples due o he ail o he e lexion in he low-Qpa and he asymme y o he e lexion.
The e o e he e a e ou e lexions o conside in each cu e ela ed wi h Li-samples. These
cu es a e a he di e en om wha was obse ed o he same measu emen s o PEG
samples. The double-peak ea u e is no p esen ed in he PEG samples and he p e iously
obse ed s ong peak a a ound 0.5˚
A−1appea s much weake in he e hanol samples.
I has been epo ed ha Li-DNA ibe s humidi ied a 75% RH ha e an o ho hombic
packing s uc u e o i s molecules wi h wo molecules pe uni cell in equi alen posi ions
(0,0,1
6) and (1
2,1
2,−1
6) [38]. The di e en alues in he z-axis mean ha neighbo ing molecules
a e displaced wi h espec o each o he along he ibe axis. In an o ho ombic la ice he
87
we e p epa ed wi h an iden ical bu e (sec. 2.1.1). The PEG-concen a ion ange o he
s udied samples was 5 < C%<40 whe e C%is he PEG concen a ion in weigh pe cen .
Th ee o he ypes o samples we e measu ed in addi ion o ibe s subme ged in PEG
solu ions: ibe s equilib a ed in a humid a mosphe e wi h 92% ela i e humidi y (Na-humid
ibe s); he same DNA used o he p epa a ion o he ibe s (salmon es es) dissol ed in
he bu e used o p epa e he PEG solu ion; and ibe s subme ged in he bu e . No e
ha subme sion in PEG- ee bu e caused pa ial dissolu ion o he ibe s, bu due o he
ela i ely low solubili y o he DNA in wa e (10 mg/ml o a saline bu e acco ding o he
p o ide ) mos o he DNA emained in ibe o m.
The calo ime y da a o e e y sample showed a well de ined single-peak ela ed wi h he
excess hea capaci y o he mel ing ansi ion. Fig. 4.9a shows ep esen a i e examples o
he da a. I displays he speci ic hea as a unc ion o empe a u e o he humid ibe s and
ibe s subme ged in a solu ion o PEG6k-20%, along wi h he espec i e i s o he cu es
using a Gaussian unc ion and he ac ion o closed base pai s ( DS) calcula ed using eq.
2.6. The mel ing empe a u es, Tm, a e highligh ed.
Fig. 4.9b shows he Tmo : he humid ibe s (92% RH); he DNA dissol ed in he bu e ;
he ibe s subme ged in PEG- ee bu e ; and o he subme ged ibe s in PEG solu ion as a
unc ion o PEG concen a ion ([PEG]).
DNA molecules dissol ed in solu ion a e less con ined han he DNA molecules o he
ibe s subme ged in he PEG- ee bu e . Excep o ha , he DNA o bo h samples a e
subjec ed o he same condi ions (hyd a ion, ionic en i onmen e c). The Tmo DNA ibe s
subme ged in bu e is highe han Tm o he DNA dissol ed in he same bu e . The e o e i
is p obable ha con inemen is he o igin o he highe Tm o he subme ged ibe s. A simila
e ec was epo ed p e iously in [99], in his s udy he ansi ion be ween DNA dispe sed in
solu ion and an agg ega ed liquid-c ys alline s a e inc eased he Tmmeasu ed by di e en ial
scanning calo ime y. Mo e ecen ly, consis en esul s we e published in [100] whe e a shi
o he DNA mel ing empe a u e o se e al deg ees occu ed due o he agg ega ion o DNA
molecules. As explained in sec. 3.3.1, in e ac ion be ween densely packed DNA molecules
94

(a) (b)
(c)
Figu e 4.9: a) The hea capaci y pe uni mass, ∆c, o Na-DNA ibe s equilib a ed in
an a mosphe e and 92% RH and subme ged in a solu ion o PEG6k-20% w/w is plo ed
wi h solid hick black lines, he solid hin ed lines ep esen he i o he da a, he blue
dashed lines a e he ac ion o closed base pai s as a unc ion o empe a u e. The Tms
a e highligh ed. b) Mel ing empe a u e measu ed o a dilu e solu ion o DNA, DNA ibe s
humidi ied a 92% RH, ibe s subme ged in bu e and ibe s subme ged in solu ions o
PEG1k, PEG6k and PEG8k as a unc ion o he [PEG]. c) Wid h o he ansi ion o he
same samples o panel b). The g een line ma ks he alue o he wid h o he humid ibe s.
E o ba s ep esen he s anda d de ia ion o measu emen s on iden ical samples.
95
can heo e ically inc ease Tm.
The Tm o PEG samples we e consis en ly highe han o ibe s subme ged in bu e
wi h no PEG. Tminc eases linea ly wi h [PEG] and he end is equi alen (wi hin e o
ba s) o PEG6K and PEG8K. The beha io o Tmas PEG1K concen a ion inc eases is
app eciably di e en .
Simila e ec s we e epo ed o DNA dissol ed in PEG solu ions [82, 83] and we e
explained ia he excluded olume e ec (sec. 3.3.2). The excluded olume could be he
main e ec explaining he s abiliza ion caused by PEG1K. PEG1K is signi ican ly sho e
han PEG6K which is supposedly he sho e PEG which is excluded om he DNA ibe s
([67] and sec. 3.1.3). I he PEG1K can pene a e he ibe s i will sha e he same space as
he DNA and he sample will be quali a i ely simila o a e y dense DNA solu ion in which
he excluded olume would be an impo an ac o .
Howe e , o PEG6K and PEG8K i is easonable o assume, based on p e ious e idence,
ha he PEG molecules did no pene a e he ibe s [11] and hus only a small pe cen age
o he DNA molecules in he sample a e in con ac wi h PEG molecules. Knowing ha he
wid h o he mac oscopic DNA ibe s is ≈0.5mm, i one assumes ha he DNA molecules
o ming he ibe ha e a ha d diame e o 20 ˚
A and hey a e closely packed so ha he e
is no sepa a ion be ween molecules, he pe cen age o DNA molecules in he su ace o
he ibe s can be oughly es ima ed as less han 1%. The e o e he excluded olume and
speci ic in e ac ions o he PEG wi h DNA canno a ec signi ican ly he mel ing ansi ion.
Mo eo e , he end o Tmas [PEG] is inc eased seems o be he same o PEG6K and
PEG8K which is consis en wi h he excluded olume ha ing a insigni ican e ec in he
ansi ion ([82] and sec. 3.3.2).
When DNA ibe s a e subme ged in PEG6K and PEG8K solu ions, he e is a well de ined
a e age in e axial dis ance which dec eases as [PEG] inc eases (due o he osmo ic p essu e
o he solu ion which g ows wi h [PEG]) as can be seen in able 4.1 and also in [10, 11].
The e o e he con inemen in hese samples is inc easing wi h [PEG]. As p esen ed in sec.
3.3.1 i may be he main ac o in he inc ease o Tmo he samples subme ged in high
96
Pa ame e Value
κ−19.63 ˚
A
Ra9˚
A
P34 ˚
A
Φs0.8π
a3.4˚
A
θ 0.8
s80
c0.4
σ016.8µC/cm2
Table 4.4: Pa ame e s used in he calcula ion o /(16π2ασ0) and he heo e ical mel ing
empe a u e. No e ha he alue o κ−1 he e was used only o he calcula ion o he
in e molecula oce. I was adjus ed o he calcula ion o Tm(see ex ).
molecula weigh PEG solu ions.
This idea can be u he explo ed by combining he calo ime y da a o Tmwi h he
in e axial dis ance (Iad) measu ed by neu ons and he models o DNA con inemen de eloped
by Ko nyshe and Leikin p esen ed in sec. 3.2. Fig. 4.10b shows a compa ison o his model
wi h ou expe imen al da a. The magni ude /(16π2ασ0) is p opo ional o he in e ac i e
o ce be ween wo DNA molecules as p edic ed by he model [68]; calcula ed using equa ions
3.6. The pa ame e s used a e p esen ed in able 4.4. (They a e Ra,P, Φsand κ−1 o
Debye leng h). The alues o Raand Pa e easonable o B- o m DNA, 0.8πis a usually
accep ed alue om he li e a u e [68] and he Debye lengh was calcula ed based on he
sal con en o he solu ion (0.1M NaCl) as done in [101]. The model p edic s an a ac i e
o ce be ween molecules which inc eases as he in e axial dis ance dec eases.
Fig. 4.10 shows ha bo h Tmand he wid h o he ansi ion a e qui e co ela ed wi h he
in e ac ion o ce o e mos o he ange s udied which suppo s he idea o he con inemen
being he main ac o in he e ec o he PEG in he ibe samples.
This co ela ion does no hold a Iad = 28.24 ˚
A. Wi hin he model he a ac ion be ween
97
(a) (b)
Figu e 4.10: a) Le scale: Blue squa es a e he mel ing empe a u es measu ed by calo ime-
y as a unc ion o he in e axial dis ance be ween molecules (Iad). Righ scale: he ed
line is p opo ional o he absolu e alue o he a ac i e o ce be ween molecules p edic ed
by eq. 3.6. b) Le axis: Blue squa es a e he wid h o he mel ing ansi ion measu ed by
calo ime y as a unc ion o Iad. Righ axis: he ed line is p opo ional o he o ce o he
p e ious panel.
98
DNA molecules is closely ela ed o he non- andom alignmen o opposi e s ands which is
de ined by he ela i e o a ion o he wo helices (Φ1-Φ2) [68]. The selec ion o Φ1-Φ2in
he p esen calcula ion was based on a minimiza ion o he in e ac ion ene gy which holds
a dis ances sho e han R∗, he c i ical sepa a ion, gi en by eq. 3.12. Subs i u ing he
pa ame e s used o compu ing he o ce o ig. 4.10 in o eq. 3.12 gi es R∗≈29.32 ˚
A. This
could ce ainly explained he b eaking o co ela ion be ween expe imen al da a and model
a Iad = 28.24 ˚
A.
Fu u e wo ks will y o imp o e he ma ching o model and expe imen al da a by chang-
ing he app oxima ion o Φ1-Φ2as R∗is app oached.
In addi ion o his quali a i e compa ison be ween heo y and expe imen , a heo e ical
p edic ion o he inc ease o Tmas Iad dec eases was ied using eq. 3.16. The pa ame e s
used o his calcula ion we e aken om he li e a u e [69] and a e p esen ed in able 4.4
excep o κ−1.θ is he ac ion od DNA cha ge compensa ed by adso bed ca ions, cis he
ac ion o adso bed ca ions in he mino g oo e o DNA and sis he dielec ic cons an o
he solu ion ( o which he alue o wa e was aken).
A Debye sc eening leng h o 9.63 ˚
A is a easonable alue o he sal concen a ion o
he solu ions he samples we e subme ged in. Howe e , when used in eq. 3.16 i ga e a
e y poo esemblance wi h he da a. Fig. 4.11 shows a compa ison o he heo e ical and
expe imen al Tmas a unc ion o Iad o a calcula ion wi h κ−1= 88 ˚
A. Eq. 3.16 allows
o p edic he a ia ion o Tmwhen Iad changes wi h espec o a e e ence Tm, which is
highligh ed in he igu e, and o which he heo e ical Tmis assumed o ma ch exac ly he
expe imen al da a.
Fig. 4.11 shows ha , wi h his la ge alue o κ−1 he model ma ches he da a ema kably
well. Theo y and model di e o he Tma 28.24 ˚
A, his p edic ion o Tmis based in he
calcula ion o he o ce p esen ed in ig. 4.10 (sec. 3.3.1 and [69]) so he ange o applicabili y
should be he same. The e o e i is no su p ising ha he p edic ion o Tm ails a Iad = 28.24
˚
A.
99

Figu e 4.11: Compa ison be ween expe imen al and heo a ical Tmas a unc ion o Iad o a
Debye sc eening leng h o 88 ˚
A.
κ−1= 88 ˚
A ela es o a solu ion wi h a sal concen a ion oughly wo o de s o magni ude
lowe ha he expec ed Debye leng h o he solu ions o he samples. The samples could
exhibi a smalle ion ac i i y han expec ed because o he p esence o PEG which was no
accoun ed o in he calcula ion o κ. Howe e , a wo o de s o magni ude dec ease in he
ionic s eng h looks un easonable. The model, which ge s he Tm igh jus by changing one
pa ame e , may ha e a ela i ely small sho coming.
4.3.2 Fibe s subme ged in e hanol
Calo ime y da a we e collec ed in Na/Li-DNA ibe s subme ged in e hanol solu ions as
a unc ion o he e hanol concen a ions be ween 20% and 85% ( / ). The solu ions a e
desc ibed in sec. 2.1.1. All samples o he calo ime y s udy o his sec ion con ained 0.1
Mo he co esponding sal .
Fig. 4.12a shows examples o calo ime ic cu es collec ed in Na- and Li-DNA ibe s
subme ged in e hanol solu ions. The cu es o Li-DNA ibe s in he whole concen a ion
ange s udied we e quali a i e iden ical o he PEG case wi h a single peak on a cons an
100
backg ound as seen in he igu e o Li-60% e hanol (black squa es). This is also he case
o Na-DNA o e hanol concen a ions up o 50%. Howe e , a 60% e hanol ( ed ci cles) a
ail appea s a he high empe a u e side o he peak making i app eciably asymme ic and
hin ing a he exis ence o a second, weake , con ibu ion o he mel ing cu e apa om he
main s ong peak. Fo Na-66% ibe s (blue iangles in he igu e) his second con ibu ion
o he mel ing cu e is pa en since he e is a smalle mel ing peak a highe Twi h espec
o he s ong main one.
Na-DNA ibe s showed some deg ee o A- o m con amina ion when subme ged in 60%
o highe e hanol solu ions (sec. 3.1.1 and sec. 4.2.2) while Li-DNA emained in B- o m o
he whole e hanol concen a ion ange s udied. These changes in he shapes o he mel ing
cu es o Na-DNA wi h inc easing e hanol concen a ion a e mos p obably ela ed wi h
he appea ance o A-con amina ion and he inc ease o he numbe o molecules in A- o m
as he e hanol concen a ion is inc eased. Wi hin his in e p e a ion, i is easonable o
assume ha mos o he molecules in he Na-66%-0.01 we e in B- o m and unde wen he
mel ing ansi ion wi h a mel ing empe a u e ≈63 ◦C. The ac ion o he sample in A
o m emained in he helical o m and mel ed a ≈70 ◦C( he cen e o he seconda y peak).
Two di e en mel ing empe a u es could be unambiguously compu ed o cu es exhibi -
ing wo clea and sepa a ed mel ing peaks. This is no he case in he samples o he p esen
s udy. All he seconda y peaks asc ibed o he mel ing o he A- o m domains a e ela i ely
e y small and supe imposed wi h he main peak. A mel ing empe a u e o A and B
domains could s ill be oughly es ima ed by i ing wo peaks o he cu e. Howe e , e en
o single peak cu es, iden i ying he mel ing empe a u e wi h he cen e o he peak can
in oduce e o s in he calcula ion [102]. In his wo k a singula Tm(calcula ed as explained
in sec. 2.2.5) was asc ibed o he double-peak samples. These alues should be unde s ood
as weigh ed a e ages be ween he Tmo domains in B and A con o ma ions o each sample.
Special ca e mus be aken i he Tm alues epo ed he e a e o be analyzed quan i a i ely.
Fo he quali a i e discussion p esen ed in his chap e he alues a e p obably su icien .
On he con a y, calcula ing he wid h o he double-peak samples as he ull wid h a
101
hal maximum o a single peak (as desc ibed in sec. 2.2.5) would be qui e meaningless. Fo
all he Na-DNA ibe s subme ged in e hanol he wid h o he ansi ion was calcula ed as
he empe a u e change necessa y o go om 25% o 75% open base pai s(using eq. 2.5).
Fo a single-peak mel ing cu e his is equi alen o ake he ull wid h a hal maximum
o he peak. This p ocedu e was used be o e, wi h calo ime y and o he echniques able o
access he ac ion o open base pai s, o compu e he wid h o he ansi ion [103].
Fig. 4.12b shows he alue o he mel ing empe a u e and he wid h o he ansi ion
o he Na-DNA case. The mel ing empe a u e dec eases om 0% un il 70% e hanol and
aises om 70% o 80% be o e dec easing again a 90%. Cau ion mus be applied when
aking in o conside a ion he inc ease in Tma 80% since only one poin cons i u es such
inc ease. Howe e , as explained p e iously (sec. 2.2.4) he p esen ed alues o Tma e he
a e age o he measu emen on h ee iden ical samples. The e o e we belie e his inc ease is
signi ican . The wid h o he ansi ion is oughly cons an un il a leas 50% e hanol and
d ops o highe concen a ions.
Fig. 4.12c shows he same da a o Li-DNA ibe s, in his case Tmdec eases mono onically
( he local maximum in Tmdoes no exis ) and he wid h inc eases signi ican ly a 70% e hanol
and hen d ops s eeply a 80%.
Fo he e hanol samples he main ac o s explaining he o e all e ec o he e hanol in
he mel ing empe a u e is dec easing o he wa e ac i i y and he dielec ic cons an o he
solu ion as p esen ed in sec. 3.3.3.
The beha io o Tmand he wid h o he ansi ion as a unc ion o he e hanol con-
cen a ion ound in his wo k a e quali a i ely iden ical o wha was epo ed by Rupp ech
e al. (sec. 3.3.3) o e y simila samples. The quan i a i e di e ence can be explained
by di e ences in sal concen a ion o he solu ions which a ec bo h Tmand wid h [103].
Rupp ech e al. also ound a B- o-A ansi ion in Na-DNA (consis en wi h he sca e ing
da a o p e ious sec ions). They e en sugges ed ha a ange o e hanol concen a ions exis
in which he ibe s a e a mix u e o B and A o m ( ig. 3.4a and [88]) which ela es o he
A/B con amina ion ound in he samples o his wo k.
102
(a) (b) Na-DNA
(c) Li-DNA
Figu e 4.12: a) Examples o calo ime ic cu es o Na−and Li−DNA ibe s subme ged in
e hanol solu ions. Mel ing empe a u e and wid h o he ansi ion o ibe s subme ged in
e hanol solu ions as a unc ion o he e hanol concen a ion ( / ).
103
The o al in ensi y o e e y empe a u e was i ed wi h he exp ession:
I(QH) = I1+I2+IAl,P b (4.7)
A0and Bwe e no i -pa ame e s. Thei alues we e calcula ed be o e i ing a gi en
cu e. Fo he D19 da a he a e age alues o he sca e ing signal o QH<0.6˚
A−1and
QH>3.4˚
A−1we e calcula ed and a line was d awn be ween he wo alues. A0and Bwe e
aken as espec i ely he in e cep and slope o ha line. Fo he WOMBAT da a, Bwas
se o ze o and A0was de e mined by a e aging he signal o QH<0.8˚
A−1. In addi ion,
o he WOMBAT da a he di use sca e ing was ep esen ed by a single ising s ep unc ion
so he e m anh(QH−Q2
s2) in eq. 4.5 ela ed wi h he declining s ep was no included.
The cu es o he PEG solu ions a oom empe a u e we e i ed using eq. 4.5. The
esul s can be seen in ig. 4.14a and 4.14b. The alues o he pa ame e s o his i (A1,Q1,
s1,Q2,s2) we e used as pa o he ini ial se o alues o i ing he DNA da a a oom
empe a u e using eq. 4.7. The es o ini ial alues we e chosen by isual compa ison.
Fo subsequen empe a u es a wo-s age p ocess was used in o de o ge an accu a e
i when he size o he B agg peak and he di use con ibu ion became compa able. Fo a
gi en empe a u e abo e oom T, he γ om he i o he p e ious empe a u e was used
o de ine a ange in QHcen e ed a ound he DNA B agg peak (Q0−0.8γ≤Q≤Q0+0.8γ).
In he i s s age he pa ame e s o he DNA B agg peak (eq. 4.4) we e ixed, da a inside
he p e iously de ined ange we e igno ed and eq. 4.7 was i ed using he esul s o he i
o he p e ious empe a u e as ini ial alues o he pa ame e s . In he second s age da a
ou side he ange we e igno ed, he pa ame e s o eq. 4.5 and 4.6 we e ixed o he i ed
alues o he i s s age and he DNA B agg peak was i ed wi h eq. 4.7. The wo-s age
p ocess was hen epea ed wice pe empe a u e. Each new i e a ion used he pa ame e s
o he p e ious i e a ion as ini ial pa ame e s o he i . A e 3 i e a ions he pa ame e s
we e s able.
Examples o he inal i s can be seen in ig. 4.14. The i ing is e y consis en bu should
be in e p e ed wi h ca e a high empe a u es, whe e he Lo en zian peak was so small in
110

compa ison wi h he di use con ibu ion ha he gene al i had ouble con e ging. A
hese empe a u es he alues o γand Q0we e ixed o he alues o he las empe a u e
in which he i con e ged and only I0was i ed.
Fig. 4.15 shows a ep esen a i e example o he empe a u e dependence o he pa ame-
e s o he double-s ep unc ion and o he cen e o he DNA B agg peak (Q0). The cen e
o he B agg peak shi s sligh ly o smalle Qs as he empe a u e aises ( ig. 4.15b) which is
consis en wi h he mal expansion and he change in he a e age base pai dis ance due o
he elaxa ion o he base s acking because o pa ial unwinding o he helix. Q0suddenly
d ops a T≈97 ◦C. This s eep dec ease could be associa ed o a pa ial un wis o he
helix due o he g ea numbe o uns acked bases a his high empe a u e. Wi h a sudden
un wis he a e age dis ance be ween adjacen base pai s will g ow as and so he cen e o
he B agg peak will dec ease. Howe e , a his high empe a u e he peak is e y small in
compa ison o he di use backg ound he e o e, as al eady men ioned, he in e p e a ion o
Q0and o he i ed pa ame e s mus be done wi h ca e. Rega ding he he pa ame e s o
he double-s ep, hei e olu ion wi h Tis easonable bu i is e y challenging o asc ibe a
physical meaning o hem.
The i ed alues o eq. 4.6 ( ela ed wi h he aluminum and lead B agg peaks) did no
change wi hin easonable limi s wi h Twhich is consis en wi h he ac ha no signi ican
changes we e expec ed om he Al o Pb in he ange o empe a u es s udied.
Fig. 4.16 shows he e olu ion o he A0pa ame e wi h empe a u e o all he samples.
A0(T) in his igu e is no malized by i s alue a T= 20 ◦C o allow easy compa ison
be ween samples. A0(T) desc ibes adequa ely he magni ude o he inc ease o he di use
sca e ing wi h T. The igu e p o es ha he di use con ibu ion ises close o he mel ing
empe a u e in e e y sample. The inc ease a he highes T eached is app oxima ely 20%
o he PEG6K-17% (measu ed a D19) and app oxima ely 5% o he es o he samples
(measu ed a WOMBAT) . I is likely ha his quan i a i e di e ence is due o he di e en
ins umen con igu a ions. The e a e wo ac o s likely o con ibu e o he di e ence:
The i s conce ns he collima ion be ween sample and analyse . D19 had no collima ion
111
(a) (b)
(c)
Figu e 4.15: Tempe a u e dependence o he pa ame e s o he double-s ep unc ion and he
cen e o he DNA B agg peak o he PEG6K-17% sample as ound by he i . a) A1, b)
Cen e s o he double s ep unc ion (Q1and Q2) and o he B agg peak (Q0). c) G adien s
o he double s ep unc ion (s1and s2).
112
Figu e 4.16: Pa ame e A0 om equa ion 4.5 as a unc ion o he educed empe a u e
(T/Tm calcula ed in Celsius) no malized by i s alue a 20 ◦C o each sample. A0is he
a e age o he in ensi y a low Qand ep esen s he magni ude o he di use con ibu ion.
The cu e o he PEG8k-20% sample is shi ed downwa ds by 0.05 uni s o cla i y.
while WOMBAT used an oscilla ing collima o . In p inciple, an oscilla ing collima o limi s
only he sca e ing gauge olume o he sample. Howe e , he di use sca e ing esembles, o
i s o de , incohe en sca e ing while he sca e ing angles o he B agg peaks a e eason-
ably well sel -collima ed. The WOMBAT oscilla ing collima o also limi s ins an aneously
he di e gence o he sca e ed beam o 0.5◦, hence educing an incohe en con ibu ion
ela i e o a cohe en signal. This pa ly explains he la ge di use signal in he D19 da a.
The second conce ns he kinema ic limi s on he ene gy in eg a ion o he neu on in-
s umen . Nei he WOMBAT no D19 had any means o analyze he inal ene gy o he
neu on. Bo h ins umen s he e o e in eg a ed o e neu on ene gy ans e s. The allowed
ene gy and momen um ans e s a e limi ed by he ene gy o he inciden neu ons, which
was 14.20 meV o D19 and 3.83 meV o WOMBAT. D19 he e o e in eg a ed o e a much
la ge ene gy window han WOMBAT. Fibe DNA has subs an ial spec al weigh om 2
o 25 meV [104] , and D19 will cap u e hese la ice dynamics whe e WOMBAT canno .
The dynamics o DNA will change subs an ially as he mel ing empe a u e is app oached,
gi ing a non-linea inc ease in he spec al weigh o all Qand p opo iona ely mo e di use
sca e ing in he D19 da a.
113
Fig. 4.16 also shows ha he alues o A0do no inc ease mono onically wi h empe a-
u e close o mel ing, pa icula ly o he PEG6k-17% (black squa es) and he PEG6k-20%
( ed ci cles) samples. The da a shows small peaks in A0which may also be obse ed in
ig. 4.13a and ig. 4.13b as e ical lines close o he empe a u e a which he B agg peak
disappea s. As p e iously s a ed, he empe a u e s abili y a he mel ing empe a u es o
hese samples was a he poo (sec. 2.4.1 and 2.4.1). The ampli ude o he di use sca e ing
inc eases s eeply wi h empe a u e in his ange. The pilo s udy [12] showed ha he mel -
ing ansi ion is, o some ex en , e e sible in hese samples gi en ha he mel ing is no
comple e. I is possible ha he a ia ions in A0a e coupled wi h he empe a u e s abili y,
and ha he inal egis e ed alues a e indica i e o he weigh ed a e age o he luc ua ing
in ensi y o e he du a ion o he measu emen .
Fig. 4.17 shows he i ed I0and γas a unc ion o empe a u e o he ou samples.
Fo all samples , he in ensi ies dec eases apidly and he peak e ec i ely disappea s o e he
ange 0.95 ≤T/Tm≤1.05. Fo he WOMBAT da a, he in eg a ed in ensi ies and wid hs
s ay oughly unchanged un il close o he mel ing empe a u e, as seen in p e ious s udies
on humidi ied ibe s [7, 8]. This sugges s ha , as o humidi ied ibe s, long segmen s o
DNA emain un il he e y las s ages o mel ing. These de ine he wid h o he B agg peak.
A he empe a u e whe e hese las segmen s dena u e, he in ensi y o he B agg peak
is so weak ha i is los in he di use sca e ing and any change in he wid h canno be
unambiguously de e mined om a i .
The PEG6k-17% sample measu ed on D19 shows a somewha di e en beha io . Bo h I0
and γinc ease s eadily be o e he Tm. This di e ence in he beha io o he i ed pa ame e s
wi h espec o he WOMBAT da a may be ela ed o he di e en in eg a ion o e neu on
ene gy ans e s o bo h ins umen s. An inc ease in he phonon dynamics wi h inc easing
empe a u e can mani es i sel as an inc easing wid h in he ails o a B agg peak. Such
e ec would be mo e d ama ic in D19 due o he expanded ene gy in eg a ion. Al hough
a neu on inelas ic sca e ing measu emen would be necessa y o p o e he hypo hesis, i
appea s likely ha he inc easing I0and γwi h empe a u e seen on D19 a e due o he
inc eased dynamics o he ibe DNA as mel ing is app oached.
114
(a) PEG6K-17% (b) PEG6K-20%
(c) PEG8K-15% (d) PEG8K-20%
Figu e 4.17: Compa ison be ween heo y and expe imen o he da a o he sample sub-
me ged in PEG. PEG6k-17% a) was measu ed on D19, he o he samples b)-d) on WOM-
BAT. A educed empe a u e, T/Tm(calcula ed in Celsius) was used whe e Tmis he mel ing
ansi ion o he sample. In each panel he h ee uppe cu es ela e o he scale in he le ,
hey a e he i ed in eg a ed in ensi y, I0(blue open ci cles), he heo e ical in eg a ed in-
ensi y ( hick ed line) and he ac ion o closed base pai s calcula ed wi h calo ime y (eq.
2.6) o a co esponding sample (black dashed line), he i ed in eg a ed in ensi ies ha e
been di ided by a bi a y numbe s o easy compa ison. The lowe cu es ela e o he scale
in he igh , hey a e γ, he i ed wid h o he peak (black close ci cles), and he heo e ical
wid h o he peak ( hin ed line).
115

Analysis using he Pey a d-Bishop-Dauxious model
The PBD model was used o make a quan i a i e analysis o he i esul s, ollowing a
p e iously- epo ed p ocedu e [7, 94]. The model can be used o calcula ed he p obabili y
ha a base pai o a gi en sequence is closed a a gi en empe a u e. The p obabili y o
a gi en size dis ibu ion o closed segmen s can hen be de e mined, as explained in sec.
3.4.1. The expec ed di ac ion pa e n, S(Q), om he sequence can hen be calcula ed (as
p esen ed in sec. 3.4.1) and compa ed o he expe imen s.
The pa ame e s o he Hamil onian he model uses o desc ibed he DNA molecule (eq.
3.17) we e e ined by compa ing he calcula ed mel ing cu e wi h he da a om calo ime y.
A segmen o he genome o A lan ic Salmon epo ed p e iously [105] (10000 bases
s a ing a si e 50000) was chosen o he calcula ion. In he modeling Wwas assumed o be
he same o all combina ions o adjacen base pai s, which has been shown o be easonable
o desc ibing he mel ing cu es o long DNA molecules [7, 92]. The DNA sequence was
aken in o accoun only o he calcula ion o he in a-pai po en ial Vj.
All alues o he pa ame e s o he Hamil onian used o model he da a, excep o DAT
and DGC, a e he same as p e iously used in he s udy o humidi ied ibe s [7]. They a e
shown in able 4.5. DAT and DGC ep esen he ene gy ba ie o base pai dissocia ion and
hus hey a e he main ac o in se ing he Tmo he heo e ical mel ing cu e. As shown
in ig. 4.9b, he mel ing empe a u e when he ibe s a e subme ged in he PEG solu ions
inc eases wi h PEG concen a ion. Thus DAT and DGC needed o be scaled o ep oduced
he mel ing empe a u e o each sample. The alues o he dep h o he Mo se po en ial
shown in able 4.5 (DAT,95,DGC,95) wi h he chosen sequence and pa ame e s co espond o
Tm= 95 ◦C. Fo a sample wi h a Tm=Tm,x in Celsius he alue o DAT was scaled by:
DAT,x =DAT,95(Tm,x + 273
95 + 273 ) (4.8)
and an analogous exp ession was used o he alue o DGC.
116
Pa ame e s Value
a3.4˚
A
yc1.5˚
A
k4.5 10−4eV/˚
A2
ρ50
b0.2 ˚
A−1
αAT 4.2 ˚
A−1
αGC 6.9 ˚
A−1
DAT,95 0.13150 eV
DGC,95 0.17150 eV
Table 4.5: Pa ame e s used in he PBD model.
Sample <Λ2>(˚
A)
PEG6k-17% 0.45
PEG8k-15% 0.35
PEG8k-20% 0.33
PEG6k-20% 0.33
Humid ibe s 0.18
Table 4.6: S anda d de ia ion o he dis ance be ween consecu i e base pai s used o calcu-
la ed he S(~
Q) o each sample.
Rega ding he calcula ion o he heo e ical S(Q) (sec. 3.4.1); a alue o <Λ2>= 0.18
˚
A, epo ed by La e y e al. [106] , was used o model he mel ing o humidi ied DNA
in p e ious wo ks [7]. This alue ga e wid hs o he B agg peak ha we e oo small in
compa ison o he expe iemn al alue o he subme ged samples. <Λ2>was inc eased o
model he cu en da a. The alues used can be ound in able 4.6.
I is unlikely ha he e ec s o he PEG can di ec ly modi y he s anda d de ia ion o
he dis ance be ween base pai s along he molecule. Mo e likely, he inc ease o <Λ2>
accoun ed phenomenologically o o he diso de e ec s, such as an inc eased a ia ion o
117
he alignmen o he molecules, when he ibe s we e subme ged.
The Debye-Walle ac o , ∆, is a unc ion o bo h < σ2>and <Λ2>and i is possible
ha he inc eased B agg wid hs a e a leas pa ly due o he mal luc ua ions ha we e
no linea wi h empe a u e. Howe e , wi hou inelas ic sca e ing da a i is no possible o
say whe he he la ge wid hs we e due o inc eased s uc u al diso de , inc eased he mal
luc ua ions, o a combina ion o bo h ac o s.
The calcula ed S(~
Q) o each Twas i ed wi h eq. 4.4 o de e mine alues o I0and γ
as a unc ion o T ha could be compa ed o he expe imen al da a.
Fig. 4.17 shows a compa ison o he expe imen al and heo e ical in eg a ed in ensi ies
and wid hs o he peaks o each sample along wi h he ac ions o open base pai s calcula ed
by calo ime y. The da a a e plo ed as a unc ion o educed empe a u e, T/Tm, as he e
a e di e ences be ween he empe a u es eco ded wi h neu ons and calo ime y due o
di e en sample en i onmen s.
O e all, he model ma ches all he da a quan i a i ely. The ag eemen is excellen o
he samples measu ed on WOMBAT. While he magni udes o he model ma ch he D19
da a and he model does p edic a linea inc ease in wid h wi h empe a u e, he model ails
o adequa ely desc ibe he g adien o he inc easing wid h and o he in eg a ed in ensi y
wi h empe a u e below Tm. This may be an aspec o he modelling ha does no ully
cap u e he DNA phonon dynamics which, combined wi h he expanded ene gy in eg a ion
on D19, a e he possible cause o he inc eases in I0and γ. Howe e , he magni udes o he
in ensi ies and wid hs a e ma ched and modelling may be ega ded as sa is ac o y.
Discussion
The da a a e an imp o emen on he pilo s udy o DNA ibe s subme ged in PEG solu ions
[12]. The use o PEG solu ions allowed he ibe s o swell wi hou losing hei o ien a ion.
The neu on expe imen was able o ollow he e olu ion o he B agg peak wi h empe a u e.
The PBD model was able o desc ibe he da a, and he desc ip ion was pa icula ly good
118
o he WOMBAT da a.
The p e ious s udy showed ha he ansi ion is, o an ex en , e e sible [12]. In his
sense, i is simila o a c i ical phase ansi ion. The di use sca e ing in ig. 4.16 inc eases
apidly a he mel ing empe a u e. The PEG6k-17% and PEG6k-20% samples show de-
pa u es om a mono onic inc ease in he di use sca e ing in ensi y close o he mel ing
empe a u e. These measu emen s su e ed om ela i ely la ge empe a u e luc ua ions
a ound he mel ing empe a u e, and i is likely ha he eco ded in ensi y a ia ions a e
a esul om he ime-a e age o he concomi an ly luc ua ing di use signal. The mea-
su emen s wi h be e empe a u e s abili y a he mel ing ansi ion did no show his
anomalous in ensi y a ia ions.
These a ia ions do no appea o be p esen in he in eg a ed in ensi ies o he B agg
peaks o he a ec ed samples. A B agg peak is due o cohe en sca e ing om long- anged,
ime-a e aged o de , while he di use sca e ing is mo e incohe en in na u e. I may be
ha he di use sca e ing is domina ed by he DNA dynamics, pa icula ly o open base
pai s, and i s empe a u e dependence is d i en by changes in he spec al weigh . This
hypo hesis is consis en wi h he obse a ion ha D19, wi h he la ge ene gy in eg a ion,
shows a la ge inc ease in he di use sca e ing.
The PBD model uses one se o pa ame e s o DNA and is able o sa is ac o ily ep oduce
all he da a despi e he change in con inemen b ough abou by he osmo ic p essu e. This
shows ha he model is, wi hin easonable limi s, insensi i e o con inemen o he DNA
and es ablishes ha he analysis shown in p e ious wo ks [7, 8, 94] is sound.
I is no ewo hy ha mos o he pa ame e s in able 4.5 a e he same as hose o he
humidi ied ibe s [7, 94] and o genomic DNA in solu ion [92]. The only di e ences lie in
he alues o DAT and DGC. Rega ding he model, he unique e ec o he subme sion o
he ibe s in PEG solu ions on he mel ing ansi ion seems o be in adjus ing he appa en
dissocia ion ene gy o he base pai s.
119
be o e he mel ing empe a u e (T/Tm≈0.9) is obse ed. This looks signi ican ly di e en
ha he s eady (linea like) inc ease o he wid h o he PEG sample measu ed in D19 ( ig.
4.17a).
Discussion
The expe imen al da a p esen ed in his sec ion p o es ha he ansi ion can be moni o ed
equally well wi h neu on sca e ing in samples subme ged in deu e a ed e hanol solu ions
wi h he ad an age o he educed incohe en sca e ing wi h espec o he samples wi h
p o ona ed PEG solu ions.
The inc ease in he di use sca e ing (quan i ied by he pa ame e A0plo ed in ig. 4.21)
is quali a i ely iden ical o he da a o PEG6K-17% which was also measu ed in D19. This
indica es ha he la ge inc ease o he di use sca e ing in he PEG6K-17% sample as T
aises is no a sample-speci ic beha io and ein o ces he idea ha he magni ude o his
inc ease is linked o he ins umen al con igu a ion.
The double-s ep unc ion seems o be in gene al less op imal o desc ibed he backg ound
o he e hanol samples. Howe e , he i o wo samples (Na-66%-0.01 and Li-60%) is
ega ded as sa is ac o y and u u e a emp s o ep oduce he expe imen al da a wi h he
PBD model will be pe o med.
I is expec ed ha he pa ame e s necessa y o model he da a o hese samples will di e
signi ican ly om he PEG. The e ec i e po en ial o he binding be ween he bases ( ela ed
wi h DAT and DGC pa ame e s) is a ec ed by he epulsion be ween he DNA s ands which
is educed by he p esence o ions a ound he DNA. This elec os a ic e ec is s ongly
a ec ed by he dielec ic cons an o he sol en which changes wi h he amoun o e hanol
added o he solu ion.
Rega ding he s acking o he bases, i is known o highly depend on he hyd ophobic
in e ac ions [23] which mus change in he p esence o e hanol. Fo he Na-66%-0.01 sample
he case is e en mo e complex. A way o include he wo peak mel ing in he ela i ely
126

(a) Na-60%-0.1 (b) Na-66%-0.01
(c) Li-60%
Figu e 4.22: Pa ame e es o he i as a unc ion o empe a u e o he e hanol samples:
in eg a ed in ensi y (I0, open blue ci cles) and wid h (γ, closed black squa es) o he DNA
B agg peak placed a QH≈1.87 ˚
A−1; pa ame e A1o he double-s ep unc ion ( ed i-
angles) which models he di use sca e ing. The dash black line ep esen s he ac ion o
closed base pai s ( DS) calcula ed by calo ime y wi h eq. 2.6.
127
simple PBD model mus be ound. This would be a oppo uni y o es he limi s o he
model.
Fu u e expe imen al wo k will be ocused on Li-DNA ibe s since ha will elimina e he
A-con amina ion which may hinde he s eng h o he conclusions.
O e all, he empe a u e dependence o he e hanol samples is consis en wi h p e ious
da a bu shows some speci i ies ha , we belie e, jus i y u he expe imen s and da a analysis
in hese kind o samples.
128
Chap e 5
Widom-601 in es iga ed by SAS
5.1 Room empe a u e s udy
The bending and lexibili y o DNA a e o c i ical impo ance o many o i s biological
unc ions like gene egula ion, p o ein-DNA in e ac ions and DNA packing in i uses and
euka yo e cells.
Howe e he ac ual magni ude, na u e and o igin o DNA lexibili y is s ill an open
p oblem. Kahn has e iewed ecen ly expe imen al wo ks on bending and wis ing o DNA
which used DNA ing closu e, a omic o ce mic oscope and op ical weeze s me hods [107].
Disc epancies in he esul s o he di e en echniques showed ha he lexibili y o DNA is
a om being unde s ood [107].
The magni ude o he lexibili y o DNA is usually accoun ed o by he pe sis ence leng h
(lp) which, wi hin he K a ky-Po od model (sec ion 3.4.2), is de ined as he cha ac e is ic
leng h in he co ela ion o he di ec ion o he segmen s ha desc ibe he polyme . The lp
o DNA was ini ially hough o be ≈500 ˚
A which would imply ha DNA is ha d o bend
o e sho e dis ances. Howe e ecen cycliza ion expe imen s [108], luo escence esonance
ene gy ans e measu emen s [109] and small angle X- ay sca e ing [110] pe o med on sho
129
Figu e 5.1: The 145 base-pai sequence in es iga ed. The agmen in he ec angle is he
s ong posi ioning elemen , cha ac e is ic o his sequence. The TA agmen s in ed a e he
possible kink posi ions conside ed in he model.
chain DNA e ealed ha DNA is likely o bend spon aneously o e much sho e dis ances
han 500 ˚
A.
The wo m-like chain model is a con inuous e sion o he K a ky-Po od model and has
been widely used o desc ibing long chain DNA. Howe e , he p e iously men ioned s udies
sugges ha he wo m-like chain may no be applicable o sho chain sequences. Also,
hese s udies poin o he possibili y ha he pe sis ence leng h depends on he leng h o
he DNA.
The close-packing o DNA inside he cell nucleus is a pa icula in e es ing e en in which
he lexibili y o DNA is key o he biological unc ion. The Widom-601 sequence, shown in
ig. 5.1, has a s ong his one posi ioning agmen which has g ea a ini y o wind a ound a
his one oc ame o o m a nucleosome which is a essen ial s ep o he packing o he genome
in he cell nucleus.
C ick and Klug ied o add ess he mechanism behind he conside able olding he DNA
unde goes o o m he ch oma in. They showed in a pionee ing s udy ha DNA can o m
sha p kinks wi hou a majo dis u bance o i s s uc u e [111]. Indeed, Kinks ha e been
130
ound in he s uc u e o sho DNA chains w apped a ound a nucleosome [112] bu C ick
and Klug also hypo hesized ha kinks could occu in solu ion. This hypo hesis was ne e
de ini i ely con i med.
The Widom sequence has been p e iously s udied unde he e ec s o he s ong in e ac-
ions wi h his one p o eins, [13] o a ached o gold nanopa icles [110]. In es iga ion o he
Widom sequence ee in solu ion may p o ide he answe o he ques ion o whe he some
in insic mechanical and/o geome ical p ope ies o DNA a e esponsible o he s ong po-
si ioning e ec . The undamen al dilemma is whe he he w apping o DNA in nucleosomes
equi es a e y high elas ic ene gy, as he wo m-like chain model sugges s, o whe he he e
is a sequence-dependen ea u e o DNA, like a enhanced local lexibili y a he posi ioning
si e, ha could explain o a ou he posi ioning e ec .
The e o e he aim is o s udy DNA molecules con aining he Widom sequence dissol ed
in solu ion. Small angle sca e ing can p obe he shape o he molecules dispe sed in he
solu ion and, when used wi h an app op ia e model, he geome y and lexibili y o he
molecules can be es ima ed.
2H2O-based solu ions o Widom-601 DNA molecules we e p epa ed as desc ibed in sec.
2.1.2. Neu on and X- ays small angle sca e ing (SANS and SAXS espec i ely) da a o
hese samples we e eco ded and educed as desc ibed in p e iously (sec. 2.5.2, 2.4.1, 2.4.2
and 2.5.3). The use o he wo echniques ga e independen and complemen a y da a. SAXS
gi es a la ge signal om a much smalle mass o DNA bu X- ays a e well-known o damage
DNA du ing long exposu es. X- ay damage can hinde he expe imen bu i can also be
used as a alida ion o he analysis om undamaged-DNA da a as i will be shown below.
Neu ons a e non-ionizing adia ion and he damage hey cause o he sample is negligible.
Howe e , since he a ailable luxes a e many o de s o magni ude smalle , a g ea e mass o
DNA is needed o ob ained a usable signal.
Figu e 5.2a p esen s he SANS and SAXS cu es (I(q)) a oom empe a u e. Fig. 5.2b
shows he co esponding pai dis ibu ion unc ion (P( )), calcula ed as desc ibed in sec.
2.5.2.
131

(a) (b)
Figu e 5.2: a) SANS and SAXS da a a oom empe a u e; b) hei co esponding P( ).
The P( ) ound by bo h echniques is quali a i ely simila bu he e a e some disc epan-
cies. These a e due o he di e ences in sca e ing leng h o neu ons and X- ays which a ise
om he di e en in e ac ion mechanism o bo h adia ions wi h ma e (sec. 2.3.2). X- ays
a e mo e sensi i e o hea ie elemen s since he sca e ing leng h o hem is p opo ional o
he numbe o elec ons in he a om. Fo neu ons hyd ogen (which has a nega i e sca e ing
leng h) has he highes con as wi h he deu e a ed sol en and he e o e he neu on da a
a e mo e sensi i e o he dis ibu ion o hyd ogen in he sample.
The wo da a se s show peaks a ound 20 ˚
A. Fo he X- ay da a he peak is ela ed o he
phospha es in he ou side o he double helix which a e 20 ˚
A apa . The DNA has many
p o ons dis ibu ed along i s s uc u e, hus o sho dis ances neu on sca e ing o DNA is
well app oxima ed by he sca e ing by a bulk cylinde wi h a diame e o 20 ˚
A. Bo h P( )
cu es show a a he la egion be ween 100 and 140 ˚
A. Fo > 140 ˚
A he P( ) dec ease
s eeply un il hey each a pla eau om 300 o 390 ˚
A be o e going o 0 o > 400 ˚
A . The
oscilla ions in he 300−390 ˚
A ange in he SAXS da a may be an a e ac due o unca ion
in he measu ed Q ange which en ails missing Fou ie componen s in he P( ) calcula ion.
Howe e , he pla eau is p obably a eal ea u e since i appea s in bo h se s o da a.
The calcula ion o P( ) using he s uc u e ac o is a well-es ablished p ocedu e, which
is based on a p ecisely de ined ma hema ical connec ion be ween he unc ions (sec. 2.5.2).
Howe e , de i ing he shape o he sca e ing molecules om P( ) is no an unambiguous
132
Figu e 5.3: Rep esen a i e examples o he ou pu o he DAMMIF p og am. The dummy
a oms show he es ima ion o he mos likely shapes o he DNA in solu ion.
p ocess. The DAMMIF p og am [113], included in he ATSAS package, was used as a i s
s ep. DAMMIF s a s om he P( ) unc ion and uses simula ed annealing o ind he
shape o a se o dummy objec s which ep oduce he P( ). DNA can ha e a g ea a ie y
o con o ma ions in solu ion and mul iple uns lead o di e en inal shapes. DAMMIF
con e ges o ei he s ongly cu ed s uc u es o b anched solu ions when he P( ) shown
in ig. 5.2b is s udied. Fig. 5.3 shows ep esen a i e examples o bo h cases. The in si u
UV-Vis measu emen s collec ed in he SANS sample (sec. 2.4.1) ensu es ha he molecules
we e no pa ially dena u ed a oom empe a u e. The e o e b anching om indi idual
molecules is no expec ed. The DAMMIF solu ion could s ill be explained i he sample
con ains a mix u e o weakly cu ed and sha ply ben molecules. In his case, he DAMMIF
esul s would be due o a supe posi ion o bo h con o ma ions.
The ab-ini io shape econs uc ion ha DAMMIF used is no conclusi e because i does
no include a p io i knowledge o he molecula p ope ies. In o de o ex ac u he
in o ma ion om he sca e ing da a a heo e ical model was de eloped.
An ex ension o he K a ky-Po od model ([96] and sec. 3.4.2) was used o analyze he
P( ) cu es. The model desc ibes he con o ma ions ha he backbone o he DNA can
adop bu no he in e nal s uc u e o he molecule. A schema ic o he model used can be
133
Figu e 5.4: Schema ic o he ex ended K a ky-Po od model used. The op pa shows how
he base pai s and segmen s we e numbe ed and he bo om shows he de ini ion o he
bond and o sional o a ion angles.
ound in ig. 5.4. The model desc ibes a single DNA molecule as consis ing o N+ 1 objec s
ep esen ing base pai s. They a e sepa a ed by Nsegmen s o leng h a= 3.34 ˚
A which
is he a e age base pai dis ance in B o m DNA. The bond angles be ween he segmen s
connec ing he pai s may a y a each base pai . The local bending angle a si e n, be ween
segmen s n−1 and n, is θn. To sional o a ion is accoun ed o by means o a second se
o angles, Φn, gi ing he dihed al angle be ween he plane con aining segmen s n−1 and n
and he plane con aining segmen s nand n+ 1.
The model allows o compu e a Hamil onian which accoun s o he he mal luc ua ions
by means o he bending and o sional ene gy. The Hamil onian is gi en by:
H=
N−1
X
n=1
Kn[1 −cos(θn−θ0n)] +
N−1
X
n=2
Cn[1 −cos(Φn−Φ0n)] (5.1)
whe e θ0nand Φ0na e local equilib ium alues o he bending and o sional angles which
can be di e en om ze o, Knand Cna e cons an s ela ed wi h he bending and o sional
ene gy. Dimensionless a iables we e used in he calcula ions wi h he model. Dis ances
we e measu ed in uni s o a, and empe a u e was exp essed in ene gy uni s ela i e o kBT
134
a oom empe a u e. Thus T= 1 gi es he p ope ies o DNA a oom empe a u e.
Fo any gi en con o ma ion o he model a heo e ical P( ) can be de e mined by pu ing
a uni sca e ing cen e a each base pai posi ion. This is a good app oxima ion o he
SAXS da a because he X- ay sca e ing om a base pai is domina ed by he phospho ous
a oms whose con ibu ion ( o > 40 ˚
A) can be e ec i ely mapped on o he cen e o he
base pai . Conside ing he base pai as a uni sca e ing cen e is a wo se app oxima ion o
he neu on da a because neu ons a e mo e sensi i e o he dis ibu ion o p o ons which is
much mo e homogeneous h oughou he molecule wi h espec o he phospho ous a oms.
The e o e he heo e ical P( ) we e compa ed o he SAXS da a which, in addi ion, ha e
be e signal o noise a io han SANS.
The da a we e i s modeled wi h he classical K a ky-Po od model which has Cn=θ0n=0
and assumes Kn=K=cons an o e e y segmen . In his si ua ion he pe sis ence leng h
is lp=Ka. A pe sis ence leng h o 500 ˚
A co esponds o K= 150. Fig. 5.5 shows a
compa ison be ween he expe imen al da a om SAXS a oom empe a u e and he esul
o he calcula ion o P( ) wi h hese pa ame e s (black line). This calcula ion has a e y
poo esemblance o he expe imen al da a. The model gi es a a be e ag eemen i lp
is dec eased o 60 ˚
A. Howe e , such a sho pe sis ence leng h seems ai ly un ealis ic. I
he molecules we e single s anded his pe sis ence leng h could be adequa e bu he in si u
UV-Vis abso p ion measu emen s pe o med con i med ha he sample was in helical o m
a oom empe a u e. This sugges s ha , a leas o sho molecules (145 bp molecules),
DNA canno be modeled as a homogeneous K a ky-Po od polyme which ag ees wi h he
conclusions o he cycliza ion expe imen s [108].
I is no possible o pe o m a e inemen o he model wi h all he pa ame e s ee because
he pa ame e space is oo la ge. A wo-s ep p ocess was adap ed o ci cum en his di icul y.
Fi s , a signi ican sample o geome ic con o ma ions able o ep oduce he expe imen al
P( ) was ound. Then, pa ame e s able o gene a e hese geome ical con o ma ions when
he model was he malized we e explo ed.
Mon e-Ca lo simula ions we e use o gene a e a la ge numbe o andom con o ma ions
135
(a) (b)
Figu e 5.8: (a) In si u UV-Vis abso p ion as a unc ion o empe a u e. (b) P( ) om SANS
a 25 and 79 ◦C.
espec o he cen e o he molecule. Fo he SAXS/SANS expe imen and o he model
he wo ends o he molecule a e indis inguishable, he e o e he 57 and 88 si es a e almos
equi alen . This is consis en wi h he ac ha models wi h he kink a n= 57 gi e also
good esul s. Whe e e he kink was placed, he bes ag eemen wi h he expe imen was
ound wi h θK= 95 ◦in good ag eemen wi h he kink angle p edic ed by C ick and Klug
[111].
The sca e ing om he DNA solu ion con aining he Widom sequence was measu ed in
unc ion o empe a u e wi h in si u UV-Vis spec oscopy as desc ibed in p e ious chap e s
(sec. 2.4.1). Tempe a u e-dependen da a will be discussed ex ensi ely in he nex sec ion
bu i is in e es ing o highligh he e some aspec s o he da a which ein o ce he conclusions
o he s udy wi h he model.
Fig. 5.8a displays he UV-Vis abso bance o he sample in he 260 nm line which is
usually used as e e ence o ollow he uns acking o he base pai s due o empe a u e
[116]. Fig. 5.8b shows a compa ison o he P( ) o he SANS da a a 25 and 79 ◦C . P( )
clea ly changes due o he inc ease in empe a u e, i inc eases in he ange 80 o 200 ˚
A and
dec eases o almos 0 o alues g ea e han 300 ˚
A. The UV-Vis da a show ha a ound 20%
o he base pai s a e opened a 79 ◦C. The changes obse ed wi h espec o oom Ta e
142

ela ed wi h he onse o he mel ing ansi ion and an inc ease o he he mal luc ua ions
o he molecules.
Fo he SAXS da a he measu emen s showed a dependence on he exposu e ime. This
was no obse ed in he neu on da a wi h simila exposu e imes. Fig. 5.9 shows h ee da a
se s, one a 23 ◦C and wo a 70 ◦C. The h ee da a se s we e measu ed on 2 aliquo s o
he same sample. One aliquo was measu ed o one hou a oom empe a u e o ob ain
he da a se labeled as 23 ◦C. Then his aliquo was he malized a 70 ◦C (wi h he beam
shu down) and measu ed o ano he hou o ob ain he da a se labeled as ”70 ◦C, sho
exposu e”. The e o e be o e eco ding he sho exposu e da a he sample was exposed
o X- ays o 1 hou . The second aliquo was measu ed o one hou a h ee di e en
empe a u es be o e being he malized a 70 ◦C o measu ing he da a labeled as ”70 ◦C,
long exposu e”. The e o e, be o e eco ding he long exposu e da a he sample was exposed
o X- ays o 3 hou s.
The sho exposu e da a ( ed line in 5.9 ) ag ee quali a i ely wi h he high empe a u e
SANS da a o ig. 5.8b, showing changes wi h espec o oom empe a u e happening in a
simila ange o Qwi h a simila magni ude. The long exposu e da a (blue line in ig. 5.9)
a e e y di e en om bo h he sho exposu e SAXS da a and he high empe a u e SANS
da a. I is belie ed ha X- ay damage due o he ela i ely long exposu e ime is he cause.
A X- ay luxes as low as he one used in his s udy he main mechanism by which X- ays
damage DNA is single s and b eaking due o ee adicals gene a ed by abso p ion o he
X- ays by he bu e [117]. Single s and b eaking will signi ican ly inc ease he lexibili y o
he DNA molecules which can explain he changes on he expe imen al P( ) as a unc ion
o exposu e ime. This p oblem is no p esen in he neu on da a since neu ons a e no
ionizing adia ion.
A con o ma ional sea ch was epea ed using P( ) om he long exposu e da a (blue
cu e in ig. 5.9). The ma ching o he a e age P( ) o he 103selec ed con o ma ions o
he expe imen al da a was again sa is ac o y and much be e han ials wi h he classic
K a ky-Po od model, e en i o sional igidi y was included ( ig. 5.10a). Fig. 5.10b shows
143
Figu e 5.9: The P( ) a 23 ◦C and 70 ◦C as a unc ion o ime o exposu e o X- ay adia ion.
The sho exposu e da a is he esul o a measu emen a e he sample was exposed o X-
ays o 1 h. The long exposu e da a is he esul o a measu emen on an iden ical sample
a e he sample was exposed o 4 h.
an his og am o he θn o he selec ed con o ma ions.
In compa ison o he oom This og am ( ig. 5.6a) he his og am o hese da a shows
many mo e si es in which θncan be la ge. Al hough he e is s ill a gap be ween he la ge
and small θn alues, he dis ibu ion o θnis much mo e homogeneous han in he oom T
case. This can be explained by he single s and b eaks caused by he X- ay damage which
would inc ease he local lexibili y d ama ically and c ea e a mo e con inuous dis ibu ion
o bending angles. The diag am on he igh o ig. 5.10b s ill shows a maximum in he
90◦-140◦, he e o e a kink seems o pe sis in hese condi ions.
In summa y, he analysis o he sca e ing da a sugges ed he exis ence o kinked Widom-
601 DNA molecules in he solu ion a oom empe a u e. The p esence o a gap be ween
he low and high bending angles nea he cen e o he molecules, obse ed in he esul s
o he con o ma ional sea ch, p o es ha an enhanced local bending lexibili y o he DNA
molecules is no enough o explain he sca e ing da a. Complemen a y c yomic oscopy
expe imen s [118], able o p o ide di ec imaging, could pe haps con i m his esul and
alida e u he he kink hypo hesis made by C ick and Klug.
144
(a)
(b)
Figu e 5.10: a) Same as ig. 5.6a o he 103con o ma ions ha p o ide he bes ma ching
wi h long-exposu e SAXS da a. b) Black ci cles a e he SAXS P( ) measu ed in a sample
a 70 ◦C a e a long exposu es o X- ays; he ed line is he a e age P( ) o he 103
con o ma ions which p o ided he bes ma ch o he expe imen al da a; he ull black line
shows he P( ) calcula ed wi h he polyme model wi h pa ame e s: Kn= 150, θ0n= 0,
Cn = 0; he dashed black line is he P( ) o he same model i one akes in o accoun he
o sional igidi y (Cn = 2,φ0n= 0).
145
The esul s sugges ha , besides ene ge ic e ec s in he in e ac ion be ween DNA and
his one, mechanical e ec s may con ibu e o posi ioning. A kink in DNA would localize he
his one oc ame ela i e o he DNA and con ibu e o he binding. This in es iga ion can
also con ibu e o he open deba e on he leng h-scale dependence o he DNA pe sis ence
leng h. In insic cu a u e e ec s a e age ou o long DNA molecules in expe imen al
s udies. Howe e , ha is no he case o sho molecules and his can esul in a educ ion
in he obse ed expe imen al pe sis ence leng h o sho DNA molecules.
5.2 Tempe a u e-dependen s udy
I has long been known ha he pe sis en leng h o DNA dec eases as empe a u e ises
[119, 120]. Theo e ical e o s ha e a emp ed o link he empe a u e dependence o lp
wi h he he mally-induced base pai openings. Models which do no include he openings
p edic ha lp a ies as 1/T, which disag ees wi h expe imen s [120]. Theodo akopoulos
and Pey a d ha e included luc ua ion openings using a combina ion o he K a ky-Po od
and he PBD models [15]. The DNA molecules we e desc ibed wi h an inhomogeneous
K a ky-Po od model wi h so and ha d join s co esponding o open and closed base pai s.
S a is ical in o ma ion abou he s a e o each pai was p o ided by he PBD model [9]. Such
an app oach can be used o s udy he sequence e ec s on local lexibili y [121] which may
ha e impo an biological consequences. Mo eo e , he link be ween luc ua ional openings
and local lexibili y p o ides e idence ha he dynamical cha ac e o DNA is e y impo an
o he desc ip ion o he molecule, e en a empe a u es well below he mel ing ansi ion.
Sca e ing da a we e used o y o expe imen ally es his heo y. The samples used in
sec. 5.1 we e hea ed and hei empe a u e-dependen small angle sca e ing was eco ded,
wi h in si u UV-Vis abso p ion spec oscopy o he SANS expe imen . SAXS da a p esen ed
he e was eco ded in samples which we e exposed o X- ay o a maximum o one hou so
he e ec o he adia ion damage can be neglec ed.
The lpo he molecules can be es ima ed by i ing he small angle sca e ing cu es
146
wi h an app op ia e model. Theo e ical p edic ions o lpcan be compu ed as in [15] wi h
he ad an age ha he sequence o sho a i icial DNA is known and so he calcula ion o
he s a is ical con o ma ions o he molecules wi h he PBD model includes no a bi a y
pa ame e s.
5.2.1 SANS
Fig. 5.11a shows an example o he SANS cu e o he DNA solu ion a oom empe a u e.
SANS da a o he bu e solu ion, measu ed unde iden ical condi ions, a e also shown. The
signal om he bu e is ea u eless and he signal om he DNA appea s mos ly a low Q
due o he signi ican size o he molecules (145 base pai s ela es o a leng h o a ound 485
˚
A).
Fig. 5.11b shows ep esen a i e examples o he SANS cu es a low and high empe -
a u e. The mos pa en change wi h empe a u e is an inc ease o he magni ude o he
in ensi y a la ge Qas empe a u e ises. Fig. 5.11c shows he mean in ensi y o he sca -
e ing o Q > 0.17 ˚
A−1 o he DNA and o e he whole Q ange o he bu e plo ed as
a unc ion o empe a u e. The bu e ollows he same end as he sample, so he inc ease
in he sca e ing is no caused by he DNA molecules bu by empe a u e- ela ed changes
in he sol en .
Fig. 5.11d show he ep esen a i e cu es no malized by he a e age in ensi y o he
cu e o Q > 0.17˚
A−1. Once he di e ence in le el is accoun ed o he cu es show a qui e
simila shape e en a he highes empe a u e eached (97◦C) whe e he UV-Vis abso p ion
indica es ha a ound 90% o he base pai s a e open ( ig. 5.8a). Wi h only 10% o he
molecule in he helical o m, he molecule is expec ed o be ex emely lexible in compa ison
wi h he oom empe a u e molecules.
Al hough no immedia ely ob ious, he DNA signal does change wi h T. Fig. 5.12a
shows he esul o di iding he da a a each empe a u e by he da a a 15 ◦C . The di ided
da a we e i ed wi h s aigh lines. The g adien s o he lines clea ly change wi h T. Fig.
147

(a) (b)
(c) (d)
Figu e 5.11: a) SANS cu e o he DNA solu ion and o he bu e he DNA was dissol ed in
a oom empe a u e in log-log scale. b) Rep esen a i e SANS cu es o he DNA solu ion a
di e en empe a u es in log-log scale. c) Value o he a e age in ensi y o Q > 0.17˚
A−1 o
he DNA sample and o e he whole Q ange o he bu e as a unc ion o empe a u e. d)
Same cu es o panel b) no malized by he a e age in ensi y o he cu e o Q > 0.17˚
A−1,
e o ba s we e emo ed o he sake o cla i y.
148
5.12b shows he g adien o he linea i s as a unc ion o empe a u e alongside he UV-Vis
abso bance o he DNA.
The g adien inc eases wi h inc easing empe a u e. This shows ha sca e ing a la ge
Qs inc eases ela i e o he signal a low Qas empe a u e aises, he e o e smalle leng h
scales a e mo e dominan in he a e age s uc u e o he molecules. This could be due o a
bending o e sho spa ial leng hs which is consis en wi h an inc ease in local lexibili y o
he molecules and hus wi h a dec ease o lp. The ac ha he U-Vis abso p ion seems o
be co ela ed wi h he beha io o he g adien sugges s ha his e ec is ela ed wi h he
p e-mel ing and mel ing o he molecules.
Fi s o he small angle sca e ing da a as a unc ion o he empe a u e we e a emp ed
using he comme cial so wa e package Sas iew [122]. The model used was called ” lexible
cylinde ” and i desc ibes he DNA molecule as a K a ky-Po od like chain (sec. 3.4.2) bu
he base pai s a e ep esen ed as ha d sphe es (no o e lap allowed) o adius Rins ead
o dimensionless poin s. Thus he model accoun s o sel excluded olume e ec when
conside ing he con o ma ions he molecule is allow o adop and also o he e ec o he
adius o he DNA in he sca e ing pa e n.
The de i a ion o he i ing unc ion is based on Mon e-Ca lo simula ions which used his
model. Pede sen and Schu enbe ge i ed he simula ions and used he esul s along wi h
nume ical app oxima ions o de i e a phenomenological exp ession o a sca e ing unc ion
o semi lexible chains (SWC(Q, L, lp)) which accoun ed o he excluded olume e ec [123].
I he Lo he chain is signi ican ly la ge han he Ro he ha d sphe es he sca e ing can
be exp essed as a mul iplica ion o wo e ms using he decoupling app oxima ion [124], hus
he sca e ed in ensi y om a DNA solu ion is:
IWC(Q, L, lp, R) = Ds[(SLDDNA −SLDsol)2SW C(Q, L, lp)PCS(Q, R)] + Ib(5.4)
whe e Dsis an scaling ac o p opo ional o he DNA concen a ion, SLDDNA is he
sca e ing leng h densi y o he DNA molecule , SLDsol is he sca e ing leng h densi y o
149
(a)
(b)
Figu e 5.12: a) Examples o he esul o no malizing he SANS cu es o di e en empe -
a u es o he da a a 15 ◦C along wi h he linea i s ( ed lines). b) Slope o he linea i o
he no malized da a and abso p ion o he sample as a unc ion o empe a u e
150
(a) (b)
Figu e 5.13: Examples o he i o he SANS da a a 15 ◦C and 97 ◦C. a) In ensi y s Qin
log-log scale. b) Expe imen al P( ) and P( ) o he i s, hey ha e been shi ed e ically
o he sake o cla i y.
he sol en , Ibis a cons an backg ound, SWC(Q, L, lp) is desc ibed in [123] (sec ion Me hod
3 wi h excluded olume) and SCS is he sca e ing unc ion om he c oss sec ion o a igid
od [125]:
SCS(Q, R) = [2J1(QR)
QR ]2(5.5)
whe e J1is a Bessel unc ion o he i s kind.
The ins umen al smea ing o SANS was accoun ed o by using dQ alues o each
Qwhich ep esen ed he s anda d de ia ion o Gaussian unc ions and we e calcula ed as
explained in [46]. The SLD o he sol en o neu ons (SLDsol,N ) was ixed o 5.754×10−6
˚
A−2, he alue o 2H2O[126]. Rwas ixed o 10 ˚
A and L o 485 ˚
Awhich is easonable
o DNA molecules o 145 base pai s in solu ion. Dswas i ed a oom empe a u e, he
alue ound was 58.23 ±9.26. This alue was ixed o he i a o he empe a u es. Th ee
pa ame e s we e i ed a e e y empe a u e lp,SLDDNA,X (SLD o DNA o X- ays) and
Ib.
151