S N T Majola
email: smajola@uj.ac.za

M A Sithole

L Mdletshe

D Hartley

J Timár

B M Nyakó

J M Allmond

R A Bark

C Beausang

L Bianco

T D Bucher

S P Bvumbi

M P Carpenter

C J Chiara

N Cooper

D M Cullen

D Curien

T S Dinoko

B J P Gall

P E Garrett

P T Greenlees

J Hirvonen

U Jakobsson

P M Jones

R Julin

S Juutinen

S Ketelhut

B V Kheswa

F G Kondev

A Korichi

W D Kulp

T Lauritsen

E A Lawrie

L Makhathini

P L Masiteng

B Maqabuka

E A Mccutchan

D Miller

S Miller

A Minkova

L Msebi

S H Mthembu

J Ndayishimye

P Nieminen

P Z Ngcobo

S S Ntshangase

J N Orce

P Peura

P Rahkila

N Redon

L L Riedinger

M A Riley

D G Roux

P Ruotsalainen

J Piot

J Saren

J F Sharpey-Schafer

C Scholey

O Shirinda

J Simpson

J Sorri

I Stefanescu

S Stolze

J Uusitalo

X Wang

V Werner

J L Wood

C.-H Yu

S Zhu

G Zimba

First candidates for γ vibrational bands built on the [505]11/2 - neutron orbital in odd-A Dy isotopes

Rotational structures have been measured using the Jurogam II and GAMMASPHERE arrays at low spin following the 155 Gd(α,2n) 157 Dy and 148 Nd( 12 C, 5n) 155 Dy reactions at 25 and 65 MeV, respectively. We report high-K bands, which are conjectured to be the first candidates of a K π = 2 + γ vibrational band, built on the [505]11/2 -neutron orbital, in both odd-A 155, 157 Dy isotopes. The coupling of the first excited K=0 + states or the so-called β vibrational bands at 661 and 676 keV in 154 Dy and 156 Dy to the [505]11/2 -orbital, to produce a K π =11/2 -band, was not observed in both 155 Dy and 157 Dy, respectively. The implication of these findings on the interpretation of the first excited 0 + states in the core nuclei 154 Dy and 156 Dy are also discussed.

I. Introduction

The conventional interpretation of first excited K π =2 + bands, that consistently appear in every even-even deformed nucleus, has been that they are a shape vibration in the γ degree of freedom perpendicular to the symmetry axis [START_REF] Bohr | Nuclear Structure[END_REF][START_REF] Wood | [END_REF]3]. These bands have both odd-and evenspin states. The energy staggering between level energies of the even-and odd-spin members of the γ-band provides an insight into the nature of triaxiality in the nucleus [4]. Furthermore, since ΔK = 2 for the out-of-band γ-rays decaying out of both bands, M1 components are Kforbidden in the ΔI =0 (from the even-spin members to the ground band) and ΔI = ±1 (from the odd-spin members to the ground band) transitions [5,6]. Similarly, due to the very inhibited M1 components, the ΔI=1 transitions between the even-and odd-spin members of the K π =2 + bands, particularly in the 150 to 170 mass region, are observed to be very weak at most [5][6][START_REF] Sharpey-Schafer | Proc. XLIX Int. Winter Meeting on Nucl. Phys[END_REF][START_REF] Zimba | [END_REF][9].

In the A≈160 region, where the focus of this work is, the K π =2 + bands usually lie about 1.0 MeV above the yrast line, which makes it difficult to populate such states in heavy-ion fusion-evaporation reactions as they are embedded in other structures which compete for intensity. Consequently, it is challenging to find cases where these bands have been identified beyond spin 14 + . However, wherever they are observed in the transitional rare-earth region, one of their notable features is that they, particularly the odd-spin members, faithfully track their intrinsic configuration (usually the ground state band in even-even nuclei), as a function of spin [START_REF] Sharpey-Schafer | Proc. XLIX Int. Winter Meeting on Nucl. Phys[END_REF][START_REF] Zimba | [END_REF][9][10][11][12][13][14].

In odd-A nuclei, the single nucleon in a Nilsson orbital [N,n x ,Λ]Ω are expected to couple to the collective states of the even-even core. For instance, a single-particle orbital with a Nilsson quantum number Ω, would couple to the so-called β vibrational band of the eveneven core to form a K= Ω band in the neighbouring odd-N nucleus. Similarly, the coupling of the single-particle state(s) with the K π =2 + excitations may result into either a parallel mode or an antiparallel mode which give K > = (Ω+2) or K < = (Ω-2), respectively. In the transitional rear earth region, examples whereby bands built on both K < and K > couplings have been reported remain a rare occurrence [15,16].

In recent years, there have been a few cases of in-beam (heavy-ion reaction) studies which have reported rotational bands built on a state resulting from the K > coupling [15,17,18,55].

Failure to observe the K > band may also be attributed to the fact that these bands are typically situated ≈ 1 MeV above the yrast line in most nuclei (particularly in the A≈160 region) and thus are most likely to be weakly populated in most fusion-evaporation reactions.

In this present paper we report and investigate the identification of structures built on the [505]11/2 -neutron orbital in odd-A 155 Dy and 157 Dy, which have been identified as candidates for the K π =2 + γ-bands coupled to the [505]11/2 -neutron orbital. It is worth noting that this work focuses mainly on results relating to bands built on the h 11/2 orbital. Results pertaining to bands built on other prominent single-particle orbitals close to the Fermi surface in N ≈ 90 nuclei such as i 13/2 , h 9/2 and f 7/2 , particularly for 157 Dy, have been presented in a separate publication [19]. A previous data set has also been examined in order to identify levels built on top of the [505]11/2 -bands in 155 Dy [13,20,21].

II. Experimental details and analysis

Excited states of 157 Dy were populated using the 155 Gd (α, 2n) reaction at a beam energy of 25 MeV. The 155 Gd target was 0.98 mg/cm 2 thick with a purity of 91%. Gamma-rays following the reaction were detected with the JUROGAM II multi-detector array [22] in JYFL, Jyväskylä, Finland. This γ-ray array consists of 39 HPGe detectors, each in its own BGO shield. Almost 2/3 of the array (24 detectors) comprises of EUROGAM II clover detectors [23] while the rest are coaxial EUROGAM Phase 1 and GASP type detectors [24].

Approximately 14 x 10 9 γ-γ events were unfolded from the data in the off-line analysis and replayed into a γ-γ Radware [25] matrix from which the level scheme for the nucleus of interest was created.

The spins and parities for the new rotational structures were assigned using the Directional Correlation from Oriented States (DCO ratios/R DCO ) [START_REF] Ekstrom | Gamma-gamma correlations with detector arrays[END_REF][START_REF] Kramer-Flecken | Use of DCO ratios for spin determination in gamma-gamma coincidence measurements[END_REF] and linear polarization anisotropy (A p ) methods [28]. While A p are defined in [29], the DCO matrices were constructed using data from detectors in the rings at 158° and 86°+94°. Thus the R DCO for the JUROGAM II array in this work is; R DCO = I γ1 (at 158º : gated on γ 2 near 90º) / I γ1 (near 90º : gated on γ 2 at 158º) (

When a gate is placed upon a known stretched quadrupole transition, an R DCO ratio close to 0.5 and 1.0 is expected for a stretched dipole and quadrupole transitions, respectively. The magnetic and electric nature of the transitions was inferred from their A p values. The A p values yield A p > 0 and A p < 0 for stretched electric and magnetic transitions, respectively.

Finally, to identify levels built on the [505]11/2 -bands in 155 Dy, previous data sets were examined. These data resulted from the 148 Nd ( 12 C, 5n) 155 Dy [13,20] and 124 Sn( 36 S,5n) 155 Dy reactions [21], which were both collected using the GAMMASHERE array. Details about the experimental setup and analysis of these experiments can be found in Refs. [13,20,21].

III. Level schemes

A. 155 Dy: Bands 1 and 2

Fig. 1 shows a partial level scheme of 155 Dy deduced from this work. The rotational band built on the 234-keV level shown in Fig. 1 is the well-known high-K band from the comprehensive work of T. Brown et al., [30] and R. Vlastou et al., [31]. This structure is understood to arise from the [505]11/2 -neutron configuration and is interlinked by strong M1 transitions [30,31]. As can be seen in Fig. 1

B. 157 Dy: Bands 3 and 4

The level scheme of 157 Dy is well known from the previous in-beam work of Hayakawa et al.,

[53], Pipidis [41] et al., and Riley [52] et al., which comprehensively explored the structural behaviour of this nucleus at medium to high spin. These studies deduced that the level scheme of this nucleus is divided into three parts with each band structure based on the well as the new structures built on them. The rest of the level scheme of 157 Dy, based on the current experimental results, has been published elsewhere [19].

The rotational structures shown in Fig. 2 form a high-K band built on an isomeric state at 199-keV with a half-life of 21.6 ms. Previous studies [41,53] assigned these structures to the

[505]11/2 -Nilsson orbital and reported them up to spins 75/2 -and 69/2 -, respectively [41].

This work has managed to confirm and validate the placements made by previous studies up to 29/2 -and 31/2 -. As can be seen in Table 4, the DCO and polarization values deduced from this work are also in agreement with the spin and parity assignments from previous work [32,41,53].

IV. Discussion

In this work we first attempt to explain and/or interpret the rotational behaviour of the new bands using the Cranked Shell Model (CSM) [44,51]. Fig. 4 shows a CSM calculation of the Routhians e' of 157 Dy, deduced using a modified oscillator potential. Concerning the interpretation of the structures in 155 Dy, we rely on the CSM diagram of 155 Dy given in Fig.

3.6 of Ref. [30]. Lastly, the labelling of the quasi-neutron states shown in Fig. 4, are given in Table 1.

A. Bands 1, 2, 3 and 4

As can be seen in Figs. 1 and transitions between them are comparable to those connecting rotational levels of the K = 11/2 -bands. This is clearly demonstrated in Table 2 where the energy difference (per given spin) between these M1 transitions averages about 3.5-and 6-keV for both 155 Dy and 157 Dy. respectively. The corresponding quasi-neutron labeling is given in Table 1.

A plot for the B(M1)/B(E2) ratios deduced for the newly established bands (high-K bands built on the [505]11/2 -structures) is shown in Fig. 7. The ratios in 155 Dy show further similarities with those measured in 157 Dy. In effect, in both cases, ratios of both structures exhibit the same trend. With these pieces of information, we therefore conclude that we are dealing with the same structure in both 155 Dy and 157 Dy. In a quest to identify the microscopic nature of these K π = 15/2 -bands, we look at the possible ways through which they can arise or be formed. The band-head energies of these structures are about 1 MeV, thus suggesting that they could either be a single-particle orbital or a three-quasi-particle excitation or a single-phonon γ vibrational band. In the Nilsson model, there are no suitable single-neutron orbital in the Fermi surface which could give K π = 15/2 -. This leaves the three-quasi-particle and γ vibration arguments as the only possibility.

- α = + 1/2 A i 13/2 [651]3/2 + - α = -1/2 B i 13/2 [651]3/2 + - α = + 1/2 C i 13/2 [660]1/ 2 + - α = -1/2 D i 13/2 [660]1/ 2 + - α = + 1/2 E h 9/2 [521]3/2 - - α = -1/2 F h 9/2 [521]3/2 - - α = -1/2 G f 7/2 [523]5/2 - - α = + 1/2 H f 7/2 [523]5/2 - - α = + 1/2 I h 9/2 [530]1/2 - - α = -1/2 J h 9/2 [530]1/2 - (-,-1/ 2) 1 α = -1/2 Y h 11/2 [505]11/2 - (-,+1/ 2) 1 α = + 1/2 X h 11/2 [505]11/2 - Band 3 α = + 1/2 - γ ⊗ h 11/2 [505]11/2 - Band 4 α = -1/2 - γ ⊗ h 11/2 [505]11/2 - ++++++++++++++++++++++++++++++++++++++++ 13
However, the Cranked Shell Model (see Fig. 4 and Fig. 3.6 of Ref. [30] for both 157 Indeed, these new high-K band structures identified in both 155 Dy (i.e., Bands 1 and 2) and 157 Dy (i.e., Bands 3 and 4) share a lot of similarities with the bands that were recently identified as a K π =2 + γ vibration, built on the [505]11/2 -orbital, in 155 Gd [17,45]. The decay pattern of these structures is also consistent with those observed for the K π = 2 + γ vibrational bands in the neighbouring even-even nuclei. The energy difference between these structures and their intrinsic states also compare very well with the excitation levels of the γ vibrational bands relative to the ground state bands in the neighbouring even-even-nuclei.

Recently, Wang et al., [18] observed that systematics of band-head energies of the γ-bands in odd-A (odd-N) nuclei are systematically lying very close in energy to those in their neighbouring N+1 even-even nucleus. For instance, the band-head energy of the γ-band is 852-keV relative to the [505]11/2 -state in 163 Er, which is close to the 860.3-keV, which is the band-head of the γ-band in 164 Er. The same feature is observed between 165 Er and 166 Er where the γ band-head is at 767-keV relative to the [505]11/2 -state, and is close to the 786-keV energy of the lowest-lying K π =2 + band-head in 166 Er. The same situation is observed for the newly established γ-bands conjectured to be K π =2 + γ bands built on the [505]11/2 -state in the odd-A Dy isotopes in the A ≈ 150-160 mass region. For instance, the band-head energy for the K π =15/2 + band in 155 Dy is at E x = 830-keV (see Fig. 1) and is close in energy to the band-head of the first excited K π =2 + band in 156 Dy, at E x = 890-keV [13]. Similarly, the same feature is observed between the K π =15/2 + band in 157 Dy (E x = 928-keV) [see Fig. 2] and the 158 Dy (E x = 946-keV) [9]. This trend is also evident in the γ-band that was recently identified in 155 Gd [17]. For instance, its relative band-head energy is 1161-keV and is close to 1154-keV, which is the γ-band band-head in 156 Gd [36]. A systematic review for dysprosium and gadolinium isotopes demonstrating this relation is given in Fig. 8.

K π =2 + γ-band band-head in
Clearly, both isotopes demonstrate a similar trend as a function of the neutron number N.

In Fig. 9 we also plot the systematics of the level energies of the γ-bands in the odd-N dysprosium isotopes to demonstrate further similarities with those in the neighbouring eveneven isotopes. In fact, the K π = 15/2 -γ-bands built on the [505]11/2 -orbital seem to mimic those observed in even-even nuclei. In particular, the K π = 15/2 -γ-bands run parallel to their intrinsic configuration, which is the [505]11/2 -bands. This feature is consistent with the behaviour of the K π = 2 + γ vibrational bands in the neighbouring even-even nuclei. In effect, recent studies have demonstrated that γ-bands faithfully track their intrinsic configuration, particularly the odd-spin members [START_REF] Zimba | [END_REF][9][10][11][12][13]33], and this seems to be a general or rather a notable feature for γ-bands in N ≈ 90 region.

In even-even nuclei, the M1 (ΔI = 1) intra-band transitions of the γ-bands are generally known to be very weak (or non-existent) due to the collective nature of γ-bands [5-7, 9, 34].

Indeed, the γ-vibrational bands of the 154 Dy [START_REF] Zimba | [END_REF] and 156 Dy [9,13] cores also have very weak (and/or non-existent) ΔI = 1 M1 intra-band transitions. This seems to be a general feature of γ-bands, particularly those of the nuclei in the 150 to 160 mass region [START_REF] Sharpey-Schafer | Proc. XLIX Int. Winter Meeting on Nucl. Phys[END_REF][START_REF] Zimba | [END_REF][9]. The apparently strong M1 intra-band transitions observed for both γ-bands of 155 Dy and 157 Dy can therefore be attributed to coupling of the K π =2 + γ excitations of the even-even cores ( 154 Dy and 156 Dy) to the high-K value of the [505]11/2 -single-particle orbital itself. , 153 Gd [37], 154 Gd [9,35], 155 Gd [17], 156 Gd [36], 158 Gd [38], 160 Gd [39], 154 Dy [START_REF] Zimba | [END_REF], 155 Dy [current work], 156 Dy [13], 157 Dy [current work], 158 Dy [9], 160 Dy [40], 162 Dy [40]). Note that the excitation energy given for the K=15/2 -band-heads (in the odd-N nuclei) has been subtracted relative to the excitation energy of the lowest lying state of the K = 11/2 -band. The discontinuity in the Gd isotopes can be attributed to the missing band-head (yet to be observed) energy of the γ-band in 155 Gd.

Clearly, in many respects, the K π = 15/2 -γ-bands in 155 Dy and 157 Dy share a lot of structural similarities with those found in their neighbouring even-even nuclei and this therefore confirms the suggestion given above that they represent a coupling of the K π = 2 + γ vibrational bands of the even-even core to the According to Refs. [17,35,45], the first excited 0 2 + states in the N ≈ 90 nuclei are actually not collective β-vibrations, but have properties resembling pairing isomers [46]. The latter refers to states which are lowered into the pairing gap by a configuration dependent pairing interaction [13,17,35,45]. In such a scenario, the 0 2 + bands can be understood as neutron 2p-2h seniority-zero states formed by raising two neutrons out of the ground-state configuration into the upsloping h 11/2 neutron orbit. This up-sloping orbit is raised from the lower filled shell to the Fermi surface at the onset of deformation after the N = 82 shell closure. Due to quadrupole pairing effects (or configuration-dependent pairing interaction), pairs of neutrons in this high-K "oblate" polar orbit do not take part in the normal monopole pairing produced by the high density of low-Ω "prolate" equatorial rotationally aligned orbitals [13]. And due to the small overlap of the wave-functions of prolate and oblate singleparticle states, [505] 2 configurations are decoupled from the pairing produced by the interactions of low-Ω i 13/2 neutron pairs that cause back-bending in the rotational bands of the deformed nuclei near N = 90 [13,47]. Consequently, the weakening of the monopole pairing strength and the increase of the quadrupole pairing strength could bring 2p-2h 0 + states within the pairing gap of 2∆. This leaves a pair of neutrons in the h 11/2 [505] orbital as "spectators" in the wider pairing correlations of the nucleus, which then forms its own low-lying 0 + state, well within the pairing gap, which in turn can compete with β bands [11].

Furthermore, according to Refs. [17,35,45], the conspicuous absence of the coupling between K π = 0 + states and the [505]11/2 -orbital in 155 Gd as well as the rest of the neighbouring odd-N nuclei (such as 155 Dy and 157 Dy) is mainly because the underlying configuration of the first-excited K π = 0 + states, in even-even nuclei in the transitional N ≈ 90 rare-earth region, are supposedly comprised of essentially an h 11/2 pair of neutrons. Thus, the coupling of the K π = 0 + band with 11/2 -[505] orbital in the neighbouring odd neutron nucleus should be Pauli-blocked. Conversely, the coupling of the K=2 + γ-band with the [505]11/2 - orbital is expected to be observed (as is the case in 155 Dy and 157 Dy), since it is not Pauliblocked.

The consideration of the new ( 155 Dy and 157 Dy) and existing ( 155 Gd) evidence supports the interpretation that the first excited 0 + states are due to configuration-dependent pairing interaction as conjectured by Refs. [17,35]. In effect, the apparent absence of the coupling of the h 11/2 neutron orbitals to the first-excited K π = 0 + states observed in the current work is consistent with the suggestion that the first excited 0 + states in the N ≈ 90 region are not due to β vibrations but are essentially comprised of a pair of h 11/2 neutrons [17,35,45].

Nevertheless, it is worth noting that this condition cannot be considered as an unambiguous proof since the absence does not necessarily imply the non-existence of these elusive states.

Clearly, more evidence is needed before a final conclusion can be reached. Therefore, future experimental and theoretical studies are essential in order to positively identify whether the h 11/2 neutron orbital plays any role in the absence of the coupling between the K π = 0 + states and the [505]11/2 -neutron in odd-A Gd and Dy isotopes in the N ≈ 90 region.

V. Conclusion

Rotational structures have been measured using the Jurogam II and GAMMASPHERE arrays at low spin following the 155 Gd(α,2n) 157 Dy and 148 Nd(

Figure 1 :

 1 Figure 1: (Color online) Partial level scheme of 155 Dy deduced from the current work. It shows band structures built on the [505]11/2 -neutron orbital in 155 Dy. New rotational structures, established in this work that have been identified as the γ band built on [505]11/2 -bands are labeled in red (and marked with asterisk symbols) while known bands, deduced from previous in-beam works, are labeled in black.

[521] 3 / 2 -

 32 Fig. 2 only shows a partial level scheme of 157 Dy, which contains the [505]11/2 -bands as

Figure 2 :

 2 Figure 2: (Color online) Partial level scheme of 157 Dy deduced from the current work. It shows band structures built on the [505]11/2 -neutron orbital in 157 Dy. New rotational structures, established in this work that have been identified as the γ band built on [505]11/2 -bands are labeled in red (and marked with asterisk symbols) while known bands, deduced from previous in-beam works, are labeled in black.

Figure 3 :

 3 Figure 3: (Color online): (a) Double and (b) Single gated coincidence spectra for the γ-band built on the [505]11/2 -neutron orbital in 155 Dy and 157 Dy, respectively. Transitions corresponding to these newly found structures are labeled in red (and marked with asterisk symbols) while contaminants from other reaction channels and/or other bands of 155, 157 Dy, not associated with the cascade of interest

Fig. 2

 2 Fig. 2 shows that this study has also identified a new strongly coupled band structure that decays to the [505]11/2 -. New bands are identified as Bands 3 and 4, and both consist of three rotational levels, connected to each other by relatively strong inter-linking transitions compared to their weak intra-band transitions. As can be seen in Fig. 2, these newly found rotational levels decay solely to the [505]11/2 -bands through medium to high energy transitions. The DCO and polarization measurements carried out for the 928-keV transition depopulating the 1127-keV (depopulating Band 4) level are consistent with it being a pure stretched E2. The most probable spin and parity assignment for the 1127-keV level then becomes 15/2 -. Similarly, for the 1347-keV level in Band 3, the DCO and polarization measurements for the transition decaying out of this level are consistent with it being a 17/2 -. Assuming that Bands 3 and 4 are signature partners (based on the 1127-keV) connected by interlinking M1 transitions, the E x = 1127-, 1347-, 1583-, 1834-, 2095-, and 2363-keV levels of Bands 3 and 4 are then respectively assigned to have spin-parity of 15/2 -, 17/2 -, 19/2 -, 21/2 -, 23/2 -and 25/2 -. Polarization and DCO measurements were also carried out for some of the inter-band transitions decaying out of Bands 3 and 4 where possible. These measurements are also consistent with the proposed spin and parity assignments. Fig. 3(b) presents a gated spectrum showing γ-rays associated with Bands 3 and 4.

Furthermore, the rigid

  Fig. 6 (a) and (b). In both cases, just like the [505]11/2 -bands, the K π = 15/2 -bands appear to have a gradual upbend, but are consistently, at the most, half a unit above the [505]11/2 - bands.

Figure 4 :

 4 Figure 4: (Color online) Neutron quasi-particle Routhians e', as a function of ħω, calculated for 157 Dy using CSM with parameters ε2 = 0.245, ε4 = -0.020 and γ = -11.8 o . The solid and dotted lines colored in red represent positive-parity states with signatures α = +1/2 and -1/2, respectively. The dotdashed and dashed lines colored in blue represent negative-parity states with α = +1/2 and -1/2,

Figure 5 :

 5 Figure 5: (Color online) Plots of excitation energy minus a rigid rotor energy for bands observed in (a) 155 Dy and (b) 157 Dy. Open symbols have α = +1/2 while closed symbols have α = -1/2.

  Dy and 155Dy, respectively) also does not predict any plausible single-neutron orbital combinations that can form a three-quasi-particle configuration suitable to explain the features of the bands in question. This rules out the possibility of describing these bands as a three-quasi-particle configuration. It is therefore likely that the K π = 15/2 -bands in both 155 Dy and 157 Dy can best be described as the K π = 2 + single-phonon γ vibrational bands coupled to the [505]11/2 - orbital.

Figure 6 : 2 h

 62 Figure 6: (Color online) Plots of alignment i x and Routhians e' for bands in 155 Dy and 157 Dy. Harris parameters used are J 0 = 32 2 h MeV -1 and J 1 = 34 4 h MeV -3 . Open symbols have α = +1/2 while

Figure 7 :

 7 Figure 7: (Color online) Experimental B(M1;I →I-1)/B(E2;I →I-2) values for ΔI = 1 M1 intra-band transitions pertaining to the [505]11/2 -bands and newly established K π =15/2 -bands in (a) 157 Dy and (b) 155 Dy.

Figure 8 :

 8 Figure 8: (Color online) The systematic review of band-head energies for γ-bands in the even (with respect to the ground state bands) and odd-N Gd and Dy isotopes (from N = 88 to N = 96, i.e.152 Gd[9],153 Gd[37],154 Gd[9,35],155 Gd[17],156 Gd[36],158 Gd[38],160 Gd[39],154 Dy[START_REF] Zimba | [END_REF],155 Dy [current

  [505]11/2 -orbital. With these findings, 155 Dy and 157 Dy are the first odd-N dysprosium isotopes in which γ vibrational bands built on the [505]11/2 -orbital have been observed. In spite of this, it worth mentioning that the K < =7/2 - band, resulting from the antiparallel coupling of the [505]11/2 -orbital with the K π = 2 + vibrational band was not observed in both 155 Dy and 157 Dy. C. Elusive coupling of the [505]11/2 -neutron orbital to the first excited K=0 + core excitations of 154,156 Dy in 155,157 Dy? As stated above, in odd-A nuclei such as 155, 157 Dy isotopes, the single nucleons in a Nilsson orbital [N,n x ,Λ]Ω are expected to couple to the collective states of the even-even core. And indeed, the present study has successfully identified for the first time, the K > =15/2 -band, resulting from a parallel coupling of the [505]11/2 -orbital with a K π = 2 + vibrational band in both 155 Dy and 157 Dy. In spite of this, the respective coupling of the first excited 0 + states or so-called β vibrational bands at 661-and 676-keV in 154 Dy and 156 Dy to the [505]11/2 - orbital, to produce a K=11/2 -band, was not observed in both 155 Dy and 157 Dy. It is worth noting that an equivalent situation has also been observed by Sharpey-Schafer et al., in the neighbouring 155 Gd [17, 45].

  2, the properties of these four new bands appear to share a lot of similarities. In effect, when comparing the structural behaviour of the new rotational states in 155 Dy namely, Bands 1 and 2, with those of Bands 3 and 4 in 157 Dy, it is clear that we are dealing with the same structure. First of all, in both 155 Dy and 157 Dy, the new bands form

high-K band structures (with K π = 15/2 -), which decay solely to the [505]11/2 -bands. The band-head energies of these high-K structures start at about 900 keV relative to the [505]11/2 -bands and have a similar decay pattern. One of the striking features about these K π = 15/2 -bands is that in both 155 Dy and 157 Dy the energies of the interlinking M1 (ΔI = 1)

Table 1 :

 1 Labelling of the quasi-neutron states in Fig.4, as well as that of the proposed configuration assignments for new band structures in155 Dy and157 Dy, where (π, α) n represent the n th rotational sequence with signature α and parity π.

	band label	Signature	Label of quasi-neutron states Configuration assignment
			155 Dy
	Band 1	α = + 1/2	-	γ ⊗ h 11/2 [505]11/2 -
	Band 2	α = -1/2	-	γ ⊗ h 11/2 [505]11/2 -
	(-,-1/ 2) 1	α = -1/2	-	h 11/2 [505]11/2 -
	(-,+1/ 2) 1	α = + 1/2	-	h 11/2 [505]11/2 -

157

Dy

Table 2 :

 2 Comparisons of M1 transitions (in keV) in the K π =11/2 -and K π =15/2 -bands, per given spin, of155 Dy and 157 Dy isotopes, respectively.

		155Dy		157Dy
	Spin(ħ)	K = 11/2 -	K = 15/2 -	K = 11/2 -	K = 15/2 -
	17/2 -	238	241	214	220
	19/2 -	255	254	231	236
	21/2 -	267	268	246	251
	23/2 -	277	281	259	261
	25/2 -	286	291	271	268

  12 C, 3n)157 Dy reactions at25 and 65 MeV, respectively. This study has identified for the first time, the K > =15/2 -band, resulting from a parallel coupling of the [505]11/2 -orbital with a K π = 2 + γ-band excitations in both 155 Dy and 157 Dy. Just like the K π = 2 + excitations observed in the neighbouring even-even nuclei, the γ-bands in both155 Dy and 157 Dy appear to faithfully track their intrinsic configuration, as a function of spin. With these findings,155 Dy and 157 Dy are the first odd-N dysprosium isotopes in which γ vibrational bands built on the [505]11/2 -orbital have been observed.The coupling of the first excited K π =0 + states or the so-called β vibrational bands at 661 and 676 keV in154 Dy and 156 Dy to the [505]11/2 -orbital, to produce K π =11/2 -bands, was not observed in either155 Dy and 157 Dy, respectively. These findings, together with the existing evidence presented in Refs.[17,45], favour the suggestion that the first excited 0 + states are due to configuration-dependent pairing interaction formed by the upsloping h 11/2 neutron orbit around N ≈ 90. However, we are of the view that the apparent absence of that coupling is indeed an essential but not a sufficient condition to prove that the microscopic identity of the first excited 0 + state is comprised of essentially an h 11/2 pair of neutrons as prescribed by Refs.[17,35,45]. In light of this, additional theoretical and experimental spectroscopic studies are needed in order to obtain further insight on the nature of the first excited K π = 0 + in even-even nuclei (in the N ≈ 90 region), notwithstanding their elusive coupling to the h 11/2 neutron orbitals in the neighbouring odd-N nucleus such as155, 157 Dy isotopes. under the K18 funding scheme with project no. K128947, as well as by the European Regional Development Fund (Contract No. GINOP-2.3.3-15-2016-00034). [53] T. Hayakawa et al., Eur. Phys. J. A15, 299 (2002). [54] W. D. Kulp et al., Phys. Rev. C 76, 034319 (2007). [55] M. A. Sithole et al., Eur. Phys. J. A (2019) 55: 178

Table 3 :

 3 Experimentally determined properties for the nucleus155 Dy. This includes excitation levels E x (in keV), γ-ray energies E γ (in keV) §, γ-ray intensities I γ , assigned multipolarities (Mult.), spins for the initial I i states, level in the band of destination Band f , DCO ratios and polarization measurements (A p ). All DCO ratios were deduced by gating on stretched E2 transitions. NB//: Quantities within parenthesis are quoted as tentative while empty entries refer to information that could not be obtained.

	π and

π

Table 4 :

 4 Experimentally determined properties for the nucleus157 Dy. This includes excitation levels E x (in keV), γ-ray energies E γ (in keV) §, γ-ray intensities I γ , assigned multipolarities (Mult.), spins for the initial I i states, level in the band of destination Band f , DCO ratios and polarization measurements (A p ). All DCO ratios were deduced by gating on stretched E2 transitions. NB//: Quantities within parenthesis are quoted as tentative while empty entries refer to information that could not be obtained. §1 Typical uncertainty of 0.3 keV and up to 0.5 keV for weak transitions (I γ <1).

	π and

π

ACKNOWLEDGEMENTS

This work is supported by the South African National Research Foundation under grants (No. 96829, 109711, and 106012). Support for L.B. and P.E.G. was provided by the Natural Sciences and Engineering Research Council of Canada. VW wishes to acknowledge support provided by the German Federal Ministry for education and Research under grant No. 05P19RDFN1. Support was also provided by the U.S. National Science Foundation under Grant Nos. PHY-1203100 (USNA), PHY-1502092 (USNA) and PHY-0754674 (FSU) as well as by the U.S. Department of energy, office of Nuclear of Nuclear Physics, under Contract Nos. DE-AC02-06CH11357 (ANL) and DE-FG02-91ER-40609 (Yale). The authors also acknowledge the support of GAMMAPOOL for the loan of the JUROGAM detectors. JYFL research is supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2006-2011, Contract No. 213503. This work was also partially supported by the National Research, Development and Innovation Fund of Hungary, financed


Pierre Poulain

Adrien Saladin

Brigitte Hartmann

Chantal Prévost
email: <chantal.prevost@ibpc.fr

Chantal Pr

Insights on protein-DNA recognition by coarse grain modelling

Keywords: Computer Simulation, DNA, chemistry, metabolism, Models, Chemical, Models, Molecular, Nucleic Acid Conformation, Protein Structure, Secondary, Proteins, chemistry, metabolism, Thermodynamics

come

Introduction

In the cell, numerous proteins interact almost continuously with DNA to ensure standard or unusual biological functions such as transcription control, integration of exogenic DNA, genetic code maintenance or storage. Most of the time, these DNA-binding proteins can also associate with other proteins to form very large macromolecular assemblies. The knowledge of the overall structure of these assemblies as well as the details of the interactions are essential to understand the underlying biological processes or to develop new therapeutic strategies. In spite of spectacular progresses, the determination of the tridimensional structure of such large complexes at the atomic resolution by means of X-ray crystallography or nuclear magnetic resonance remains a difficult task. As a consequence, most experimentally determined structural informations only concern a limited part of the assembly, in other terms, two partners interacting together. However, even in the case of binary complexes, the number of available structures only represents a minor fraction of the existing assemblies.

Given the deficit of structural information on these assemblies, theoretical approaches appear as promising tools. Docking methods are more and more reliable and efficient for assembling macromolecular complexes, especially when the partners do not present any large internal deformation. Numerous studies were dedicated to protein protein interactions and the world wild challenge Critical - [1 ] "

Assessment of PR-edicted Interactions (CAPRI) , reveals the interest of the scientific community for this domain. The prediction of

" [2 3 ]
protein DNA complexes is also a subject of interest for different groups that use several methods such as discretization on grid and Fourier transform or ambiguous interaction restraints in the HADDOCK program developed by Bonvin and collaborators .

[4 ] [5 ] Both protein protein and protein DNA complexes are large size systems. From the point of view, the prediction of -in silico macromolecular complexes from a systematic sampling of the energy landscape is computationally expensive because of the large number of atoms involved and the multiple calculations of the interaction energy. This has prompted the emergence of simplified macromolecule representations, which reduce the dimensionality of the problem by using a reduced number of particles, or pseudo-atoms. This type of approach, called coarse grain , aims at rendering specific characteristics of the molecules, like the steric and electrostatic properties of the " "

complex. In the molecular biology framework, a coarse grain approach based on the reproduction of steric and electrostatic characteristics has been used by Marrink and coworkers for lipid and surfactant systems. It has then been extended to proteins by Bond and Sansom [6 ] for the purpose of the insertion of proteins into membranes . For the protein protein docking purpose, Zacharias and collaborators , [7 ] -

[8 9
have shown that low resolution approach is valuable to predict with a good confidence the geometry of protein protein complexes.

] -

Particularly, the combination of the docking procedure ATTRACT with this reduced model performed very well at rounds 3 and 5 of [8 ] the CAPRI contest .

[10 ]

To our knowledge, there is so far no DNA coarse grain model dedicated to the docking problem. However, some coarse grain models of DNA have been developed recently for other purposes, with resolution ranging from 1 to 16 beads (or pseudo-atoms) per structural block, the latter being the complementary nucleotides considered as the relevant units for DNA. The model of Mergell is et al. [11 ] composed of one rigid ellipsoid per base pair with an internal energy derived from the Gay-Berne potential. This resolution allows the study of phase transition from B-to S-DNA upon stretching. Other models rely on a more common bead and spring representation of the internal energy. bead for the backbone/sugar and base elements. Starting from a straight ladder conformation, this model reproduces the helicity of DNA.

More recently, Knotts and coworkers proposed a topological model with 3 beads per nucleotide (phosphate, sugar and base). This [13 ] model successfully reproduces several physical and mechanical properties of DNA, including salt-dependent melting.

In this article, we propose a DNA coarse grain model specifically designed for modelling protein DNA complexes, that is very efficient in term of prediction for a low computational cost. In a first part, we introduce the reduced DNA model we have developed with 11 beads per complementary nucleotides. We show its compatibility with the Zacharias protein model and also the good stability of protein DNA complexes represented at low resolution using the two combined models. In the second part, we show on a large range of protein

- -
DNA complexes that our model is able to predict protein DNA assemblies, using the rigid body docking procedure ATTRACT . We - [8 ] then assess the relative contribution of the electrostatics and van der Waals terms in the energy function, thus exploring the energetic components that participate to the recognition process.

Materials and Methods

Protein representation

With the protein protein docking issue in mind, Zacharias proposed a reduced protein model with up to three pseudo-atoms per residue , which makes about 4 heavy atoms per bead. In this model, each amino acid is represented by one pseudo-atom located at the [8 ] position of the C atom and up to two pseudo-atoms for each side chain, depending on its length.

α This model assumes no internal energy evaluation since it has been developed for systematic rigid body docking. Actually, only the interaction energy is needed to evaluate the geometry of a complex. The effective interaction between two partners and is the sum of a I J soft Lennard-Jones potential and an electrostatic potential, with ( ) and ( ) . In the previous formula, is the distance between bead of partner and bead of

B ij = A A i j R i + R j 8 C ij = A A i j R i + R j 6 r ij i I j partner ,
, and are the Lennard-Jones parameters, and are the charges of bead and respectively, and finally, is a J. A i A j R i R j q i q j i j ε distance-dependant dielectric function defined as 15 .

ε = × r ij
The protein model is described by 29 types of beads with three parameters each, namely , and . Charges are only set on charged A i R i q i amino acids, as full charges ( 1 or 1) on the last bead of the residues.

+ -

DNA representation

Our central assumption is that the design of a DNA model for the study of protein DNA complexes requires a good reproduction of the volume occupied by the DNA. This volume is characterized by a contrast between the minor and major grooves and the sharp phosphodiester backbones. Both the level of resolution and the parameters have been determined to be coherent with the protein model of Zacharias . The bead partition is also related to a model developed by Khalid and Sansom for the insertion of a DNA into a

[8 ] [14 ]
membrane. Hence, our model is defined by 5 to 6 beads per nucleotide: one bead per phosphate backbone, two beads per sugar and 2 to 3 beads per base (2 for cytosine and thymine, and 3 for adenine and guanine). Between three and four heavy atoms are grouped within each bead. Only one bead of thymine contains five heavy atoms in order to represent the methyl group. The topology of our DNA model is depicted in . The center of a given bead is the geometric center of the heavy atoms included in this bead. Each bead is defined by 3 figure 1 parameters, which are consistent with the reduced protein model (

). The parameters have been derived from the chemical table 1 composition of each bead. The Lennard-Jones parameters are 0.6 RT for all beads, reflecting their identical polarities. The van der A i 0.5

Waals radii (

) were directly calculated from the radius of the atomic components of the beads. For a given bead that reduces Table 1 N atoms , the van der Waals radius is i R

where is the distance between the center of the grain and the center of atom , and is the van der Waals radius of atom .

d i i R vdw,i i
Finally, charges are set only on phosphate beads using a 30 screening, that gives a charge of 0.7 when starting with a full negative % -Docking simulations were performed with the ATTRACT protocol developed by Zacharias . ATTRACT performs systematic [8 ] docking without using any experimental data concerning the native complex. This algorithm relies on a minimization of the interaction energy, the DNA center being placed at regular positions around the protein surface at a distance slightly larger than its biggest dimension.

For each starting position, around 230 initial DNA orientations are generated. For each starting geometry, energy minimization (quasi-Newton minimizer) is performed using translational and rotational degrees of freedom of the DNA. During this minimization, no cut-off is used to compute the interaction energy. The full sampling of the 60,000 positions and orientations of the DNA around the ≈ protein required 14 hours on a 3 GHz monoprocessor in the case of compound 1A74 (see below). Since the minimizations are independent, the sampling can easily be distributed on many processors. For instance, when distributed on 14 processors, the full calculation on 1A74 takes about one hour.

Protein DNA complexes

-

We have tested our coarse grain DNA model on six systems that represent a large range of protein DNA interactions. These systems are namely:

the transcription factor ETS-1 with DNA (2.4 resolution, PDB code 1K79).

[15 ] Å the Arc repressor-operator complex (2.6 resolution, PDB code 1PAR).

[16 ] Å the complex between the E2 transcription factor of the bovine papillomavirus and DNA (1.7 resolution, PDB code 2BOP).

[17 ] Å the intron-encoded homing endonuclease I-I dimer complexed with DNA , (2.2 resolution, PDB code 1A74). Ppo [18 ] Å the yeast TATA-box binding protein (TBP) interacting with a DNA TATA box sequence (1.8 resolution, PDB code 1YTB) [19 ] Å

the NMR complex between the core DNA-binding domain of human transcription factor NFATC1 and DNA (PDB code 1A66).

[20 ]

As usual for NMR determined structures, several models are proposed within the PDB. Out of the 18 available, we have performed docking tests on several models. The results being equivalent, we present here those obtained with the first model.

Atomic coordinates of these test cases were obtained from the Protein Data Bank . The DNA curvature has been characterized [21 ] with CURVES , while B-DNA structures were generated by JUMNA . Hydrogen bonds between DNA phosphate and charged [22 ] [23 ] residues were determined by HBPLUS .

[24 ]

Quality and quantity assessment of the simulated complexes

The quality of our simulations is evaluated by the Root Mean Square Deviation (RMSD) calculated on all beads of the DNA between the reference and the simulated complexes. However, this measure may be insufficient to precisely characterize the position of DNA with respect to its proteic partner . We thus used an additional parameter, namely the geometric center distance (GCD). This distance is [4 ] calculated between the geometric center of the DNA in the reference complex and the geometric center of the DNA in the simulated complex, after superposition of the protein partners of both complexes.

Exploring the effect of the DNA sequence and shape on recognition does not easily allow a comparison in terms of RMSD. In these cases, we analyzed the fraction of the protein interface residues in the native structure which are recovered in the prediction, . A protein f pib residue is defined to belong to the interface when one of its beads is within 7 from any DNA bead . In the same way, is the fraction

Å [9 ]
f dib of native DNA interface nucleotides which are recovered in the predictions. In this article, and are expressed as percentages. f pib f dib Final geometries are clustered within 0.1 RT units in energy and 0.1 in RMSD.

Å

Results

To assess the robustness of our model, the studied complexes were chosen to encompass a large range of protein DNA interactions. In this purpose, we used the taxonomy of Luscombe and collaborators , to select six representative complexes suitable for the rigid transcription factors except 1A74 which is a hydrolase.

The five first complexes are crystallographic structures with DNA Binding Domain (DBD) identified as respectively [25 ] helix-turn-helix, -hairpin/ribbon, other helix, enzyme and sheet structural groups (see ). The last complex 1A66 is issued from

β α β table 2
NMR measurements and has been selected for its interface made of loops.

The DNA interfaces are characterized in , as well as some structural features of the DNA. The contacts are mainly made in the table 2 major groove apart from 1YTB. The continuous DNA stretches implied in the interface with the cognate protein range from 8 to 18 base pairs (bp). For 1PAR and 2BOP, there are two identical half sites separated by 5 and 4 base pairs, respectively. The curvature intensity is variable, ranging from 14 in 1A66 to 69 in 1YTB. The ratio between the number of contacted phosphates and bases displays high °°variability, as well as the ratio between the number of contacted phosphates and the total number of phosphates (

). The sequence table 2 varies between GC rich sequences (2BOP) and AT rich sequences (1YTB). Finally, two sequences (2BOP and 1A74) are palindromic and one (1PAR) is quasi-palindromic. Although not comprehensive, our selection aimed to cover a large variety of protein DBD as well as DNA structures.

The coarse grain representations of the complexes introduced above are shown in . The reduced models reproduce correctly figure 2 the overall shape of both the DNA and the protein. The change in resolution, from atomic to coarse grain, induces a reduction of 70 to 80 of the total number of particles that allows systematic docking simulations within a reasonable simulation time.

%

Coarse grain minimization

The diminution of resolution increases the particle radii up to 2.94 ( ). In order to remove possible steric clashes introduced by Å table 1 the coarse grain representation, we relaxed the complex structures taken from the PDB with both partners in their reduced representation. We performed an ATTRACT minimization that allows the DNA to move in translation and rotation around the fixed protein. This procedure is called coarse grain optimization in what follows. The interaction energy and both the RMSD and the GCD between the

" "
native and the minimized DNA structures are reported in . The average values of RMSD and GCD are 0.7 and 0.5 respectively, table 3 Å ensuring that the reduced models introduce a negligible shift compared to the native all-atom complexes. In this article, the non-minimized PDB structures will be taken as references.

Rigid body protein DNA systematic docking

-For each complex, we then performed systematic docking simulations to determine if the combination of the DNA and protein coarse grain models with the ATTRACT systematic docking procedure could generate and select the reference complexes. For these simulations, the conformations of both protein and DNA are exactly those found in the experimental complexes. All final geometries generated by the docking algorithm were sorted out according to their interaction energy. In parallel, the RMSD and GCD relative to the native structure were calculated on all DNA beads. The plot of the interaction energy versus RMSD is represented in for each complex. figure 3 For the six studied systems, the energy rank, the interaction energy, the RMSD, the GCD and the cluster population are given in table for the four most stable geometries. In five cases out of six (1K79, 1PAR, 2BOP, 1A74 and 1A66), the lowest energy conformation 4 corresponds to the lowest RMSD and GCD, demonstrating that the interaction energy works efficiently as a scoring function for the docking purpose. The most stable geometries are identical to the structures obtained upon coarse grain minimization, showing the efficiency of the conformational space sampling by ATTRACT. Furthermore, these favorable geometries are generally highly populated, indicating the good convergence of the simulation. However, some low energy conformations are also characterized by high RMSDs (roughly 30 ) and low GCDs. Most of them are head-to-tail geometries, corresponding to a half-turn rotation of the DNA around the Å normal of the protein interaction surface starting from its position in the native complex (as described by Aloy and coworkers ). These [4 ] "

reverse conformations occur with palindromic or quasi-palindromic DNA (1PAR, 2BOP and 1A74), with energy difference lower than 2

"
RT with respect to the most stable prediction. For the DNA sequence found in 2BOP, which is both palindromic and structurally symmetric, the energy gap vanishes and the cluster with the head-to-tail DNA (cluster rank 2) is perfectly equivalent to the near native geometry (cluster rank 1), both in terms of energy and structure. In the case of 1A74, the DNA is not exactly structurally symmetric, with a RMSD between the reference and the head-to-tail DNA conformations of 0.6 . This explains the slight energy penalty of 0.2 RT units Å found between the clusters of ranks 1 and 3.

In the case of 1YTB, the second most stable structure (energy difference of 2.8 RT units with respect to the most stable conformation) is exactly the structure obtained after coarse grain optimization. The fact that this structure, which is the prediction closest to the native complex, is not the lowest energy one is probably linked to the structural particularity of the DNA within this complex. Indeed, the severe DNA curvature (69 ) induced by the TBP renders the minor groove convex instead of, as usual, concave. As a consequence, the geometric °contrast between grooves and backbones almost disappear, rendering the surface of interaction of the DNA less distinctive than in the other complexes.

Among other geometries located very close to the native interface, we find predictions with screwing displacements of the DNA along the helical axis by 2 or 3 bp with respect to the native or head-to-tail conformations. These structures are separated from the most stable geometries by an energy difference between 2 and 5 RT units (see cluster 3 for 1A66 and clusters 2 and 3 for 1K79 in ), reflecting table 4 that a good proportion of the correct interaction is found.

Finally, the energies of the most stable predictions are generally clearly separated out from the energy bulk of other conformations ( ). In most cases, and if one excludes the head-to-tail and screwed geometries, the energy gap is at least 10 to 12 RT. Except for the figure 3 very deformed TBP complex (1YTB), our model does exactly retrieve the important features of atomic resolution protein DNA interactions in easily discriminating the correct candidate among the multiple combinations of the partner geometries.

Balance of terms in the interaction energy

DNA is a highly charged macromolecule and it can be expected that its electrostatic nature plays a significant role in protein DNA interactions. Nadassy and collaborators showed from the analysis of crystallographic data that the protein DNA interfaces often [START_REF] Nadassy | [END_REF] present a protein side scattered with positively charged amino acids (lysine and arginine), responding to the DNA trace dominated by the negative phosphate groups. It is therefore interesting to explore which role electrostatics plays in the interaction energy, and what is its contribution to our scoring function.

To study the influence of electrostatics, we performed additional docking simulations with DNA phosphate bead charges all set to 1 or to 0, removing in the later case the electrostatic part of the interaction energy. Setting phosphate charge to 1 did not improve the prediction. The results with uncharged phosphate beads are represented in . Comparing to the results obtained with charges set to table 5 -0.7 (

), the weight of the electrostatic component in the total energy is between 20 and 30 . For all complexes but one, the table 4 % predictions closest to the reference structures are found at first rank, even for 1K79 and 2BOP for which the ratio between the contacted phosphates and bases are very high (

). Only for one case, i.e. 1YTB, no geometry is found at less than 3.6 from the reference table 2 Å complex, showing that electrostatics is essential for the quality of the prediction of this particular complex.

Considering the relative population of the targeted complexes, the inclusion of the electrostatic term clearly increases the number of best predicted geometries in all cases (see columns 5 and 6 of

). The Coulomb interaction acts as an electrostatic guide towards the table 5 native complex.

Sensitivity to DNA sequence

The DNA sequence can be discriminated on the basis of direct contacts between nucleic base functional groups and amino acid side chains in the minor and major grooves (direct recognition), but also via the energy level necessary to deform DNA in such a way that it optimally fits the protein structure (indirect recognition). Due to the absence of hydrogen-bonding potential in our reduced representation of DNA and protein, the coarse grained model presented here does not pretend to correctly reproduce the direct contacts between amino acid side chains and DNA functional groups. We have nevertheless evaluated the sequence sensitivity in the light of the steric differences that arise in our model from the differential van der Waals radii of GA3, GG3, GC2 and GT2 pseudo-atoms of A, G, C and T, respectively (see ). table 1 Among our complexes, we considered two contrasted cases, 2BOP for which the consensus DNA contains 75 of GC and 1PAR % where the consensus DNA counts 41 of GC ( ).

% table 2

We use as references the docking simulations of 2BOP and 1PAR with the consensus DNA sequences described in . We also table 4 generated d(AT) and d(CG) repeated sequences threaded on the structure of the reference DNAs. Since the RMSD is meaningless here, we compared the fractions of protein interface beads in the native structure which are recovered in the prediction, (see Materials and f pib Methods). Concerning 2BOP, most stable structures have energies of 49.7, 50.1 and 52.7 RT units, for respectively the consensus, energy complex obtained with the consensus DNA has also the highest . Indeed, hydrogen bonds are equally distributed between A, T, f pib C or G bases in the native complex.

Although our model has not been designed to be sequence attuned, we found here a good sensitivity to sequence, confirming the pertinence of our coarse grain representation.

Sensitivity to deformation

Designed with a shape recognition in mind, we expect our model to be sensitive to DNA and protein deformations but we also hope it will accept some structural fluctuations. This tolerance was evaluated by docking a non-native form of either DNA or protein on the native conformation of their partner.

Keeping the original base composition, we began to dock the proteins belonging to our set of complexes with consensus DNA presenting structures that deviate more or less from the experimental structures. In these calculations, the quality of the predicted complexes will be assessed by the fractions of conserved interface residues in protein ( ) and DNA ( ) rather than the RMSD, which f pib f dib results both from the differences between native and non-native DNA conformations and from the deviations in the positioning.

We first used DNA average structures extracted from a 15 ns molecular dynamics (MD) simulation of 2BOP . In this trajectory, [28 ] the E2 protein was rather rigid and remained very close to its X-ray counterpart. In contrast, the DNA was significantly flexible, so that the structures could be gathered in four clusters. The cross-RMSD between the four corresponding average structures were around 1.0 , and Å they all differed by at least 1.0 from the crystallographic conformation. Using these structures allows us to test the effect of moderate Å distortions on the docking efficiency. Indeed, we found that, whatever the MD average DNA structure, the best complex in terms of energy is very close to the reference one (at worst, a difference of 1.3 RT). Also, the average and are similar to the values obtained with the f pib f dib corresponding crystallographic DNA, i.e. cleaned from non pairing bases that do not exist in the MD oligomer (see first line of ). table 6 These results mean that our docking simulations well tolerate some fluctuations around the native conformation. Nevertheless, in this case, the global structural DNA features are preserved, in particular the curvature. A more severe test is to consider the recognition between proteins and straight canonical B-DNA. The results of these docking simulations are summarized in for the best predictions in term table 6 of energy for the 1A66, 1K79, 2BOP and 1A74 complexes. In these complexes, the reference structures of the bound DNA exhibit different curvature intensities ( ), from 14 (1A66) to 55 (1A74). The RMSD calculated between experimental and B oligomers table 6 °reflect these distortions, with values lying between 1.0 (1A66) and 7.6 (1A74) (

). A large proportion of the reference interface

Å Å table 6
is predicted with 1A66 protein and B-DNA, which is very close to the reference DNA (RMSD of 1.0 ). We found ~ 70 and ~ 45

Å f pib % f dib
for the first ranked complex structure, 81 and 83 for the second ranked prediction that is within 0.1 RT units in energy of the first.

% % %

For 1K79, the results are even better ( ~ 85 , ~ 80 ) while the B-DNA is significantly different from the bound DNA reference f pib % f dib % structure (RMSD 3.2 ). However, in the case of 2BOP, where the DNA also differs by 3.2 from the B-DNA but with a marked

= Å Å
curvature, we find a relatively low value of ( 50) and (20 ). Indeed, one DNA half-site is well located while the second does not f pib % f dib % contact its cognate protein part. Finally, our procedure fails to retrieve the right protein DNA interface in 1A74, the complex that contains the most distorted DNA. Nevertheless, even in this case, the B-DNA is located near the protein region where the native interaction occurs, so that, 22 of the protein residues implicated in the native interface are retrieved in the best predictions. For an illustration purpose, the % output geometries for 2BOP, clusterized within 0.1 RT in energy and 0.1 in , are reported in . It can be noted that in spite of a % f pib figure 4 35 curvature deformation of the DNA, the best ranked geometries in terms of energy recover more than 50 of the interface residues of °% the protein.

To complete this study, we have explored the sensitivity of the protein DNA model to protein conformational variation, by carrying out similar tests with structures of proteins that are not complexed with any DNA, keeping intact the conformation of the bound DNA.

Among our data set, X-ray structures of DNA-free (unbound) proteins are available for 1PAR, 2BOP and 1K79. The global structures of bound and unbound proteins are very similar, as shown by the rather low values of RMSD ( ). However, some noticeable table 7 differences are observed in protein interfaces. Focusing on amino acids of the DNA/protein interfaces highlights that between 27 and 41% of them differ from 1.6 to 4.5 in RMSD ( ), reflecting that side chain conformations are submitted to dramatic changes upon DNA Å table 7 binding. In addition, 30 and 25 of the amino acids belonging to the DNA binding domains are lacking in 1BAZ and 1JJH , the

% [30 ] [31 ]
unbound counterparts of 1PAR and 2BOP proteins. The results of the docking simulations are summarized in for the first ranked table 7 predictions. Note that the interaction energies reported here for 1BAZ and 1JJH cannot be compared to those of native protein native DNA docking (

), because of differences in protein interface compositions. The use of IJJH and 1BAZ leads to very good docking table 3 predictions. The best complex simulated with 1GVJ , related to 1K79, shows a very large RMSD associated to low GCD and high [START_REF] Tahirov | To be published 33[END_REF] f pib and values, a feature that corresponds to a head-to-tail conformation, as described above. Reminding that, in these complexes, the f dib proteins contact the major groove of their targets, these results mean that DNA major grooves in coarse grain representation remain large enough for supporting amino acids side chain conformations significantly altered comparing to their native form. Also, deletions of several amino acids in protein DNA binding domains can occur without damaging the prediction.

In sum, these results show that our procedure is sensitive to DNA and protein distortions. However, the major part of the beads composing the interaction surface can be predicted without prerequisite about deformations, providing that they are not too much important. Actually, our model seems to support differences in DNA curvature up to 30 and variations in a third of the interacting amino °acids conformers.

Discussion

In this work, we propose an original DNA coarse grain model dedicated to protein DNA docking. Our representation is derived from -Zacharias reduced model of proteins, with 13 bead types for electrostatics and Van der Waals interaction. Such model is devoted to reproduce the volume occupied by the DNA, and thus the shape of its interaction surface. A special attention was directed to the groove dimensions and the curvature in order to render at best the global DNA conformation. Actually, because DNA is often deformed within protein DNA complexes, it is reasonable to expect that DNA protein recognition mainly depends on the form of the two partners. A second element is the charge-charge attractions between the negative DNA phosphate groups and the positively charged amino acid side chains. This is taken into account in our DNA model through negative charged beads representing the phosphate groups.

Despite its simplicity, our model has shown remarkable performances when used to assemble a representative set of protein DNA complexes, differing by both the DNA binding domain in proteins and the deformations in bound DNAs, in particular their curvatures. The correct geometry of association could be predicted unambiguously in all cases, except for the TBP complex in which the DNA structure, markedly distorted, loses the typical contrast between hollow grooves and sharp backbones. However, even in this case, the first ranked prediction was very close to the correct geometry and the second was the correct one. So, the loss of atomic details did not appear to be an obstacle to the docking prediction of DNAs on their cognate proteins.

When dealing with coarse grained models, it is important to delineate their scope, i.e. the molecular properties that can be reproduced, comprising the features that do not benefit from explicit treatment. First, we examined the sensitivity of our methodology to the DNA sequence. The base composition appears as a fundamental element of protein DNA complexes, via the hydrogen bonds occurring between the DNA bases and the amino acid side chains. At the low resolution used to represent proteins and DNA in our model (nucleic acid beads often group together both acceptor and donor groups), this type of direct interactions is not explicitly treated. This may obliterate the capacity of the model to confidently retrieve the sequence the most appropriate for a given protein. For this investigation, we drastically muted the DNA sequence without modifying its conformation. In all cases, the base composition of the sequence energetically favored well correlated to that of the consensus sequence. Thus, even in absence of any explicit energetic formulation of the hydrogen bonds between the DNA bases and the amino acids, the differences between A, G, C and T in terms of van der Waals parameters are sufficient for detecting DNA sequence preferences. Besides, this result illustrates the role of the steric hindrance of the functional groups within the DNA grooves in the protein DNA interactions.

-Second, we investigated the tolerance of the coarse grain model to DNA and protein structures. For this purpose, we docked the proteins with conserved DNA sequences but with structures altered with respect to their native forms. Conversely, we also tested native DNA with free-DNA protein conformations. Slight alterations in terms of curvature of the DNA target, with RMSD up to 1 , were fairly Å tolerated and did not at all modify the docking results. A more stringent test consisted to use a canonical straight B-DNA. Deviations in DNA curvature up to 28 did not notably modify the predicted protein interface. For more intensive DNA bending, the interaction surfaces °were either partially predicted (curvature of 35 ) or only indicative of the protein region where the DNA interacts (curvatures > 55 ). °°Comparable results were obtained when using deformed protein structures and native DNA forms. So, differences in more than 40 of the % side chain conformations belonging to the interface did not prevent the complex to occur in the right place. Since no aberrant positioning was generated, these results are encouraging in the view of further docking applications, suggesting that a rough exploration of DNA and protein deformations should be sufficient to succeed a realistic docking. However, at the same time, they highlight the importance for the DNA to be pre-deformed or flexible to correctly realize their interaction with a protein.

Finally, the electrostatics was completely eliminated on the phosphate groups of the DNA model, in order to estimate its role in the docking prediction. Unexpectedly, we found that electrostatics was not really essential for achieving reliable interaction between the two species. The steric complementarity was sufficient in most cases to unambiguously predict the correct geometry of the complex, underlining again the role of the structural complementarity of the partners. It must be noted however that alternative interfaces could also be found among the firstly ranked candidate geometries, but they were easily discriminated upon reintroduction of electrostatics. So, inclusion of electrostatics on DNA was found to strengthen the interaction and broaden the attraction energy well, in addition to eliminating non electrostatic-matching interfaces. This coarse grain model is an exciting working model, one of the most attractive aspects being its simplicity which makes it a promising tool in large system treatment, due to the consequent gain in computer time. The present calculations already indicate that this new type of method, specifically developed to treat protein DNA associations, is instrumental in obtaining an overall structure of a representative set of complexes. Furthermore, it allows to infer valuable informations about the elements that guide such macromolecular constructs. We anticipate that our approach could be used for successfully predict the interface between numerous protein DNA systems, on condition that the partners are not strongly distorted in the complex. Many complexes involving transcription factors respond to this requirement. Their DBD domains are often highly structured and are not submitted to dramatic changes upon binding. Similarly, the curvatures of DNA engaged in such complexes rarely exceed 30 . Nevertheless, it is clear that a general and complete comprehensive view °of macromolecular docking should include flexibility of both partners, protein and DNA. We have already shown that it is possible to account for protein fragment flexibility in the course of docking simulations ( , ). Our next task will thus be to couple a stochastic [9 ] [33 ]

exploration of DNA deformations with the present coarse grain systematic docking procedure. complexes. The protein and the DNA are in green and red respectively. Pictures were obtained with Pymol .

[ MG stands for major groove whereas mg means minor groove. * For 1A66, the curvature range on all conformations is 6 22 .

-°

Table 3

Interaction energy and RMSD relative to the native complex obtained after coarse grain minimization.

complex interaction energy RT

[ ]

RMSD /native

[Å]

GCD /native

RMSD /native

[Å]

RMSD /CG opt.

[Å] † The symbol shows head-to-tail configurations and ‡ indicates a screwing along the DNA helical axis.

GCD /native

Table 5

Energy rank, interaction energy, RMSD relative to the native structure and cluster population for the four lowest energy geometries of the six studied complexes after systematic docking without charge.

The rank of the closest cluster in the simulation with charges is also reported. 41.0 1 -The RMSD with respect to the uncharged corresponding cluster and the population are also indicated in parentheses. A dash indicates that no cluster was found with a RMSD less than 0.5 . 22 29

complex energy rank interaction energy RT

Table 7

Docking simulation results on proteins in their unbound forms (PDB codes are in the column 2). Columns 3 and 4 indicate the level of structural differences between the bound and the unbound protein.

The RMSD in column 3 is a global measure, taken on the heavy atoms. is the percentage of amino acids implicated in the protein DNA interface for which the RMSD calculated between their bound F aac and unbound forms is more than 1.6 . We consider that a residue belongs to the interface if it is located at less than 5 from any DNA atom. Columns 5 to 9 present the results of the docking Å Å simulations using the unbound protein for the best ranked prediciction: interaction energy, RMSD and GCD compared to the native position of the DNA, and . f pib f dib complex unbound protein RMSD /bound

  ) and d(CG) repeated sequences, while are 100, 95 and 100 respectively. The high values of obtained here indicate that the f pib % f pib predictions are very close to the reference complex. Besides, the very low energy and large obtained with d(CG) repeated sequence f pib may be interpreted by the fact that 80 of the intermolecular hydrogen bonds involve bases G and C of the native DNA sequence. % In the case of 1PAR, the lowest energies are respectively of 73.0, 67.9 and 59.0 RT units for the consensus, d(AT) and d(CG) --repeated sequences. The values of are 95 for the consensus while 92 and 91 for the AT and CG repeats. In this case, the lowest f pib % % %

Figure 1

 1 Figure 1 Coarse grain partition of the DNA model. Each colored domain represents a different bead.

Figure 2

 2 Figure 2 All-atom cartoon, all-atom surface and coarse grain representation for (a) 1K79, (b) 1PAR, (c) 2BOP, (d) 1A74, (e) 1YTB and (f) 1A66

Figure 3

 3 Figure 3 Plots of the interaction energy versus the RMSD for (a) 1K79, (b) 1PAR, (c) 2BOP, (d) 1A74, (e) 1YTB and (f) 1A66. Circle radii are proportional to the square root of the cluster populations.

Figure 4

 4 Figure 4 Fraction of the protein interface residues in the native structure of 2BOP, which are recovered in the prediction ( ), against the interaction f pib energy for the docking simulations of the E2 protein with (a) the native DNA structure and (b) the canonical B-DNA conformation. Output geometries are clustered within 0.1 RT units in energy and 0.1 in . Circle radii are proportional to the square root of the cluster % f pib

  Tepper and Voth built for instance a spring network model with 16 beads per structural block and 2 different types of

	[12 ]

Table 4

 4 Energy ranks, interaction energies, RMSD relative to the native structure, RMSD relative to the coarse grain optimized structures, GCD relative to the native structure and cluster population for the four lowest energy geometries obtained by systematic docking simulations.

	[Å]

[ ]

Table 6

 6 Docking simulation results on systems where the DNA conformations differ from their native structures. Columns 2 to 4 figure the curvature, lowest energy, and for the best prediction with both f pib f dib docking partners in their native conformation (see ). Columns 6 to 9 present results obtained with a modelled DNA: RMSD between the reference and the non-native DNA, lowest predicted table 4 energy and the corresponding and . For 2BOP , the native DNA has been cleaned from its terminal non-pairing bases. Non-native DNAs were extracted from a 15 ns molecular dynamics f pib f dib a simulation of the complex (see text) and the corresponding RMSD, interaction energy, and are averaged over these MD structures. For the four other complexes, the non-native DNA structure was f pib f dib a straight canonical B-form.

	complex	reference DNA

16

16

16

16

16

16

16

16

16

16

16

16

Ackowledgements:

P. P. thanks Dr. Syma Khalid for helpful discussions and the CNRS for financial support. Martin Zacharias is also acknowledged for kindly providing his protein model and the ATTRACT program.

Table 2

For each complex, the protein DNA Binding Domain (DBD) and the DNA interface are provided, as well as the length of the DNA part implied in the interface, the number of specific interaction sites (DNA bases involved in intermolecular hydrogen bonds) and the curvature intensity. This table also presents the ratio between the number of contacted phosphates (P) and the number of contacted bases, the ratio between the number of contacted phosphates and the total number of phosphates, the CG percentage and if the DNA sequence is palindromic ( ) or not ( ).

+ -