domain: chim spi

text:
Weidong Zhao

Daoxin Liu

Xiaohua Zhang

Ying Zhou

Ruixia Zhang

Hao Zhang

Chang Ye

Improving the fretting and corrosion fatigue performance of 300M ultra-high strength steel using the ultrasonic surface rolling process

Keywords: 300M ultra-high strength steels, Ultrasonic surface rolling process (USRP), Compressive residual stress, Corrosion Fatigue, Fretting fatigue

300M ultra-high strength steels (300M steels) are frequently used in the manufacture of aircraft landing gear due to their high strength and ductility. However, their high sensitivity to surface defects accelerates fatigue failure and hinders their wider application. In this work, ultrasonic surface rolling processing (USRP) was used to process 300M steel. The surface roughness, hardness, microstructure, and residual stresses before and after USRP treatment were compared, and the surface roughness for USRP-treated samples (0.062 μm) was found to be lower than that for untreated samples (0.32 μm). In addition, a plastically deformed layer was generated on the surface of USRP-treated samples that resulted in higher hardness. Beneficial compressive residual stresses were introduced as a result of USRP treatment. The better surface finish, higher surface hardness and compressive residual stresses lead to significant improvement in the resistance of the 300M steels to fretting fatigue and corrosion fatigue. The fretting fatigue life increased from 11.9K cycles to 56.3K cycles, while the corrosion fatigue life increased from 29.9K cycles to 702.1K cycles.

Introduction

Compared with common steels, 300M ultra-high-strength steels have extremely high tensile strength (~1900 MPa) and yield strength (~1600 MPa) and thus are commonly used in the manufacture of aircraft landing gear. Landing gear requires high fretting fatigue strength to A c c e p t e d M a n u s c r i p t withstand a high number of takeoffs and landings. In coastal areas, fatigue damage to the landing gear is exacerbated by corrosion damage induced by ocean air and seawater. Thus, damage due to fretting fatigue (FF) [START_REF] Winkler | Fretting fatigue behavior of high-strength steel monostrands under bending load[END_REF] and corrosion fatigue (CF) [START_REF] Pérez-Mora | Very high cycle fatigue of a high strength steel under sea water corrosion: A strong corrosion and mechanical damage coupling[END_REF] can reduce the service life of the landing gear. Fatigue crack nucleation and the growth of defects, which frequently occur at the material surface, can be increased by fretting wear and corrosion damage. However, Sih and Macdonald [START_REF] Sih | Fracture mechanics applied to engineering problems-strain energy density fracture criterion[END_REF] indicated that 300M steel is very sensitive to surface defects. If the surface of landing gear made from 300M steel is damaged, the fatigue crack nucleation rates will be further increased. Therefore, an effective surface modification technique for decreasing surface defects and improving the fatigue life of 300M steel is desperately needed.

Surface mechanical strengthening methods are frequently used to increase fatigue resistance of metallic materials by changing the surface microstructure and the distribution of residual stresses [START_REF] Zhou | Effect of surface mechanical attrition treatment on low cycle fatigue properties of an austenitic stainless steel[END_REF][START_REF] Ganesh | Studies on fatigue life enhancement of pre-fatigued spring steel specimens using laser shock peening[END_REF][START_REF] Kattoura | Effect of laser shock peening on residual stress, microstructure and fatigue behavior of ATI 718Plus alloy[END_REF][START_REF] Majzoobi | The effects of deep rolling and shot peening on fretting fatigue resistance of Aluminum-7075-T6[END_REF][START_REF] Ye | Fatigue performance improvement in AISI 4140 steel by dynamic strain aging and dynamic precipitation during warm laser shock peening[END_REF].For example, Prevéy et al. [START_REF] Prevéy | Mitigation of Scc and Corrosion Fatigue Failures in 300M Landing Gear Steel Using Mechanical Suppression[END_REF] reported that low plasticity burnishing technology can effectively improve the high cycle CF strength of 300M steel by generating high surface compressive residual stress. Bertini and Santus [START_REF] Bertini | Fretting fatigue tests on shrink-fit specimens and investigations into the strength enhancement induced by deep rolling[END_REF] used deep rolling (DR) technology to generate a smooth surface and residual stresses that significantly increased the FF properties of 7075 aluminum alloy. In the fields of aviation and machining, shot peening (SP) is widely used because it can effectively increase fatigue resistance and is easy to implement [START_REF] Naidu | Effect of shot blasting on plain fatigue and fretting fatigue behaviour of Al-Mg-Si alloy AA6061[END_REF][START_REF] Lv | Effect of shot peening on the fatigue resistance of laser surface melted 20CrMnTi steel gear[END_REF][START_REF] Xu | The influence of A c c e p t e d M a n u s c r i p t shot peening on the fatigue response of Ti-6Al-4V surfaces subject to different machining processes[END_REF]. Namjoshi et al. [START_REF] Namjoshi | Effects of Shot-Peening on Fretting-Fatigue Behavior of Ti-6Al-4V[END_REF] illustrated that SP effectively impeded the FF micro crack nucleation from the surface of Ti6Al4V by transforming tensile residual stress to compressive residual stress. Majzoobi and Abbasi [START_REF] Majzoobi | On the effect of shot-peening on fretting fatigue of Al7075-T6 under cyclic normal contact loading[END_REF] also observed that SP could remarkably increase the FF resistance of an aluminum alloy. However, Tekeli [START_REF] Tekeli | Enhancement of fatigue strength of SAE 9245 steel by shot peening[END_REF] found that SP could damage the surface of steel by subjecting it to impacts from non-uniform shot blasting. Zhang and Liu [START_REF] Zhang | Effect of shot peening on fretting fatigue of Ti811 alloy at elevated temperature[END_REF] also observed that SP increased surface roughness and generated some micro-cracks in the surface of Ti811. This shortcoming of SP limits its use in treating 300M steel. Traditional SP by itself cannot meet the requirements for fewer surface defects and a deeper strengthening of the surface layer in 300M steel.

Ultrasonic surface rolling processing (USRP) is a recently developed technology that combines the advantages of traditional rolling technology with ultrasound technology [START_REF] Li | Effect of ultrasonic surface rolling at low temperatures on surface layer microstructure and properties of HIP Ti-6Al-4V alloy[END_REF][START_REF] Liu | Surface nanocrystallization of 17-4 precipitation-hardening stainless steel subjected to ultrasonic surface rolling process[END_REF][START_REF] Zhang | Microstructure and surface properties of 17-4PH stainless steel by ultrasonic surface rolling technology[END_REF]. Compared with a traditional rolling technique, USRP relies mainly on ultrasonic energy instead of using force to treat the surface of a sample, forming a deeper plastic deformation layer at the sample surface by using a lower load. For instance, Liu et al. [START_REF] Liu | Determination of the plastic properties of materials treated by ultrasonic surface rolling process through instrumented indentation[END_REF] noted that the surface grains of 40Cr steel were severely refined after USRP treatment. Li et al. [START_REF] Li | Effects of the different frequencies and loads of ultrasonic surface rolling on surface mechanical properties and fretting wear resistance of HIP Ti-6Al-4V alloy[END_REF] also reported that USRP is able to induce plastic deformation and compressive residual stresses in the surface of Ti6Al4V that can significantly improve the fretting friction and wear resistance. In addition, because the loading in USRP is much lower than that used in traditional rolling technology, no changes in the overall size and shape of a sample will occur. Wang et al. [START_REF] Wang | Influence of the ultrasonic surface rolling process on stress corrosion cracking susceptibility of high strength pipeline steel in neutral pH environment[END_REF] also reported that USRP decreased the surface roughness of X80 steel from 1.3 μm to 0.2 μm. The reason is that during USRP treatment, the sample surface is struck by a freely rotating ball in a liquid lubricant, which can reduce surface defects and achieve a much smoother surface. Compared with SP-which is conducted using an automated shot peening machine and may not strike recessed areas on the surface or other areas that are difficult to reach-USRP equipment can be installed on a computer numerical control (CNC) lathe, allowing the surface of the sample to be treated homogeneously by accurately controlling the strike intensity and density. At present, many A c c e p t e d M a n u s c r i p t studies try to use USRP to change the surface state and mechanical properties of metal materials. Lu et al. [START_REF] Lu | Study on surface characteristics of 7050-T7451 aluminum alloy by ultrasonic surface rolling process[END_REF] reported that USRP significantly increased the surface finish and compressive residual stress and hardness of aluminum. Wang et al. [START_REF] Wang | Influence of Ultrasonic Surface Rolling on Microstructure and Wear Behavior of Selective Laser Melted Ti-6Al-4V Alloy[END_REF] used USRP technology to treat Ti6Al4V, which significantly enhanced the surface hardness and wear resistance. In summary, USRP technology has obvious advantages in improving surface finish and mechanical properties of some metallic materials.

USRP technology has been widely used in materials that are soft to moderately hard, such as titanium alloy and aluminum alloy, to improve the mechanical properties. However, no studies have used USRP treatment to decrease surface defects on 300M steel, a material that is typically difficult to deform. Specifically, the relationship between surface integrity (surface finish, microstructure, residual stress, etc.) and mechanical behaviors (FF and CF) of 300M ultra-high-strength steel after USRP treatment has not been investigated in any studies published in the literature to date. In this study, we report the impact of USRP on surface defects and the mechanical performance (in terms of FF and CF) of 300M steel. The surface microstructure and distribution of surface hardness and residual stress of 300M steel were also characterized.

Experimental Materials and Methods

Ultrasonic Surface Rolling Process treatment

By combining ultrasonic striking and static load, as shown in Fig. 1, USRP treatment can produce a plastic deformation layer in the surface of a target sample by using a tungsten carbide cobalt (WC/Co) ball (with a diameter of 14 mm) that freely rotates at high speed to strike and roll the surface. In this study, an ultrasonic frequency of 28 kHz, a vibration amplitude of 12 μm and a static load of 900 N were used. To process the surface of a rod-shaped sample, the USRP equipment was mounted on a CNC lathe. A rotation speed of 45 r/min and a feed rate of 0.08 mm/min were used in this study.

Materials

Table 1 exhibits the chemical composition of the 300M steel. After double annealing (at 870°C for 30 min, followed by cooling in oil at 300°C for 2 h, followed by air cooling), the main microstructure of 300M steel was found to be tempered martensite; very few bainites and residual austenites were observed in the microstructure. As shown in Table 2, the 300M steel showed great strength and ductility.

Rod-shaped samples were prepared for tests to determine FF and CF (Fig. 2). To ensure a certain contact strength between the fatigue sample and the fretting pads, the fretting pads were also made of 300M steel. The surface roughness for all samples was 0.32 μm as produced by sequential mechanical polishing using different grades of silicon carbide sandpaper (#320, #400, #600, #800, #1000 and #1200).

Testing and characterization methods

The following tests were conducted to determine the surface integrity and mechanical properties of the USRP-treated 300M samples:

 Microstructure characteristics: Microstructure characteristics of USRP-treated samples were determined by using a JEOL JSM-6390 scanning electron microscope (SEM) at 20 kV. The cross sections of the samples were mechanically polished using silicon carbide sandpaper (#300, #400, #600, #800 and #1200) and diamond suspensions (3 µm and 1 µm). After polishing, each sample was etched using a 4% nital solution.

A c c e p t e d M a n u s c r i p t

 Identification of phase composition: A Rigaku D/Max 2200 PC X-ray diffraction (XRD) unit was used to identify surface phase changes in untreated and UNSM-treated samples at 40 kV and 40 mA. The test conditions were as follows: copper was used as the radiation source, and the XRD scanning was conducted at a 2θ angle ranging from 30° to 85° at a rate of 1 degree/minute.

 Surface morphology and roughness: The surface fluctuation and unevenness of 300M steel before and after USRP treatment were investigated by using SEM (JEOL JSM-6390 microscope). A TR-300 surface roughness tester from Time Instrument Indonesia was also applied to further study the surface state changes.

 Residual stress: A Proto LXRD-MG2000 residual stress tester was utilized to analyze the residual stress of 300M steel before and after USRP treatment by the classical sin 2 Ψ method. The test conditions were as follows: the target radiation was Cr (30 kV, 8 mA) and the diffraction crystal surface was (211). To measure the in-depth residual stresses, all samples were electrochemically polished using a solution of 25% H2SO4+65% H3PO4 +10% H2O at a temperature of 60°C and a rate of 5 μm/min). The X-ray beam size was Φ 3 mm and the area of area of electro-polishing was 94.2 mm 2 .

 Hardness: The micro-hardness in the cross section of untreated and USRP-treated samples was measured using a Knoop HV-1000 micro-hardness tester. All samples were tested under a load of 25 g at a dwell time of 20 s. Each measurement was repeated at least five times.

 Fretting fatigue: A self-designed experimental apparatus was used to carry out FF testing in an SDS100 electro-hydraulic servo fatigue tester. The loading method was set as pull-pull. As shown in Fig. 3, the form of contact between the sample and fretting pad was cylinder to camber. The fatigue cyclic loading waveform was a sine wave of 10 Hz. The contact force between the sample and the fretting pad was imposed by a bolt and was controlled at 200 MPa. The contact pad, which is also made from 300M steel, was polished using carbide sandpapers (from 300# to 1200#). The contact pad had a surface roughness Ra of 0.118 μm and a surface hardness of 647 HK. The constant stress ratio R was 0.1, and the maximum axial cycle stress Max was 1100 MPa. The number of cycles before the sample fracture was used to evaluate the FF resistance of the 300M steel samples. Each measurement was repeated three times. To investigate the mechanism of FF fracture, the fatigue fracture surface features were studied using SEM.

A c c e p t e d M a n u s c r i p t Fig. 3. Schematic diagram of the fatigue fracture testing system (inset adopted from Liu et al. [START_REF] Liu | Effect of the Ultrasonic Surface Rolling Process on the Fretting Fatigue Behavior of Ti-6Al-4V Alloy[END_REF]).

 Corrosion fatigue: To determine corrosion fatigue performance, each 300M sample was fixed on the self-designed CF testing system, which consisted of a SDS100 electro-hydraulic servo fatigue tester and a glass container that was used to hold an aqueous solution of 3.5% NaCl. Fig. 4 presents a schematic diagram of the CF test setup.

The gauge section of the sample was completely submerged in the solution, and the ratio of the volume of the corrosion solution to the surface area of the gauge section was not less than 20 mL/cm 2 . The CF test was carried out at 24 ± 3°C using a pull-pull axial loading mode. The fatigue cyclic loading waveform was a sine wave, and the axial loading force was 1100 MPa. The uniform frequency was 10 Hz, and the stress ratio R was 0.1. Each measurement was repeated three times. After CF testing, selected fracture surfaces were analyzed using SEM.

Results and discussion

Surface morphology and roughness

The surface state of untreated and USRP-treated 300M steel samples are presented in Fig. 5. The untreated samples were mechanical polished using a grinder to obtain low surface roughness (~ 0.3 μm). Obvious grooves can be noticed in the surface of the untreated sample, and these grooves contribute to the initiation of fatigue cracking. After USRP treatment, most mechanical scratches on the surface of the samples were noted to have healed, and the number of surface defects were dramatically reduced. The surface roughness Ra of untreated samples is 0.32 μm (as shown in Fig. 5c). Following USRP treatment, the sample surface has become much smoother, and the surface roughness is decreased to 0.062 μm. Because the loading in USRP is much lower than that used in traditional rolling and the ball in USRP is able to freely rotate over the surface of sample, any micro-pits and mechanical furrows in the surface can be flattened.

A c c e p t e d M a n u s c r i p t

Microstructure

SEM micrographs of the cross sections of 300M steel samples before and after USRP treatment are shown in Fig. 6. Before USRP treatment, a martensitic structure with different orientations can be observed. After USRP treatment, a plastic deformation layer can be observed with the martensite laths aligned in the scanning direction. The thickness of the severe plastic deformed layer is about 6 μm (Fig. 6b). Wang et al. [START_REF] Ting | Investigations on the nanocrystallization of 40Cr using ultrasonic surface rolling processing[END_REF] observed similar surface microstructure in USRP-treated 40Cr steel. However, due to the severe surface deformation, it was difficult to determine the grain size.

XRD

Figure 7 shows the change in the XRD patterns of 300M steel samples before and after USRP treatment. After USRP treatment, the three main peaks at (100), ( 200) and (211) become much lower and wider, and the relative intensities of the three peaks are also decreased. At the same time, USRP is able to refine the microstructure and induce surface compressive residual stress on the samples by striking the sample surface at high frequency; as a result, the (100), ( 200) and (211) peaks are shifted to the right following USRP. To facilitate a further comparison of the XRD images obtained before and after USRP treatment, the full width at half maximum (FWHM) values were determined (Table 3). From Table 3, it can be noticed that the FWHM values of the three XRD peaks were slightly increased after USRP treatment, indicating a reduction in the surface grain size and an increase in the surface dislocation density following USRP.

A c c e p t e d M a n u s c r i p t

Hardness

Figure 8 compares the hardness of the 300M steel samples before and after USRP treatment.

The mean hardness at the top surface of the untreated samples is 644 HK, while that for samples after USRP treatment is 876 HK, corresponding to a 36% increase. At the same time, in the direction along the cross section, the hardness of the USRP-treated samples gradually decreases. The work-hardening and grain refinement induced by the plastic strain results in an improvement in hardness. Due to the gradient nature of the plastic strain induced by USRP, the plastic strain in the top surface is also the highest and decreases gradually with depth; thus, the hardness in the top surface is the highest and decreases gradually with depth. In addition, Carlsson and Larsson [START_REF] Carlsson | On the determination of residual stress and strain fields by sharp indentation testing. PartI: theoretical and numerical analysis[END_REF] reported that residual stress also affects the surface hardness. USRP can induce high-magnitude compressive residual stress in the top layer; this also contributes to the increase in hardness. It should be noted that the hardened layer is around 140 μm, while the obvious plastic deformation layer is only 6 μm (Fig. 6). The actual work-hardened layer can be much deeper than the depths that can be observed using SEM. Similar hardening behavior has been observed when using USRP or other mechanical surface strengthening methods for treating other metals [START_REF] Lu | Study on surface characteristics of 7050-T7451 aluminum alloy by ultrasonic surface rolling process[END_REF][START_REF] Liu | Effect of the Ultrasonic Surface Rolling Process on the Fretting Fatigue Behavior of Ti-6Al-4V Alloy[END_REF][START_REF] Yasuoka | Improvement of the fatigue strength of SUS304 austenite stainless steel using ultrasonic nanocrystal surface modification[END_REF][START_REF] Qin | Effects of ultrasonic nanocrystal surface modification on the wear and micropitting behavior of bearing steel in boundary lubricated steel-steel contacts[END_REF][START_REF] Zhang | The effects of ultrasonic nanocrystal surface modification on the fatigue performance of 3D-printed Ti64[END_REF].

Residual stress

Figure 9 presents the change of in-depth compressive residual stresses in 300M steel before and after USRP treatment. It can be observed that the un-treated specimen is almost stress-free while a deep layer of compressive residual stresses was introduced in the USRP-treated specimen. The mean compressive residual stress on the top surface increases to 1285 MPa, and the depth of surface compressive residual stress layer is 520 µm. Similar to the results of other studies [START_REF] Zhang | Microstructure and surface properties of 17-4PH stainless steel by ultrasonic surface rolling technology[END_REF][START_REF] Ting | Investigations on the nanocrystallization of 40Cr using ultrasonic surface rolling processing[END_REF][START_REF] Liu | Finite element modeling of ultrasonic surface rolling process[END_REF], USRP was found to produce a large and deep layer of compressive residual stress. Even though the residual stress introduced has some effect on the hardness [START_REF] Carlsson | On the determination of residual stress and strain fields by sharp indentation testing. PartI: theoretical and numerical analysis[END_REF], the effect if not that significant compared with that by grain refinement and work-hardening. The increased hardness is mainly attributed to microstructure refinement and work hardening. Because of the low microstructure refinement and work hardening at locations farther below the top surface, the hardened layer is not as deep as the layer with compressive residual stress. In addition, based on the Hertz contact model, the area of maximum shear stress is located in the subsurface, and the maximum compressive residual stress of the USRP-treated specimen is found at a depth of 20 µm below the top surface.

Fretting fatigue test

FF testing was carried out to evaluate the FF resistance of 300M steel before and after USRP treatment. Fig. 10 shows the average FF life of 300M steel before and after USRP treatment (σmax= 1100 MPa). The mean number of FF cycles before failure for the three untreated samples is 11.9×10 3 . For USRP-treated samples, the mean number of FF cycles is 56.3×10 3 , corresponding to a 4.7-fold increase. These results demonstrate that the FF resistance of 300M steel was significantly enhanced by USRP treatment. The improvement in the FF properties of 300M steels following USRP treatment is attributed to three main causes. First, the enhancement of surface hardness after USRP treatment is an A c c e p t e d M a n u s c r i p t important reason for the improvement of the FF properties of 300M steel by hindering FF crack nucleation. Generally, FF crack nucleation is caused not only by the fretting wear damage but also by the high concentration of stress near the contact edge [START_REF] Mutoh | Fracture mechanics approach to fretting fatigue and problems to be solved[END_REF][START_REF] Endo | Initiation and propagation of fretting fatigue cracks[END_REF]. It is important to note that the enhanced hardness can simultaneously improve the resistance of fretting wear damage and the concentration of stress. On one hand, the improvement of surface hardness can significantly reduce the fretting wear damage. Because the fretting pads are also made from 300M steel, the surface hardness of USRP-treated samples is higher than that of fretting pads. Hence, the fretting wear damage of the USRP-treated samples against the fretting pad is much less than that of untreated samples against the fretting pad. On the other hand, the stress concentration at the contact edge is also decreased by improved hardness. In general, hardness is proportional to the yield strength of metallic materials [START_REF] Zhang | General relationship between strength and hardness[END_REF]. Due to the formation of a hardening layer on the surface of USRP-treated samples, the surface local yield strength is also improved. Enhanced surface yield strength can improve the stress concentration resistance of metallic materials [START_REF] Yang | Investigation on the fretting fatigue behaviors of Ti-6Al-4V dovetail joint specimens treated with shot-peening[END_REF]. Therefore, the surface of a USRP-treated sample has a lower stress concentration at the contact edge than that of the untreated sample. In summary, the higher hardness of the USRP-treated sample is able to slow FF crack initiation from the fretting wear and stress concentration zone.

Second, the introduction of compressive residual stress after USRP treatment can hinder FF crack nucleation and early crack propagation, which is another important reason for the improved FF properties of 300M steel. First, the compressive residual stress reduces the FF crack nucleation rate for the following two reasons: 1) It was reported that the surface residual compressive stress not only weakens the effective fretting fatigue that drives stress and stress concentration [START_REF] Guo | The basic relationships between residual stress, white layer, and fatigue life of hard turned and ground surfaces in rolling contact[END_REF][START_REF] Yongshou | Finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole[END_REF], but it also slows fretting wear [START_REF] Amanov | Fretting wear and friction reduction of CP titanium and Ti-6Al-4V alloy by ultrasonic nanocrystalline surface modification[END_REF][START_REF] Kumar | Fretting Wear Behavior of Laser Peened Ti-6Al-4V[END_REF]. Reduced stress concentration and fretting wear damage is conducive to the inhibition of FF crack nucleation, and 2) According to prior studies [START_REF] Majzoobi | On the effect of shot-peening on fretting fatigue of Al7075-T6 under cyclic normal contact loading[END_REF][START_REF] Fridrici | Prediction of cracking in Ti-6Al-4V alloy under fretting-wear: Use of the SWT criterion[END_REF], induced compressive residual stresses can enhance the tangential force threshold level. When the tangential force is below a certain threshold level, there will be no FF crack nucleation at the trailing edge of contact. Due to the formation of a larger and deeper layer of compressive residual stress at the surface, the USRP-treated samples require a larger tangential force to promote FF crack nucleation. Hence, the induced compressive residual stress after USRP treatment contributes to the slowing of the FF crack nucleation. In addition, it has been reported that the major contribution of compressive residual stress is to prevent early FF crack propagation [START_REF] Majzoobi | On the effect of shot-peening on fretting fatigue of Al7075-T6 under cyclic normal contact loading[END_REF][START_REF] Waterhouse | Residual stress and surface roughness in fretting fatigue[END_REF]. In the early FF crack propagation stage, compressive residual stress can significantly decrease tensile stress at the crack tip [START_REF] Waterhouse | Residual stress and surface roughness in fretting fatigue[END_REF]. Similar to clamping stress, compressive residual stress can also close up FF cracks in the early stages of FF crack propagation [START_REF] Liu | Improvement of the fretting fatigue and fretting wear of Ti6Al4V by duplex surface modification[END_REF]. Therefore, the early FF crack propagation rate is significantly reduced by the induction of large compressive residual stress in the near-surface region after USRP treatment [START_REF] Cadario | Influence of residual stresses from shot peening on fretting fatigue crack growth[END_REF][START_REF] Lee | Fretting fatigue behaviour of shot-peened Ti-6Al-4V at room and elevated temperatures[END_REF][START_REF] Lee | Fretting behavior of shot peened Ti-6Al-4V under slip controlled mode[END_REF][START_REF] Lee | Analysis of fretting fatigue of cavitation shotless peened Ti-6Al-4V[END_REF]. In summary, the compressive residual stress introduced by USRP treatment can improve the FF resistance of 300M steel.

Finally, many studies have reported that the surface roughness has a more complex influence on the FF properties of materials [START_REF] Zhang | Effect of shot peening on fretting fatigue of Ti811 alloy at elevated temperature[END_REF][START_REF] Waterhouse | Residual stress and surface roughness in fretting fatigue[END_REF][START_REF] Fu | Improvement in fretting wear and fatigue resistance of Ti-6Al-4V by application of several surface treatments and coatings[END_REF]. To study the influence of surface roughness on FF, surface roughness in the fretting wear zone of all samples was also measured after FF testing. The surface roughness (Ra) of both untreated and USRP-treated samples after FF A c c e p t e d M a n u s c r i p t testing is enhanced (0.44 μm and 0.188 μm, respectively). However, the surface roughness of untreated samples is always larger than that of USRP-treated samples before and after FF testing. This proves that reduced surface roughness also has a positive influence on the improvement of FF properties, since fretting fatigue cracking has been reported to be easily initiated at the location of maximum stress-strain (a location near the contact edge), which mainly depends on the tangential stress induced by fretting action on the contact interface of the contact pad and the sample [START_REF] Mutoh | Fracture mechanics approach to fretting fatigue and problems to be solved[END_REF]. In the actual fretting action process, the fretting pad and sample only have some points of contact rather than complete contact. When the surface roughness of a sample decreases, there will be a larger number of real contact points between the fretting pad and sample, which can reduce the real contact pressure [START_REF] Liu | Finite element modeling of ultrasonic surface rolling process[END_REF]. As a result, adhesion damage will be inhibited, and the tangential stress of USRP-treated samples induced by fretting action will also be decreased. Therefore, the enhanced surface roughness in the USRP-treated sample is also attributed to the increase in FF resistance.

The morphologies of the FF fracture and fretting wear zone of untreated and USRP-treated 300M steel (σmax= 1100 MPa) can be observed in the SEM images presented in Fig. 11. The main FF cracks on all samples are detected at the fretting contact edge, where the maximum value of tangential stress and severe fretting wear is found [START_REF] Mutoh | Fracture mechanics approach to fretting fatigue and problems to be solved[END_REF][START_REF] Szolwinski | Mechanics of fretting fatigue crack formation[END_REF]. Many obvious grooves, adhesions and fatigue cracks can be observed in the fretting wear zone of the untreated samples (Fig. 11a). The fretting damage mechanisms in the untreated 300M steel samples are adhesive wear, abrasive wear and fatigue wear. Following USRP treatment, the hardness of the USRP-treated samples is higher, so there are fewer grooves in the surface of the fretting wear zone (Fig. 11c). The surface damage mechanisms in the fretting wear zone of the USRP-treated samples are adhesive wear and fatigue wear only (with no abrasive wear). Severe wear damage occurred at the surface of untreated samples in the fretting wear zone, which provides numerous sites for fatigue crack nucleation. In Fig. 11b, many fatigue crack sources can be seen following FF fracture of untreated samples, which demonstrates that the life of FF is significantly controlled by the FF crack nucleation stage. Once these cracks generate from the surface, they expand rapidly and cause fatigue fracture. Compared with untreated samples, USRP-treated samples have fewer surface defects and larger compressive residual stresses that decrease the fatigue crack nucleation rate, such that only one fatigue crack was found in the USRP-treated sample (Fig. 11d). In other words, the fatigue life of 300M steel samples after USRP treatment is improved due to the decrease in surface defects and the induction of larger surface compressive residual stresses and higher surface hardness.

Corrosion fatigue test

The CF test was performed in 3.5% sodium chloride solution to evaluate the CF properties of 300M steel before and after USRP. The average CF life of untreated and USRP-treated 300M steels (σmax= 1100 MPa) is illustrated in Fig. 12. After repeating three parallel tests, the number of CF cycles (which represent the CF resistance) was recorded for untreated and USRP-treated samples. The mean number of CF cycles for untreated 300M steel samples is 29.9×10 3 . For USRP-treated samples, the mean number of CF cycles, which is 702.1×10 3 , represents a 23-fold increase over the number of cycles for untreated samples. This demonstrates that the tendency of USRP to decrease the surface corrosion activity by reducing surface defects is a major reason for the improvement in CF life in the USRP-treated samples. There are two main reasons for the increase in CF resistance of 300M steel in USRP-treated samples. On one hand, USRP can decrease surface defects by producing a sample surface with uniform electrochemical activation. Zuo et al. [START_REF] Zuo | The aspect ratio of surface grooves and metastable pitting of stainless steel[END_REF] have reported that the ratio w/d (where w and d indicate the mean width and mean depth of the grooves in the sample surface, respectively) can be used to evaluate the capability of corrosion pits to nucleate. With a decrease in roughness, the w/d ratio increases and corrosion pits in the sample surface become more difficult to nucleate. USRP can flatten the sample surface, which reduces the surface roughness. Compared with untreated samples, nucleation of corrosion pits on the surface of USRP-treated samples becomes more difficult, so the process of fatigue crack nucleation from corrosion pits is also restricted. On the other hand, if some fatigue micro-cracks are able to nucleate from the corrosion pits of USRP-treated 300M steel, the deeper and larger compressive residual stresses can heal the micro-cracks and hinder their further expansion. Thus, the CF resistance of 300M steels can be significantly enhanced by USRP. Due to the different failure mechanisms of FF and CF, FF will more easily damage the surface of USRP-treated samples and release the surface residual stresses than CF. Thus, compared with the FF life, the improvement in the CF life of USRP-treated sample is more obvious.

The morphologies of the CF fracture of 300M steel before and after USRP treatment (σmax= 1100 MPa) are shown in Fig. 13. Numerous corrosion pits can be observed in the untreated samples (Fig. 13a). Because of the ubiquity of surface defects, the surface electrochemistry of the untreated samples is not uniform, and corrosion pits can easily nucleate from these defects. When the metal is subjected simultaneous alternating loading and corrosion attack, corrosion pits will lead to stress concentration, such that fatigue micro-cracks can be easily initiated from these areas. Thus, numerous fatigue cracks can be observed in the surface of the untreated samples (Fig. 13b). Compared with untreated samples, USRP-treated samples have only one fatigue crack source in the CF fracture (Fig. 13c,d). Moreover, the CF crack that initiated from the corrosion pits is delayed for a distance of ~120 µm. Because A c c e p t e d M a n u s c r i p t electrochemical activation at the surface decreases after USRP treatment, the process of corrosion pit nucleation is prolonged. At the same time, the larger surface compressive residual stresses in the USRP-treated sample also hinder fatigue crack nucleation from corrosion pits and can delay the propagation of fatigue cracks into the interior of the sample. Therefore, after USRP treatment, it is obvious that the CF resistance of 300M steel can be enhanced by decreasing the surface roughness and increasing the surface compressive residual stresses.

Conclusion

In this study, USRP was used to decrease surface defects and improve the FF and CF resistance of 300M steel. The results demonstrate that USRP, by combining traditional rolling technology with ultrasound techniques, can significantly reduce surface defects in 300M steel and induce a surface strengthening layer, adjusting the distribution of residual stress and hardness. Following USRP treatment, the FF and CF properties of 300M steel are also improved, resulting from the reduction in surface defects and the increase in compressive residual stress and hardness. This research proves that USRP can potentially be used to treat 300M steel components for improved properties and performance in industrial applications.

Fig. 1 .

 1 Fig.1. Schematics of the USRP test setup (inset adopted from Liu et al.[START_REF] Liu | Effect of the Ultrasonic Surface Rolling Process on the Fretting Fatigue Behavior of Ti-6Al-4V Alloy[END_REF]).

  A c c e p t e d M a n u s c r i p t

Fig. 2 .

 2 Fig. 2. Dimensions of samples for fretting fatigue and corrosion fatigue (in mm).

Fig. 4 .

 4 Fig. 4. A schematic diagram of the CF testing system.

Fig. 5 .

 5 Fig. 5. The surface morphology of 300M steel (a) before and (b) after USRP treatment.(c) Surface roughness of 300M steel before and after USRP treatment.

A c c e p t e d M a n u s c r i p tFig. 6 .

 6 Fig. 6. The cross-sectional microstructure of 300M steel (a) before and (b) after USRP treatment (where RD is the rolling direction and ND is the normal direction).

Fig. 7 .

 7 Fig. 7. XRD patterns of 300M steel before (untreated) and after USRP treatment.

Fig. 8 .

 8 Fig. 8. In-depth hardness of 300M steel before and after USRP treatment.

Fig. 9 .

 9 Fig. 9. Compressive residual stress of 300M steel before and after USRP treatment.

Fig. 10 .

 10 Fig. 10. The number of cycles until FF failure (σmax= 1100 MPa) of 300M steel before (untreated) and after USRP treatment.

  A c c e p t e d M a n u s c r i p t

Fig. 11 .

 11 Fig. 11. Fatigue fracture SEM images of 300M steel before and after USRP treatment (maximum stress level σmax=1100 MPa): The fretting wear zone of an untreated sample, (b) the FF fracture of an untreated sample, (c) the fretting wear zone of a USRP-treated sample, and (d) the FF fracture of USRP-treated sample.

A c c e p t e d M a n u s c r i p tFig. 12 .

 12 Fig. 12. The number of cycles before CF failure of 300M steel before (untreated)and after USRP treatment.

Fig. 13 .

 13 Fig. 13. Corrosion fracture SEM images of 300M steel before and after USRP treatment (maximum stress level σmax = 1100 MPa): (a,b) The CF fracture of an untreated sample; (c,d) CF fracture of a USRP-treated sample.

  s c r i p t

Table 1 .

 1 Chemical composition of 300M steel (wt.%)

	Carbon	Chromium	Vanadium	Manganese	Silicon	Nikel	Molybdenum	Copper	Iron
	(C)	(Cr)	(V)	(Mn)	(Si)	(Ni)	(Mo)	(Cu)	(Fe)
	0.42	0.84	0.09	0.82	1.57	1.94	0.38	0.84	Bal.

Table 2 .

 2 Mechanical properties of 300M steel after double annealing

	Yield strength	Tensile strength	Elongation	Section shrinkage
	(MPa)	(MPa)	(%)	(%)
	1631	2015	12.3	52.8

Table 3 .

 3 FWHM values of the main peaks identified from XRD patterns of 300M steel

	Crystal plane	Untreated	USRP
	(110)	0.433	0.443
	(200)	0.531	0.547
	(211)	0.629	0.635

Acknowledgments:

This work was supported by the National Natural Science Foundation of China (Award no. 51771155) and China Scholarship Council (CSC).


Jasmin Cevost

Cédric Vaillant

Sam Meyer
email: sam.meyer@insa-lyon.fr

ThreaDNA: predicting DNA mechanics' contribution to sequence selectivity of proteins along whole genomes

Motivation: Many DNA-binding proteins recognise their target sequences indirectly, by sensing DNA's response to mechanical distortion. ThreaDNA estimates this response based on high-resolution structures of the protein-DNA complex of interest. Implementing an efficient nanoscale modeling of DNA deformations involving essentially no adjustable parameters, it returns the profile of deformation energy along whole genomes, at base-pair resolution, within minutes on usual laptop/desktop computers. Our predictions can also be easily combined with estimations of direct selectivity through a generalised form of position-weight-matrices. The formalism of ThreaDNA is accessible to a wide audience. Results: We demonstrate the importance of indirect readout for the nucleosome as well as the bacterial regulators Fis and CRP. Combined with the direct contribution provided by usual sequence motifs, it significantly improves the prediction of sequence selectivity, and allows quantifying the two distinct physical mechanisms underlying it.

Introduction

Virtually all genomic processes are achieved by proteins which bind a subset of target DNA sequences among millions to billions of possible sites. This sequence recognition process, or readout, involves dif-ferent mechanisms [START_REF] Harteis | Making the bend: DNA tertiary structure and protein-DNA interactions[END_REF], as illustrated on Fig. 1 in the example of the bacterial architectural and regulatory protein Fis. The most natural one is a direct interaction of aminoacids with specific bases (G/C at positions ±7), allowing a strong sequence selectivity. This selectivity is often described in the form of "sequence logos" (as shown on Fig. 1A) or position weight matrices (PWMs), which represent the frequency of occurrence of each nucleotide at all positions relative to the protein, as computed from a set of experimentally identified binding sites. But interestingly, in the central region of the Fis-DNA complex, depicted here in blue, the PWM also exhibits significant sequence preferences, without there being any physical contact between protein and DNA. DNA mechanics plays a central role in this indirect readout. Through distal interactions, Fis imposes a significant bending to DNA in this central region. Since DNA's structure and flexibility depend on its sequence, the propensity of the double-helix to accommodate the deformation will result in sequence selectivity [START_REF] Becker | Indirect readout: detection of optimized subsequences and calculation of relative binding affinities using different DNA elastic potentials[END_REF]. This recognition mode is typically less specific than direct contacts, but may be particularly relevant to abundant proteins that bind many different sites along the genome, such as architectural proteins or global regulators [START_REF] Harteis | Making the bend: DNA tertiary structure and protein-DNA interactions[END_REF]. Notably, since DNA flexibility is defined at least at the level of dinucleotides (and possibly further) rather than individual nucleotides, descriptors based on the latter, such as position weight matrices, might be poorly suited to this mechanism, as we will also show. Recent studies showed indeed that incorporating DNA shape parameters as descriptors significantly improves the prediction of regulatory protein binding sites [START_REF] Zhou | Quantitative modeling of transcription factor binding specificities using DNA shape[END_REF] and subsequent gene expression patterns [START_REF] Peng | Quantitative modeling of gene expression using DNA shape features of binding sites[END_REF].

The objective of ThreaDNA is to predict DNA mechanics' contribution to sequence selectivity of various proteins, based on a physical model of the complex without any protein-specific adjustable parameters. Such computations could be addressed with all-atomic molecular dynamics simulations [START_REF] Paillard | Analyzing protein-DNA recognition mechanisms[END_REF], but these involve a considerable computational effort even for a single DNA oligomer, and cannot be used for entire genomes. Instead, ThreaDNA is based on a nanoscale description of DNA as an elastic chain of base-pairs [START_REF] Meyer | Temperature Dependence of the DNA Double Helix at the Nanoscale: Structure, Elasticity, and Fluctuations[END_REF]. In this computationally cheaper coarsegrained scheme, the mechanical energy associated to protein binding depends on (i) the equilibrium structure and elasticity of the DNA oligomer and (ii) its conformation in the complexed state (Fig. 1B). The former ingredient has been obtained for all possible sequences, from a combination of experimental [START_REF] Xu | DNA architecture, deformability, and nucleosome positioning[END_REF] and numerical simulation [START_REF] Pasi | muABC: a systematic microsecond molecular dynamics study of tetranucleotide sequence effects in B-DNA[END_REF] data. The latter ingredient is generally more difficult to obtain, because it requires some level of modeling of the protein-DNA interaction in the complex. Such models were developed mainly for the nucleosome, with various levels of complexity [START_REF] Anselmi | A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability[END_REF][START_REF] Alexandre V Morozov | Using DNA mechanics to predict in vitro nucleosome positions and formation energies[END_REF][START_REF] Xu | Long-range effects of histone point mutations on DNA remodeling revealed from computational analyses of SIN-mutant nucleosome structures[END_REF][START_REF] Stolz | ICM Web: the interactive chromatin modeling web server[END_REF][START_REF] Deniz | Physical properties of naked DNA influence nucleosome positioning and correlate with transcription start and termination sites in yeast[END_REF][START_REF] De | Sequence-dependent collective properties of DNAs and their role in biological systems[END_REF][START_REF] Fathizadeh | Rigid-body molecular dynamics of DNA inside a nucleosome[END_REF][START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF], which demonstrated the relevance of DNA nanoscale models in predicting sequence preferences of proteins. In particular, if the protein is stiffer than DNA, it can be treated implicitly [START_REF] Anselmi | A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability[END_REF][START_REF] Xu | Long-range effects of histone point mutations on DNA remodeling revealed from computational analyses of SIN-mutant nucleosome structures[END_REF][START_REF] Deniz | Physical properties of naked DNA influence nucleosome positioning and correlate with transcription start and termination sites in yeast[END_REF] as imposing a rigid conformation to the bound DNA, which can then be directly taken from a high-resolution of the complex, obtained by X-ray crystallography or by NMR. ThreaDNA is based on an improvement of this rigid description, which provides several key advantages as a bioinformatics tool. The very limited computational requirements of the approach make it possible to compute protein distributions on entire genomes on a desktop or laptop computer in a few minutes. In spite of this efficiency, in the case of the nucleosome, the predictive power of the algorithm matches that of more complex models developed specifically for this nucleoprotein complex (see below).

But more importantly, in contrast to previous software, ThreaDNA allows generalising the approach to a large class of DNA-binding proteins. In this paper, we illustrate the software on the important bacterial transcriptional regulators Fis and CRP. Many programs are dedicated to the prediction of transcription factor binding sites; however, most of these do not rely on physico-chemical descriptions, but rather on statistical sequence models, which must be trained on a large dataset of experimentally known binding sites, and this independently for each analysed protein. In contrast, ThreaDNA is based on validated physical models, involving essentially no free parameter, and requires no training. Its main restriction is the knowledge of a high-resolution structure of the protein-DNA complex of interest without disruption of the double-helical structure. Although this is a limiting requirement, the software remains applicable to a large class of proteins of wide interest. Importantly, to our knowledge, this is the first software to make the present approach easily accessible to the community of experimental or computational biologists interested in various proteins that distort DNA upon binding. In order to facilitate its diffusion, the algorithm was therefore implemented in a user-friendly interface designed for non-specialist users, and is also available as an installation-free online tool on the Galaxy platform [START_REF] Enis Afgan | The Galaxy platform for accessible, reproducible and collaborative biomedical analyses: 2016 update[END_REF]. The software also provides computational tools to combine the indirect contribution with direct contributions given by standard PWMs, with a strong improvement in predictive power.

Models and Methods

Parametrisation of DNA nanoscale elasticity

DNA's deformations are described with 6-vectors q corresponding either to base-pair or base-pair step deformations [START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF]. For a given sequence s, the average conformation of naked DNA is quoted q 0 (s), and its rigidity is given by the stiffness matrix K(s).

The software includes two parameter sets ("NP" or "ABC"), and the length of s (di/tri/tetranucleotide) depends on this choice. The "NP" parameter set describes the elasticity of base-pair steps at the dinucleotide level, and was obtained from a collection of high-resolution DNA or DNA-protein crystallographic structures [START_REF] Xu | DNA architecture, deformability, and nucleosome positioning[END_REF]. In the "ABC" parameter set, obtained from microsecond-long molecular dynamics simulations [START_REF] Pasi | muABC: a systematic microsecond molecular dynamics study of tetranucleotide sequence effects in B-DNA[END_REF], the base-pair step elasticity depends on the tetranucleotide sequence ("ABC_s"), and the internal base-pair deformations on the trinucleotide sequence ("ABC_i"). In all cases, under the elastic approximation, the associated deformation energy follows the same quadratic form: U (q, s) = 1 2 (qq 0 (s)) t K(s)(q -q 0 (s)). (A) Fis directly contacts the DNA bases at positions ±7 (red background), where it exhibits a strong preference for G/C bases. In the central region (blue), DNA is not contacted, but Fis still exhibits significant sequence preferences, possibly for sequences most favourable to Fis-induced bending. Adapted from [START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF]. (B) ThreaDNA estimates DNA mechanical energy associated to protein binding from highresolution structures of the complex, which provides a significant contribution to sequence selectivity.

Estimation of sequence-dependent deformation energy from protein-DNA structural models

The deformation of a given DNA base-pair (step) conformation is the result of a mechanical equilibrium between the external potential exerted by the protein F ext (q), and the DNA internal elastic energy U (q, s). Even in the case of non-specific binding (F ext (q) independent of the sequence), the resulting equilibrium conformation q e minimising the total energy still depends on the sequence, and so does also the deformation energy, see details in [START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF]. Computing these conformations generally requires an involved modeling of this external force field [START_REF] Alexandre V Morozov | Using DNA mechanics to predict in vitro nucleosome positions and formation energies[END_REF][START_REF] Fathizadeh | Rigid-body molecular dynamics of DNA inside a nucleosome[END_REF][START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF]. To simplify the calculation, we take advantage of the strong stiffness of many DNA-binding proteins, as compared to DNA stiffness. In the limit of infinite stiffness, the conformation q e becomes sequence-independent, and the deformation free energy can be computed very efficiently from the formula above. This approach (hereafter referred to as a "rigid approach") has been proposed for the nucleosome [START_REF] Anselmi | A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability[END_REF][START_REF] Xu | Long-range effects of histone point mutations on DNA remodeling revealed from computational analyses of SIN-mutant nucleosome structures[END_REF][START_REF] Xu | DNA architecture, deformability, and nucleosome positioning[END_REF][START_REF] Deniz | Physical properties of naked DNA influence nucleosome positioning and correlate with transcription start and termination sites in yeast[END_REF]. Its main limitation is that the histone core is actually not infinitely stiff: the observed structures depend quite strongly on the incorporated sequence [START_REF] Olson | Working the kinks out of nucleosomal DNA[END_REF], and the predictions of these programs depend equally strongly on which structural model is used as template (see Results). Our algorithm overcomes this limitation by combining the whole dataset of known structures into a single computation of deformation energy, as follows. If different conformations {q i e } i=1,...,P were observed in different crystals, the calculation is based on the hypothesis that this set is representative of the configurational space accessible to the complex incorporating any sequence. For a given sequence s, the equilibrium conformation q adopted will then be a statistical "mix" of these states, with a respective weight given by the Maxwell-Boltzmann equilibrium statistics: the total deformation free energy F (s) is then given by exp(-βF (s)) = P i=1 exp(-βU (q i e , s)), where β = 1/(k B T ) is an effective temperature parameter. Our algorithm extends the method to other proteins, where direct as well as indirect readout contribute to the binding free energy.

Implementation of algorithm

The algorithm was written in Python2 using the NumPy library [START_REF] Van Der Walt | The NumPy array: a structure for efficient numerical computation[END_REF] and the Tkinter cross-platform graphical library. This makes the code easy to change, and natively executable on recent Linux or MacOS systems, as well as on Windows after installing these tools. The user-friendly graphical interface is designed for non-specialist users focusing on a protein of interest; and the program is numerically optimised so as to allow genome-wide computations on a desktop computer. The first (and delicate) step is the inclusion of the protein-DNA complex of interest into the software database. It can be provided either in the form of a NDB ID [START_REF] Buvaneswari Coimbatore Narayanan | The Nucleic Acid Database: new features and capabilities[END_REF], or an output file of the popular conformational analysis programs 3DNA [START_REF] Lu | 3dna: a software package for the analysis, rebuilding and visualization of three-dimensional nucleic acid structures[END_REF] (available on the webserver Web3DNA) or Curves+ [START_REF] Lavery | Conformational analysis of nucleic acids revisited: Curves+[END_REF]. For new proteins, it is crucial to check that the DNA structure was not broken during the conformational analysis, otherwise the computation will be meaningless; usually, one only has to check that no base-pair is missing in the base-pair step list. A previously observed difficulty in the analysis is that, because of thermal and experimental noise in the structures, the computed energy profiles are affected by an unknown scaling factor ("effective temperature") [START_REF] Nils | DNA nanomechanics in the nucleosome[END_REF][START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF]: combining different structures of different non-thermal energy scales thus imposes an arbitrary rescaling choice. We choose the normalising constant such that, for a random sequence, the profiles computed with all structural models have the same standard deviation. An "effective temperature" parameter then fixes the global energy scale: for the default value of 1, all incorporated structural models contribute significantly to the combined profile, and a smaller value gives more weight to the most favourable structures. As a result, the computed profiles are all given in arbitrary units. Details of the computation parameters are described in the software documentation. The memory requirement and computation time is proportional to the protein size (in contacted base-pairs) and genome length.

Results

ThreaDNA: a new tool to analyse physical features involved in protein binding at the genomic scale

ThreaDNA is a new software that predicts the contribution of DNA deformations in the sequence selectivity of proteins. Such deformations are often described extensively in structural studies [START_REF] Andrew A Napoli | Indirect Readout of DNA Sequence at the Primary-kink Site in the CAP-DNA Complex: Recognition of Pyrimidine-Purine and Purine-Purine Steps[END_REF][START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF], but their translation into sequence-dependent binding preferences requires a suitable physical model of the DNA-protein complex. The efficient "rigid" approach proposed by ThreaDNA relies on a nanoscale description whereby the protein imposes the conformation of the DNA base-pairs in the complex [START_REF] Anselmi | A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability[END_REF][START_REF] Xu | Long-range effects of histone point mutations on DNA remodeling revealed from computational analyses of SIN-mutant nucleosome structures[END_REF][START_REF] Deniz | Physical properties of naked DNA influence nucleosome positioning and correlate with transcription start and termination sites in yeast[END_REF]. This approximation considerably simplifies the analysis of the system, which can then be implemented by a nonspecialist user for a large class of DNA-binding proteins of interest, provided high-resolution structures of the complex involving no double-helix disruption are available from X-ray crystallography or NMR experiments. The inclusion of several alternate structural models for the same protein results in a refined physical description of the interaction, while preserving its strong computational efficiency. As an example, for the proteins described in this paper, computing DNA deformation energies at all possible positions along a bacterial or yeast genome of a few megabases typically takes less than a minute on a laptop or desktop computer, using less than 1 Gb RAM. In a first step, ThreaDNA requires the user to incorporate the DNA conformation of the nucleoprotein complex of interest into the software database. We recommend using the Web3DNA webserver [START_REF] Lu | 3dna: a software package for the analysis, rebuilding and visualization of three-dimensional nucleic acid structures[END_REF] to analyse a PDB file of interest. The output (.out) file can be provided to ThreaDNA together with the original PDB file. In a second step, the main program can then use this conformation to compute mechanical energies on any sequence provided in the standard Fasta format. The details of the calculation (list of considered struc-tures, DNA stiffness parameter set...) are specified in an input file of standard format.

The program can be executed via a user-friendly graphical interface, available as a Supplementary File, which runs natively on MacOS/Linux distributions. Additionally, a web-server version is available on a local version of the Galaxy bioinformatics platform (bioinfo.insa-lyon.fr) [START_REF] Enis Afgan | The Galaxy platform for accessible, reproducible and collaborative biomedical analyses: 2016 update[END_REF], which provides an installation-free access to all users. The returned profiles are in the standard BedGraph format and can be visualised on genome browsers (Fig. S1). The indirect selectivity of the protein is also returned as a generalised position weight matrix (PWM), that represents the energy or occurrence probability for each di/tetranucleotide along the protein (see below), in the standard JASPAR format. An additional subprogram facilitates the manipulation and combination of such generalised PWMs.

The nucleosome: genomic and highaffinity sequences

To illustrate the predictive power and possible applications of the software, we start with the nucleosome. Since most previous comparable models were developed specifically for this complex, we use it as a benchmark, keeping in mind that our software aims at generalising the approach to other proteins. We first use ThreaDNA to compute nucleosome occupancies on the entire Saccharomyces cerevisiae genome (Fig. 2A). These predictions are compared to experimental data obtained from DNA digestion experiments by micrococcal nuclease followed by high-throughput sequencing [START_REF] Kaplan | The DNA-encoded nucleosome organization of a eukaryotic genome[END_REF], either on in vitro reconstituted chromatin, or on the native ("in vivo") fibre. The calculation involves computing (i) deformation energies at all genomic positions without any free parameter, and (ii) a Boltzmann inversion of the profile to get occupancies, using a single global scaling parameter (effective temperature). Note that the latter operation coarsely neglects the interaction between adjacent nucleosomes [START_REF] Chevereau | Thermodynamics of intragenic nucleosome ordering[END_REF][START_REF] Van Der Heijden | Sequencebased prediction of single nucleosome positioning and genome-wide nucleosome occupancy[END_REF]; this is justified here by our focusing on the former computation by the present software.

The agreement is good with in vitro data (r 2 = 0.56), and only slightly less so with in vivo data, suggesting that in yeast, the positions occupied by most nucleosomes are thermodynamically encoded in the sequence through DNA mechanical properties. These results are comparable to previous ones obtained by rigid approaches, e.g., a correlation of 0.45 is reported in [START_REF] Vincent Miele | DNA physical properties determine nucleosome occupancy from yeast to fly[END_REF]. In contrast, better correlations could only be obtained using a different class of sequence-based models trained on the analysed data [START_REF] Kaplan | The DNA-encoded nucleosome organization of a eukaryotic genome[END_REF][START_REF] Van Der Heijden | Sequencebased prediction of single nucleosome positioning and genome-wide nucleosome occupancy[END_REF], involving a large number of fitted parameters. However, it was noted that, with some exceptions [START_REF] Van Der Heijden | Sequencebased prediction of single nucleosome positioning and genome-wide nucleosome occupancy[END_REF], even these specialised models fail to reproduce the strong affinity of specific sequences used in crystallisation experiments. A possible explanation is that these sequences bind the histones with qualitatively different conformations [START_REF] Olson | Working the kinks out of nucleosomal DNA[END_REF], which is difficult to take into account within a single model. Notably, ThreaDNA takes this plasticity into account, by letting each sequence statistically "choose" its favourite shape from a combination of crystallised structures, rather than imposing a single one. Although this treatment is simplified compared to previous schemes [START_REF] Alexandre V Morozov | Using DNA mechanics to predict in vitro nucleosome positions and formation energies[END_REF][START_REF] Fathizadeh | Rigid-body molecular dynamics of DNA inside a nucleosome[END_REF][START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF], it successfully reproduces the strong affinity of various sequences (Fig. 2B, lower panel), which is not possible based on a single structural template (upper panel and Fig. S3) [START_REF] Xu | Long-range effects of histone point mutations on DNA remodeling revealed from computational analyses of SIN-mutant nucleosome structures[END_REF][START_REF] Stolz | ICM Web: the interactive chromatin modeling web server[END_REF][START_REF] Deniz | Physical properties of naked DNA influence nucleosome positioning and correlate with transcription start and termination sites in yeast[END_REF]. Although the structural landscape sampled by ThreaDNA may not be comprehensive with respect to other high-affinity or genomic sequences of yet unknown conformation [START_REF] Meyer | Inferring coarsegrain histone-DNA interaction potentials from high-resolution structures of the nucleosome[END_REF], new structures will likely be obtained regularly in the future, thereby "automatically" refining our model. Altogether, considering the simplifications imposed by its purpose, our model stands the comparison with most reported predictive models dedicated specifically to the nucleosome, including for the delicate prediction of high-affinity sequences. But more importantly, our program is the first to generalise the approach to other proteins, for which none is currently available.

Sequence selectivity of Fis, a major bacterial architectural and regulatory protein

Factor for inversion stimulation (Fis) is one of the most abundant DNA-binding proteins in Escherichia coli in conditions of rapid growth [START_REF] Travers | DNA supercoiling and transcription in Escherichia coli: The FIS connection[END_REF]. As shown in Fig. 1, Fis binds around 15 bp of DNA, with specific contacts at positions ±7, and indirect sequence readout occurring in the central region. It has been suggested that the latter recognition might be achieved through DNA denaturation [START_REF] Nowak-Lovato | Binding of nucleoid-associated protein Fis to DNA is regulated by DNA breathing dynamics[END_REF]; however, since existing crystallographic models of the complex exhibit significant DNA bending without disruption of the double-helix, we address the question, whether double-stranded flexibility of DNA might rather be the relevant mechanism. To answer this question, we used ThreaDNA to compute deformation energies imposed by Fis at all positions along the E. coli chromosome, and asked if experimentally known binding sites are associated to significantly low values. Fis binding sites were detected in many separate studies, each of them often focusing on a particular gene promoter, and this information was collected into the RegulonDB database [START_REF] Gama-Castro | RegulonDB version 9.0: high-level integration of gene regulation, coexpression, motif clustering and beyond[END_REF]. The database thus contains around 250 binding sites at base-pair resolution, with different levels of confidence depending on the experimental method used. Fig. 3 shows that the average mechanical energy profile around experimental binding sites (blue) drops at the binding position, indicating that Fis binding sequences are associated to weaker mechanical energies than their neighbours, and than genomic average. Consistently, the associated histogram is significantly shifted to the left (p-value P < 10 -6 , Kolmogorov-Smirnov test), as compared to the whole genome. This observation is expected if DNA mechanical properties play a significant role in the selectivity, as hypothesised. On the other hand, we also note that the deformation energies of most experimental binding sites are not among the lowest in the genome, indicating that other mechanisms are involved in the recognition process, including the aforementioned direct readout at positions ±7.

Fis was crystallised in complex with several DNA sequences, which adopt different conformations [START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF]. We analysed this flexibility by computing the deformation energy associated to these sequences, depending on which conformation is used as template in the program (Fig. S4). In most cases, ThreaDNA correctly predicts the observed binding position, associated to a low deformation energy, when the computation is based on the specific conformation adopted by the considered sequence, but not necessarily by other conformations. Thus, as observed previously for the nucleosome, the conformational freedom exhibited in the crystals is an important ingredient for the prediction of high-affinity sequences. Indeed, the prediction of binding affinities for these sequences is strongly improved by the use of a combined structure (r 2 = 0.44) compared to a single structure (r 2 = 0.3).

DNA sequence-encoded mechanical

properties are essential determinants of CRP selectivity cAMP receptor protein (CRP) is another important global bacterial regulator, involved in cell metabolism. It binds several hundred sites along the E. coli genome, also with a combination of direct and indirect sequence recognition [START_REF] Andrew A Napoli | Indirect Readout of DNA Sequence at the Primary-kink Site in the CAP-DNA Complex: Recognition of Pyrimidine-Purine and Purine-Purine Steps[END_REF], and bends the DNA by al-most 90°(Fig. 4A). The degeneracy of recognised sequences in the non-contacted central region thus also points to a role for DNA mechanics. However, in absence of physical models of the interaction, little is known on this contribution. We start with the approach already used for Fis, with the ∼350 experimental binding sites listed in the Reg-ulonDB database, and the 1CGP structural model for DNA deformations [START_REF] Schultz | Crystal structure of a CAP-DNA complex: the DNA is bent by 90 degrees[END_REF]. The results are shown on Fig. 4: the decrease observed at experimental positions is here much stronger than for Fis (P < 10 -16 , Kolmogorov-Smirnov test). Importantly, in contrast to the latter case, the large majority of observed values are among the weakest of the genome. This observation suggests that DNA distortions could not only be a significant, but even the dominant contribution to the sequence selectivity of CRP. Yet this hypothesis seems contradicted by the presence of a minority of datapoints in the right side of the histogram. We reasoned that these points might also correspond to false positives of the database, as RegulonDB incorporates data of heterogeneous levels of confidence, and considering that the spatial resolution of most methods used (including DNA footprinting by DNAse I) is lower than a single basepair. As an example, two gene regulatory regions (sohB and proP) reportedly contain two binding sites separated by a single basepair, which seems unlikely. In both cases, only one of the two sites has a low bending energy, whereas the other is very unfavourable (identifiers ECK120012440 and ECK120015998), likely indicative of false positives. The same is true of 6 out of 11 reported regions with overlapping CRP sites.

To weaken the effect of such issues, we repeated the analysis on an independent dataset obtained by genomic SELEX [START_REF] Shimada | Novel roles of cAMP receptor protein (CRP) in regulation of transport and metabolism of carbon sources[END_REF]. In contrast to the previous case, these sites are obtained from a single genome-wide experiment, where DNA fragments enriched in CRP binding are isolated, and a subsequent bioinformatics analysis allows identifying the strongest binding sites at base-pair resolution. The resulting list is shorter than that of RegulonDB (∼260 sites), but since it does not result from a mixing of heterogeneous studies, it might include less false positives. Indeed, the histogram is quite similar (Fig. 4C), but remarkably, the group of datapoints on the right part has almost entirely vanished. Taken together, these observations clearly show that CRP binding sites are systematically characterised by very low deformation energies, suggesting an important or even dominant role for indirect readout.

We now quantitatively test the predictive power of the software on a group of 25 mutants of the highaffinity LacP1 sequence from E. coli, whose affinities for CRP were measured in vitro by [START_REF] Lindemose | A novel indirect sequence readout component in the E. coli cyclic AMP receptor protein operator[END_REF]. The mutants were selected either randomly, or for their high affinity (with a maximal 14-fold change). Importantly, mutations all occurred in the central, non-contacted region of the DNA oligomer. It is thus reasonable to assume that direct readout contributes only marginally to these affinity variations, which can then be directly compared to the predictions of ThreaDNA. For all sequences, we found the lowest deformation energy at the experimental binding position (data not shown). Fig. 5A shows that these deformation energies correlate well with the measured affinities (correlation coefficient r 2 = 0.53, p-value P = 2.6 × 10 -5 ). Remarkably, this correlation coefficient is much higher than that obtained with the position weight matrix (PWM) constructed with all RegulonDB sites (r 2 = 0.3, see also Fig. S6). Thus, even though our model is based on structural information only and involves no training on CRP binding sequences, in this indirect readout assay, it outperforms a PWM that concentrates our knowledge of CRP binding selectivity obtained through hundreds of studies. Note that although the PWM theoretically provides binding affinities in absolute units, in practice we had to rescale them as we did for ThreaDNA, using a single slope parameter.

At this point, the reader should keep in mind that since ThreaDNA tells nothing on direct recognition, its general objective is not to compete with sequence motifs, but rather to pinpoint and quantify the indirect contribution to the binding selectivity represented in these motifs. In the next paragraph, we show that this information can be combined with usual PWMs containing complementary information about direct readout, with a notable improvement in predictive power.

Combining indirect and direct readout significantly improves the prediction of binding selectivity

Our previous results immediately suggest to combine our estimation of the indirect contribution with the PWM describing the total (direct+indirect) interaction, in order to infer the direct contribution. Theoretically, this can be achieved by computing a new PWM, where each nucleotide is weighted according to its indirect contribution. In practice, this "subtraction" operation is challenging: for instance, any wrong binding site in the list (false positive), associated to a high deforma-tion energy, will get an enormous weight in the new PWM. Fortunately, it is possible to avoid this difficulty, by noticing that the indirect contribution computed from ThreaDNA acts at least at the level of dinucleotides, as represented in Fig. 5C (lower panel), rather than mononucleotides. The software provides such generalised "di-PWMs", which can be manipulated and combined with usual PWMs with a subprogram. Importantly, if we try to project this di-PWM into a traditional mono-PWM, we lose most of its predictive power (r 2 = 0.2), which shows that indirect readout cannot be described at the mononucleotide level. As a consequence, it is a reasonable approximation to consider the usual mono-PWM as a representation of the direct contribution rather than the total interaction. In other words, the ThreaDNA di-PWM and the traditional mono-PWM can be considered as providing orthogonal information about indirect and direct readout contributions respectively, which can then simply be added to compute the total interaction. Their relative weight cannot be predicted, but may be estimated by comparison to the data. For the Lindemose et al. sequences, the combination remarkably improves the predictive power, with up to 0.88 correlation with the experimental values for 35% direct readout (P < 10 -11 , Fig. 5B). To confirm that this result is not an accident, we repeated the analysis on Fis, where the combination also improves the results significantly (Fig. S5). The lower correlation values compared to CRP might be due to the mutations occuring in the regions in direct contact with the protein, which may be more difficult to describe.

Discussion

In order to recognise their target sequences, DNAbinding proteins often use a combination [START_REF] Harteis | Making the bend: DNA tertiary structure and protein-DNA interactions[END_REF] of direct readout of DNA bases and indirect readout of the "analogue" mechanical code encoded in the DNA sequence [START_REF] Aa Travers | DNA information: from digital code to analogue structure[END_REF]. ThreaDNA implements a systematic approach to estimate the latter contribution for a large class of nucleoprotein complexes. Being based on a nanoscale physical analysis of structural data, it does not require any training on protein-specific binding datasets. All essential model parameters are proteinindependent and chosen from known experimental values. Starting from a structural model of the protein-DNA complex, the software provides genome-wide deformation energy profiles within minutes on standard computers.

We wish to give some emphasis on the assumptions and limitations of ThreaDNA, in order to avoid erro-neous applications of the software. Firstly, the only DNA deformations analysed are those located within the structural models provided as input. As a consequence, regarding proteins that bind together distant DNA sites or act collectively, e.g. by bridging, looping, polymerisation, etc., ThreaDNA might give useful information on their individual binding affinity, but tells nothing of the collective process, for which additional detailed modeling of the interaction is required [START_REF] Vladimir | General transfer matrix formalism to calculate DNA-protein-drug binding in gene regulation: application to OR operator of phage lambda[END_REF][START_REF] Chevereau | Thermodynamics of intragenic nucleosome ordering[END_REF]. The main assumption of the model is that the elasticity of (naked) double-helical DNA remains valid within the protein-DNA complexes analysed, which is incompatible with proteins that disrupt the Watson-Crick bonds of the base-pairs or distort them too strongly. Such problems can generally be identified in the form of missing or aberrant values in the list of base-pair step geometrical parameters given in the Nucleic Acids Database [START_REF] Buvaneswari Coimbatore Narayanan | The Nucleic Acid Database: new features and capabilities[END_REF]. As noted earlier, caution must therefore be paid upon including a new structure into the database.

Still, previous analyses suggest that the software can be useful even for proteins exerting extreme constraints on DNA. One such example is the HIV integrase, a large nucleoprotein complex that inserts viral DNA into the genome of a host human cell, with non-uniform insertion preferences. Using a structural model of the pre-integration complex [START_REF] Michel | Structural basis for HIV-1 DNA integration in the human genome, role of the LEDGF/P75 cofactor[END_REF] exhibiting significant deformations of the genomic DNA prior to its disruption, we predicted insertion preferences in surprisingly good agreement with the inhomogeneous patterns observed both in vitro and in vivo [START_REF] Naughtin | DNA Physical Properties and Nucleosome Positions Are Major Determinants of HIV-1 Integrase Selectivity[END_REF]. A possible interpretation is that indirect readout might be used in intermediate kinetic steps by proteins that end up disrupting or even breaking the double-helix. This seems a reasonable hypothesis in the speculative point of view of a protein which has to find its targets among millions of possible sites: the "cheap" (low energy-barrier) DNA deformation steps might contribute in "preselecting" favourable sequences, while "expensive" base-pair disruption occurs only as a less frequent second step. Although these kinetic views go beyond our thermodynamic approach, a better understanding of the latter might prove helpful in deciphering the whole process.

Our analysis shows that ThreaDNA may substantially improve the prediction of binding sequences for proteins that distort DNA, by complementing the usual approach based on position weight-matrices. The software includes Python modules that facilitate their combination. It is well-known that many proteins use a combination of direct and indirect readout [START_REF] Harteis | Making the bend: DNA tertiary structure and protein-DNA interactions[END_REF], but to our knowledge, our approach is the first to explicitly use this distinction for quantitative sequence binding predictions. In addition to practical applications in binding selectivity prediction for various proteins, it will therefore also provide a new understanding of the mechanistic features underlying this selectivity. 3: DNA mechanics provides a significant contribution to the sequence selectivity of Fis in Escherichia coli. (A) Crystallographic structural model 3IV5 of the Fis-DNA complex [START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF]. (B) Average mechanical energy profile around experimental binding sites collected in the RegulonDB database [START_REF] Gama-Castro | RegulonDB version 9.0: high-level integration of gene regulation, coexpression, motif clustering and beyond[END_REF] (blue) vs random sites (grey). Obtained with 3JR9 structure [START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF] and ABC step parameter. (C) The histogram of mechanical energies at experimental binding sites (position 0 in B) is significantly shifted toward low energies (P < 10 -6 ). Still, a large fraction of these sites exhibits medium or high energies, confirming that other mechanisms are involved in Fis sequence selectivity (Fig. 1). [START_REF] Lindemose | A novel indirect sequence readout component in the E. coli cyclic AMP receptor protein operator[END_REF] with predictions of the position weight matrix (PWM) based on all RegulonDB sites, of ThreaDNA, and of a combination of the two. The reference energy is for the wild-type LacP1 site. The arbitrary unit of ThreaDNA results was converted into kcal/mol using the slope of the regression (one adjusted parameter), and the PWM predictions were equally rescaled (by a factor of 2.5). The computation was carried with a combination of the 1CGP and 1ZRF structures [START_REF] Schultz | Crystal structure of a CAP-DNA complex: the DNA is bent by 90 degrees[END_REF][START_REF] Andrew A Napoli | Indirect Readout of DNA Sequence at the Primary-kink Site in the CAP-DNA Complex: Recognition of Pyrimidine-Purine and Purine-Purine Steps[END_REF], with the NP parameter set. (B) Combining the indirect (ThreaDNA) and direct (PWM) contributions to sequence selectivity considerably improves the prediction. In this assay, a fraction of ∼ 35% direct readout contribution gives the best results (shown in A). (C) In our combination scheme, the direct contribution is approximated by the "traditional" PWM (see text) obtained from all RegulonDB binding sites of CRP (top panel), while the indirect contribution is given by a generalised "dinucleotide" step PWM provided by ThreaDNA. The grey box indicates the mutated region in the Lindemose et al. study.

FUNDING

Figure 1 :

 1 Figure 1: Sequence recognition mechanisms illustrated on the bacterial nucleoid-associated protein Fis.(A) Fis directly contacts the DNA bases at positions ±7 (red background), where it exhibits a strong preference for G/C bases. In the central region (blue), DNA is not contacted, but Fis still exhibits significant sequence preferences, possibly for sequences most favourable to Fis-induced bending. Adapted from[START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF]. (B) ThreaDNA estimates DNA mechanical energy associated to protein binding from highresolution structures of the complex, which provides a significant contribution to sequence selectivity.

  This work was supported by a Bonus de Qualité Recherche (BQR) INSA Lyon 2016 grant, and an IXXI 2016 grant.

Figure 2 :

 2 Figure 2: ThreaDNA provides efficient predictions of nucleosome binding preferences encoded in DNA elasticity. (A) Comparison of nucleosome occupancy profiles predicted by ThreaDNA along the S. cerevisiae genome with MNAse-seq profiling of nucleosomes on in vitro reconstituted or in vivo (native) chromatin [25]. Upper panel: illustration on a particular location of chromosome 2. Lower panels: Correlation histograms along the whole genome (logarithmic density scale): linear correlation coefficients 0.56 and 0.36 respectively, both p-values P < 10 -16 . (B) Prediction of wrapping energies of high-affinity sequences. While a single structural template (here 1KX3) overestimates the energy of other high-affinity sequences, ThreaDNA combines their structures into a single model (lower panel), which accurately predicts low energies for all sequences. All calculations involved the NP parameter set (see Figs. S2 and S3 for comparison).

Figure

  Figure3: DNA mechanics provides a significant contribution to the sequence selectivity of Fis in Escherichia coli. (A) Crystallographic structural model 3IV5 of the Fis-DNA complex[START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF]. (B) Average mechanical energy profile around experimental binding sites collected in the RegulonDB database[START_REF] Gama-Castro | RegulonDB version 9.0: high-level integration of gene regulation, coexpression, motif clustering and beyond[END_REF] (blue) vs random sites (grey). Obtained with 3JR9 structure[START_REF] Stella | The shape of the DNA minor groove directs binding by the DNA-bending protein Fis[END_REF] and ABC step parameter. (C) The histogram of mechanical energies at experimental binding sites (position 0 in B) is significantly shifted toward low energies (P < 10 -6 ). Still, a large fraction of these sites exhibits medium or high energies, confirming that other mechanisms are involved in Fis sequence selectivity (Fig.1).

Figure 4 :

 4 Figure 4: Role of indirect readout in CRP sequence recognition. (A) The deformation energy is strongly lower at experimental CRP binding sites (from RegulonDB), compared to random sites (same legend as Fig. 3). (B) Associated histogram of energies (position 0 in A): in contrast to Fis, DNA deformation energy is very low at almost all CRP binding sites. (C) Binding sites identified by SELEX [31], possibly incorporating less false positives, the group of sequences with high deformation energies has almost vanished.

Figure 5 :

 5 Figure 5: (A) Comparison of in vitro experimental affinities for mutants of the high-affinity LacP1 sequence[START_REF] Lindemose | A novel indirect sequence readout component in the E. coli cyclic AMP receptor protein operator[END_REF] with predictions of the position weight matrix (PWM) based on all RegulonDB sites, of ThreaDNA, and of a combination of the two. The reference energy is for the wild-type LacP1 site. The arbitrary unit of ThreaDNA results was converted into kcal/mol using the slope of the regression (one adjusted parameter), and the PWM predictions were equally rescaled (by a factor of 2.5). The computation was carried with a combination of the 1CGP and 1ZRF structures[START_REF] Schultz | Crystal structure of a CAP-DNA complex: the DNA is bent by 90 degrees[END_REF][START_REF] Andrew A Napoli | Indirect Readout of DNA Sequence at the Primary-kink Site in the CAP-DNA Complex: Recognition of Pyrimidine-Purine and Purine-Purine Steps[END_REF], with the NP parameter set. (B) Combining the indirect (ThreaDNA) and direct (PWM) contributions to sequence selectivity considerably improves the prediction. In this assay, a fraction of ∼ 35% direct readout contribution gives the best results (shown in A). (C) In our combination scheme, the direct contribution is approximated by the "traditional" PWM (see text) obtained from all RegulonDB binding sites of CRP (top panel), while the indirect contribution is given by a generalised "dinucleotide" step PWM provided by ThreaDNA. The grey box indicates the mutated region in the Lindemose et al. study.

ACKNOWLEDGEMENTS

We thank Caroline Gaud, Adelme Bazin and Adeline Roatta who contributed to the implementation and testing of the software, Patrice Baa-Puyoulet for his involvement, Ralf Everaers for useful discussions, William Nasser for his support and advice, and Sylvie Reverchon and Georgi Muskhelishvili for their critical reading of the manuscript.

Conflict of interest statement.

None declared.