Kara A Bernstein

Serge Gangloff

Rodney Rothstein
email: rothstein@cancercenter.columbia.edu

The RecQ DNA helicases in DNA Repair

Keywords: RecQ, Werner Syndrome, Bloom Syndrome, Rothmund-Thomson Syndrome, Homologous Recombination, DNA repair Mini

whether they are published or not. The documents may come     The RecQ DNA helicases in DNA repair

Introduction

Unrepaired DNA damage can lead to genomic instability. When a DSB occurs, the DNA ends need to be processed for efficient repair from a homologous chromosome. Repair of DSBs requires many proteins with enzymatic activities such as nucleases, helicases, ligases, topoisomerases, etc. One important family of enzymes is DNA helicases and these enzymes function by unwinding complementary strands of DNA. The RecQ DNA helicases, conserved from bacteria to humans (Figure 1), are critical to ensure proper repair of DNA damage. Bacteria and budding yeast have one RecQ homologue, RecQ and Sgs1 respectively. In humans, there are five RecQ homologues and mutations in three of these genes (BLM, WRN, RTS/RECQ4) are associated with cancer predisposition and/or premature aging, Bloom, Werner, and Rothmund-Thomson syndromes, respectively [START_REF] Ellis | The Bloom's syndrome gene product is homologous to RecQ helicases[END_REF][START_REF] Kitao | Cloning of two new human helicase genes of the RecQ family: biological significance of multiple species in higher eukaryotes[END_REF]111,121,159).

Unwinding of double-stranded DNA (dsDNA) is necessary in many different processing steps. One of the challenges in studying the function of the RecQ helicases is that mutation of the RECQ genes leads to a pleiotropic phenotype, exhibiting traits that include increased chromosomal rearrangements, increased sister chromatid exchanges, premature aging, etc. The RecQ helicases have been pinpointed to function in both early and late recombination steps where they promote homologous recombination (HR) and prevent crossover events. This review will focus on the recent findings that the RecQ proteins function at multiple DNA processing steps and how these functions enable these proteins to act on many different biological substrates.

RecQ and human disease

In humans, mutations in three of the five members of the RecQ family lead to the separate genetic diseases, Bloom (BLM), Werner (WRN), and Rothmund-Thomson syndromes (RTS/RECQ4) (120) (Table 1). The other two RecQ helicases, RECQ1/RECQL1 and RECQL5 have not been associated with heritable diseases. However, a single nucleotide polymorphism in RECQ1 correlates with decreased survival of pancreatic cancer patients [START_REF] Li | Single nucleotide polymorphisms of RecQ1, RAD54L, and ATM genes are associated with reduced survival of pancreatic cancer[END_REF] and Recql5 knockout mice also display increased cancer rates [START_REF] Hu | RECQL5/Recql5 helicase regulates homologous recombination and suppresses tumor formation via disruption of Rad51 presynaptic filaments[END_REF].

Bloom syndrome

Bloom syndrome is a rare autosomal recessive genetic disorder characterized by growth retardation, light sensitivity, immunodeficiency, male infertility, and increased cancer (14, 120) (Table 1). However, it is the predisposition of Bloom patients to develop cancer, frequently occurring by the forth decade of life, which is the primary cause of death. This disease is due to mutations in the BLM gene and there are approximately 230 documented cases of Bloom syndrome patients [START_REF] Ellis | The Bloom's syndrome gene product is homologous to RecQ helicases[END_REF][START_REF] German | Syndrome-causing mutations of the BLM gene in persons in the Bloom's Syndrome Registry[END_REF]. From the extensive mutational analysis of the BLM gene in these patients, it was concluded that this disease likely originated with a small number of founder mutations [START_REF] German | Syndrome-causing mutations of the BLM gene in persons in the Bloom's Syndrome Registry[END_REF]. The increased cancer incidence correlates with chromosomal breaks and sister chromatid exchanges, both of which are increased in Bloom patient cells [START_REF] German | Chromosomal Breakage in a Rare and Probably Genetically Determined Syndrome of Man[END_REF].

Mouse models of Bloom syndrome have been created to mimic the phenotype observed in humans with this disease. Blm is expressed during embryogenesis in mice in most tissue types with highest expression in spleen, thymus, testis, and ovaries [START_REF] Chester | Stage-specific apoptosis, developmental delay, and embryonic lethality in mice homozygous for a targeted disruption in the murine Bloom's syndrome gene[END_REF]. Disruption of the Blm gene, by insertion of a neomycin cassette in the region upstream to the helicase domain, leads to embryonic lethality at 13.5 days gestation in homozygous mutant mice, suggesting that in mice Blm expression is essential during embryogenesis [START_REF] Chester | Stage-specific apoptosis, developmental delay, and embryonic lethality in mice homozygous for a targeted disruption in the murine Bloom's syndrome gene[END_REF]. When embryos are analyzed at 9.5 days post conception (dpc), Blm -/-mice are 50% smaller than WT or heterozygous Blm +/-mice and this size discrepancy continues until death at 13.5 dpc, indicating that, like humans with Bloom disease, Blm -/-mice also display growth retardation [START_REF] Chester | Stage-specific apoptosis, developmental delay, and embryonic lethality in mice homozygous for a targeted disruption in the murine Bloom's syndrome gene[END_REF]. Also consistent with the human disease, embryonic fibroblasts derived from Blm -/-mice display increased sister chromatid exchanges, which can be seen in metaphase spreads of differentially stained chromosomes [START_REF] Chester | Stage-specific apoptosis, developmental delay, and embryonic lethality in mice homozygous for a targeted disruption in the murine Bloom's syndrome gene[END_REF].

To mimic more closely the mutations found in humans, another Blm mutant mouse was generated. This mutant mouse mimics the predominant mutation found in Ashkenazi Jews, a truncation in the helicase domain of the BLM gene [START_REF] Ellis | The Bloom's syndrome gene product is homologous to RecQ helicases[END_REF][START_REF] Goss | Enhanced tumor formation in mice heterozygous for Blm mutation[END_REF]. In this mouse model, exons 10, 11, and 12 were replaced [START_REF] Ellis | The Bloom's syndrome gene product is homologous to RecQ helicases[END_REF][START_REF] Goss | Enhanced tumor formation in mice heterozygous for Blm mutation[END_REF]. Complete disruption of exons 10, 11, and 12 leads to embryonic lethality [START_REF] Goss | Enhanced tumor formation in mice heterozygous for Blm mutation[END_REF]. However, mice heterozygous for this truncation are more susceptible to cancer when combined with other heterozygous mutations such as those that inactivate tumorsuppressor genes like Apc [START_REF] Goss | Enhanced tumor formation in mice heterozygous for Blm mutation[END_REF]. This mouse model demonstrates that haplo-insufficiency is adequate to promote tumor formation.

Additional mouse models, created using ES cells with Cre-loxP excision, were also generated that have altered Blm transcripts. Using this technology, a few different Blm mutant alleles were made including one that truncated the protein similar to an allele observed in several Bloom patients [START_REF] Luo | Cancer predisposition caused by elevated mitotic recombination in Bloom mice[END_REF]. Blm mice with this truncation are viable and do not display growth retardation; however, they do show increased sister chromatid exchange [START_REF] Luo | Cancer predisposition caused by elevated mitotic recombination in Bloom mice[END_REF]. Unlike WT mice, by 20 months these Blm mice exhibit about a 30% rate of cancer development. Furthermore, similar to Bloom patients, the cancers observed in these mice represent a broad range (i.e. sarcomas, lymphomas, and carcinomas) [START_REF] Luo | Cancer predisposition caused by elevated mitotic recombination in Bloom mice[END_REF]. Consistent with increased sister chromatid exchange, ES cells derived from these mice have a 18-fold increase in loss-of-heterozygosity, which is one of the mechanisms that can lead to complete loss-of-function of tumor-suppressor genes in cancer [START_REF] Luo | Cancer predisposition caused by elevated mitotic recombination in Bloom mice[END_REF].

Together, these mouse models demonstrate that the Blm protein normally functions by repressing sister chromatid exchange, which when unregulated, leads to loss-of-heterozygosity, providing a mechanism to explain why Bloom patients are particularly susceptible to a wide range of cancers.

Werner syndrome

Werner syndrome leads to premature aging, such as an early onset of diseases like cataracts and osteoporosis, as well as genomic instability causing predisposition to tumor formation (120) (Table 1). Interestingly, Werner patients typically exhibit normal development until adolescence and subsequently symptoms emerge in their early 20s that result in death around 46-54 years of age [START_REF] Goto | Hierarchical deterioration of body systems in Werner's syndrome: implications for normal ageing[END_REF]. Cells derived from Werner patients show an increased frequency of chromosomal rearrangements such as translocations, inversions, and deletions [START_REF] Fukuchi | Mutator phenotype of Werner syndrome is characterized by extensive deletions[END_REF][START_REF] Fukuchi | Elevated spontaneous mutation rate in SV40-transformed Werner syndrome fibroblast cell lines[END_REF]119). However, Werner patient tumors have mesenchymal origin, such as sarcomas, which are distinct from those of Bloom patients [START_REF] Huang | The spectrum of WRN mutations in Werner syndrome patients[END_REF]. The vast majority of patients with Werner syndrome have been linked to a founder mutation in Japan [START_REF] Goto | Hierarchical deterioration of body systems in Werner's syndrome: implications for normal ageing[END_REF].

Several mouse models have been created to mimic the phenotype observed in Werner patients. In one mouse model, the helicase domain was disrupted (specifically helicase domains III and IV) resulting in a truncated but stable protein [START_REF] Lebel | A deletion within the murine Werner syndrome helicase induces sensitivity to inhibitors of topoisomerase and loss of cellular proliferative capacity[END_REF]. ES cells derived from these mice are not sensitive to many DNA damaging agents (i.e. UV, gamma irradiation, mitomycin C) but are sensitive to camptothecin, which specifically inhibits topoisomerase I [START_REF] Lebel | A deletion within the murine Werner syndrome helicase induces sensitivity to inhibitors of topoisomerase and loss of cellular proliferative capacity[END_REF]. Disappointingly, this mutant mouse does not display the premature aging phenotype observed in Werner syndrome.

A breakthrough in recapitulating Werner syndrome in mice occurred when the effect of the Wrn mutation was examined in animals altered for telomere function [START_REF] Chang | Essential role of limiting telomeres in the pathogenesis of Werner syndrome[END_REF]. In a study by Chang et al, Wrn -/-mice were combined with null alleles of Terc, which encodes the telomerase RNA needed for telomere lengthening [START_REF] Chang | Essential role of limiting telomeres in the pathogenesis of Werner syndrome[END_REF]. After homozygous null mice were interbred for 4-6 generations, approximately 60% of the 14-16 week old Terc -/-Wrn -/-mice displayed features of premature aging (i.e. hair loss, cataract formation, hypogonadism) after a normal early adulthood [START_REF] Chang | Essential role of limiting telomeres in the pathogenesis of Werner syndrome[END_REF]. Many of these mice also showed early-onset osteoporosis, type II diabetes, and decreased wound healing. These results demonstrate that many of the key features observed in Werner patients could be explained, at least in part, by the role of WRN in maintenance of telomeres. By fluorescence in situ hybridization (FISH) studies, it was shown that cells derived from these mice had fused chromosome arms and shortened telomeres. Furthermore, mouse embryonic fibroblasts (MEFs) derived from these mice exhibit increased 53BP1 foci, a marker for DSB repair, and increased gamma-H2AX foci, an indicator of DSBs. Interestingly, the Terc -/-Wrn -/- mice are not cancer prone. However, Terc -/-Wrn -/-mice that were crossed to each other for 1-3 generations do develop many osteosarcomas and soft tissue sarcomas [START_REF] Chang | Essential role of limiting telomeres in the pathogenesis of Werner syndrome[END_REF]. Therefore, creation of the Werner mouse model demonstrated that, unlike the other RecQ homologues, WRN's distinct role in telomere maintenance is likely inter-related to the clinical features observed in Werner patients.

RECQ4-associated diseases

Mutations in RECQ4 are associated with three unrelated disorders; Rothmund-Thomson syndrome (RTS), RAPADILINO syndrome, and Baller-Gerold syndrome (BGS) [START_REF] Kitao | Mutations in RECQL4 cause a subset of cases of Rothmund-Thomson syndrome[END_REF]126,127,136) (Table 1). All of these disorders are characterized by growth retardation and radial defects. However, RAPADILINO syndrome patients do not exhibit poikiloderma, which is characteristic of both RTS and BGS. RAPADILINO is most prevalent in Finland, unlike the other two RECQ4 disorders (126). RTS is the best characterized of the RECQ4 diseases and these patients also have skeletal abnormalities, skin disorders, light sensitivity, and age prematurely [START_REF] Kitao | Mutations in RECQL4 cause a subset of cases of Rothmund-Thomson syndrome[END_REF]120,127). Rothmund-Thomson patients are especially susceptible to forming bone and skin cancer and their cells display increased chromosomal rearrangements like translocations and deletions [START_REF] Miozzo | Chromosomal instability in fibroblasts and mesenchymal tumors from 2 sibs with Rothmund-Thomson syndrome[END_REF].

Several mouse models have been created to mimic RTS. Since most Rothmund-Thomson patients have mutations in RECQ4 that predominately map to the helicase region, the mouse models have focused on this region. In one model, RECQ4 exon 13, which encodes motif III of the helicase domain, was deleted [START_REF] Hoki | Growth retardation and skin abnormalities of the Recql4-deficient mouse[END_REF]. Although the majority of the mice die within two weeks after birth, those that survived are smaller than wild-type mice [START_REF] Hoki | Growth retardation and skin abnormalities of the Recql4-deficient mouse[END_REF]. These mice also display skin abnormalities such as hair loss, graying hair, and thin, dry skin. However, unlike Rothmund-Thomson patients, these mice do not exhibit poikiloderma, osteosarcomas, and cataracts [START_REF] Hoki | Growth retardation and skin abnormalities of the Recql4-deficient mouse[END_REF].

Another viable mouse model was created that more closely mimics RTS by disrupting the helicase domain encoded by exons 9 through 13 of Recq4 [START_REF] Mann | Defective sisterchromatid cohesion, aneuploidy and cancer predisposition in a mouse model of type II Rothmund-Thomson syndrome[END_REF]. This disruption leads to a truncated protein due to a premature stop codon and 16% of these mice die within 24 hours of birth. The surviving mice develop hypo-/hyper-pigmentation on their tails and show an increased incidence of skeletal defects in their limbs [START_REF] Mann | Defective sisterchromatid cohesion, aneuploidy and cancer predisposition in a mouse model of type II Rothmund-Thomson syndrome[END_REF]. Unlike RTS patients, all of these mice have palatal patterning defects and a wild-type life span. Like the Blm mutant mouse model, when the Recq4 mutant is combined with a mutant Apc tumor suppressor gene, the double mutant mice are more likely to develop cancer [START_REF] Mann | Defective sisterchromatid cohesion, aneuploidy and cancer predisposition in a mouse model of type II Rothmund-Thomson syndrome[END_REF]. MEFs derived from the Recq4 mutant mice exhibit chromosome instability resulting in aneuploidy. These mouse models for RTS demonstrate that many aspects of the phenotype observed in humans are also seen in mice with mutations in Recq4.

Structure of RecQ helicases, complex formation and binding partners

RecQ helicases have been found in bacteria, fungi, animals and plants, and their copy number ranges from one in E. coli and S. cerevisiae to up to seven in Arabidopsis (reviewed in [START_REF] Hartung | The RecQ gene family in plants[END_REF]). They all share a similar overall structural organization where the helicase domain, containing a DEAH box, functions to unwind DNA in an ATP and Mg++ dependent manner (Figure 1). RecQ helicases belong to the SF2 superfamily [START_REF] Gorbalenya | Helicases: amino acid sequence comparisons and structure-function relationships[END_REF], are involved in the resolution of DNA structures and travel on single-stranded DNA (ssDNA) in a 3'→5' direction (reviewed in (4)). The RQC domain (RecQ C-terminal) is characteristic of most RecQ helicases and is believed to mediate protein-protein interactions; however, it is absent in RECQ4 and RECQ5. The HRDC (Helicase and RNase D C-terminal) domain (80 amino acids) found at the C-terminus of many RecQ helicases, allows interactions with nucleic acid [START_REF] Liu | The three-dimensional structure of the HRDC domain and implications for the Werner and Bloom syndrome proteins[END_REF], but is absent from RECQ1, RECQ4 and RECQ5. The HRDC domain forms a structural scaffold; however, models of the HRDC domain have indicated that the surface properties are not equivalent in different RecQ helicases suggesting that they could be involved in the positioning of a specific substrate through steric interactions or secondary contacts with the DNA [START_REF] Liu | The three-dimensional structure of the HRDC domain and implications for the Werner and Bloom syndrome proteins[END_REF]. In addition to the helicase, RQC, and HRDC domains, some members possess a 3'→5' exonuclease domain in their N-terminus (WRN and Xenopus FFA-1), a nuclear localization signal in their C-terminus (BLM and WRN) or acidic patches (BLM, WRN, RECQ1, RECQ4, Rqh1 or Sgs1) (Figure 1) [START_REF] Bachrati | RecQ helicases: suppressors of tumorigenesis and premature aging[END_REF][START_REF] Khakhar | RecQ helicases: multiple roles in genome maintenance[END_REF]139,152).

The quaternary structure of several RecQ helicases has been investigated. BLM forms principally hexameric ring structures, but a four-fold symmetric square form is also detected perhaps representing a distinct oligomeric species or a side view of the hexameric form [START_REF] Karow | Oligomeric ring structure of the Bloom's syndrome helicase[END_REF]. Unlike BLM, E. coli active RecQ exists as a monomeric protein (154, 160), while RECQ1 can form monomers or dimers (101, 107). Therefore, RecQ enzymes may adopt different structures depending on the cofactor bound to them (reviewed in (139)).

An evolutionarily conserved feature of RecQ helicases is their physical association with the Top3 type IA topoisomerase (Figure 2). In budding and fission yeast, Sgs1 and Rqh1, respectively, interact physically with Top3 [START_REF] Ahmad | The N-terminal region of the Schizosaccharomyces pombe RecQ helicase, Rqh1p, physically interacts with Topoisomerase III and is required for Rqh1p function[END_REF][START_REF] Bennett | Interaction between yeast sgs1 helicase and DNA topoisomerase III[END_REF][START_REF] Fricke | Mapping the DNA topoisomerase III binding domain of the Sgs1 DNA helicase[END_REF][START_REF] Gangloff | The yeast type I topoisomerase Top3 interacts with Sgs1, a DNA helicase homolog: a potential eukaryotic reverse gyrase[END_REF]. Of the two isoforms of TOP3 in humans, BLM interacts with TOP3α (68, 151) while RECQ5 interacts with either TOP3α or TOP3β (125). Similar interactions for the other human RecQ homologues have either not been tested or not been found. Recently, a second conserved partner (Rmi1/Nce4-BLAP75) was identified in yeast [START_REF] Chang | RMI1/NCE4, a suppressor of genome instability, encodes a member of the RecQ helicase/Topo III complex[END_REF]100) and human cells (158) (Figure 2). RMI1 proteins contain an OBfold found in many DNA binding proteins like RPA or Cdc13 (132), and biochemical studies have shown that Rmi1 forms a stable heteromeric complex with Sgs1-Top3 (BLM-TOP3α). Genetically, rmi1 mutants behave like top3 mutants [START_REF] Gangloff | The yeast type I topoisomerase Top3 interacts with Sgs1, a DNA helicase homolog: a potential eukaryotic reverse gyrase[END_REF]141) and exhibit premature DNA damage checkpoint activation (158). Rmi1 is a structure-specific DNA binding protein with preferences for cruciforms that may help target Sgs1-Top3 to appropriate substrates (100). Rmi1 stimulates Top3 by promoting its interaction with ssDNA and its superhelical relaxation activity [START_REF] Chen | Binding and Activation of DNA Topoisomerase III by the Rmi1 Subunit[END_REF]. Recently, in mammalian cells, an additional partner, RMI2 (BLAP18), was found to interact with RMI1 through two OB-fold domains. RMI2, an integral component of the BLM complex, is important for the stability, localization and function of the BLM complex in vivo (128, 153). It has been hypothesized that RMI multi-OB-folds mediate two modes of BLM action: via RPA-mediated protein-DNA interaction, where it promotes unwinding and via RMImediated protein-protein interactions, which promotes dissolution.

In addition to Top3 and the Rmi subunits, RecQ helicases interact with many proteins involved in DNA replication and repair, although the exact natures of these interactions are poorly understood. As we are limiting this review to Sgs1, BLM and WRN, only those proteins participating in DNA repair/replication are mentioned. Sgsl interacts with the type II topoisomerase Top2 (146), with Rad16/Pso5, a protein responsible for repair of silent DNA (118), with the Rad51 recombinase (150), with the mismatch proteins Mlh3 (142) and Mlh1 [START_REF] Argueso | Systematic mutagenesis of the Saccharomyces cerevisiae MLH1 gene reveals distinct roles for Mlh1p in meiotic crossing over and in vegetative and meiotic mismatch repair[END_REF][START_REF] Dherin | Characterization of A Highly Conserved Binding Site of Mlh1 Required for Exonuclease I-Dependent Mismatch Repair[END_REF], as well as with Srs2 helicase and Mre11 nuclease, both of which can form various subcomplexes with Sgs1 (30)(Figure 2). On the mammalian side, BLM and WRN interact with each other (140), with RPA [START_REF] Brosh | Functional and physical interaction between WRN helicase and human replication protein A[END_REF][START_REF] Brosh | Replication protein A physically interacts with the Bloom's syndrome protein and stimulates its helicase activity[END_REF]124) and p53 [START_REF] Blander | Physical and functional interaction between p53 and the Werner's syndrome protein[END_REF]129,143). In addition, BLM interacts with the largest subunit of chromatin assembly factor 1 (CAF-1) (67) and, like Sgs1, also interacts with RAD51 (150) and MLH1 (79) (Figure 2).

Recently, another intriguing conserved interaction was discovered between Sgs1 and WRN and jumonji domain proteins, where in yeast, Gis1 is a DNA damage-responsive effector capable of activating genes under conditions of stress (106, 133). Since the jumonji domain contains histone demethylase activity (134, 156), it raises the question of a connection between DNA repair and histone demethylation. In yeast, Gis1 interacts with many proteins including the Nfi1/Siz2 SUMO ligase to form a complex. In mammals, several related jumonji interacting proteins are found in promyelocytic leukaemia nuclear bodies (PML NBs), which also contain transcription factors, BLM, WRN and a SUMO ligase [START_REF] Blander | Physical and functional interaction between p53 and the Werner's syndrome protein[END_REF]143,161). Perhaps the jumonji interacting proteins in yeast are acting in a fashion similar to that of PML NBs, where the recruitment of transcription factors modulates their activity in response to specific signals. However, it is unknown whether the activities of the RecQ helicases themselves are modulated in these bodies by post-translational modification.

Double-strand break repair by homologous recombination

Many types of DNA damage can lead directly or indirectly to the formation of DSBs. When DNA repair is mis-regulated, mutations and genomic rearrangements can occur which are precursors to tumorigenesis and even cellular death. One mechanism to repair DSBs is homologous recombination (HR), which uses a homologous template for repair and is generally considered an error-free mechanism. In the absence of RecQ helicase function, genome instability is increased, consistent with an important function for these enzymes in HR. The RecQ proteins function at multiple repair steps in HR and therefore, this repair pathway will be the focus of this review.

When a DSB occurs, the DNA ends are first recognized by the Mre11-Rad50-Xrs2 complex in yeast or the MRE11-RAD50-NBS1 complex in multi-cellular eukaryotes (DSB repair is reviewed in [START_REF] Lisby | Choreography of recombination proteins during the DNA damage response[END_REF]). The DNA ends are then resected in a 5' to 3' direction by the exonuclease activity of Mre11/MRE11 in conjunction with the endonuclease Sae2/CtIP, revealing 3' ssDNA overhangs. These initial processing steps are critical since they target the DNA to be repaired using a homologous template and inhibit other repair mechanisms such as non-homologous end joining. The DNA ends are then further resected by one of two pathways, one that utilizes Exo1/EXO1 and the other that uses Sgs1 and Dna2. The surprising involvement of the RecQ proteins in this processing step will be discussed in depth below. The ssDNA is subsequently coated by RPA, the ssDNA binding protein. Rad52 then recruits Rad51 to the RPA-coated ssDNA, displacing RPA and leading to the formation of a Rad51 nucleoprotein filament. This Rad51-ssDNA filament performs a homology search followed by strand invasion leading to Dloop formation. Several RecQ helicases have also been shown to function in disruption of Rad51 nucleoprotein filaments or by preventing D-loop formation. After formation of the D-loop, branch migration occurs. This structure can be resolved by second end capture of the homologous chromosome by two different mechanisms: 1) a process called synthesis dependent strand annealing (SDSA) where the DNA strand re-anneals to the original template or 2) by formation of double-Holliday junctions (dHJs) that can be resolved by the Sgs1-Top3-Rmi1/BLM-TOP3-RMI1 (BLAP75)-RMI2 (BLAP18) complex. Therefore, the RecQ proteins perform distinct functions during HR: aiding in the resection of the DSB, inhibiting Rad51 filaments and D-loop formation, and resolving dHJs. Some of these steps are also conserved in meiosis (104).

Role of yeast and human helicases in DNA end resection

After a DSB forms, DNA end resection leads to the formation of 3' ssDNA tails (147). Although many of the key players involved in DNA end resection were known, it was hypothesized that there may be additional proteins involved. For example, in E. coli the RecBCD, a complex of helicases and a nuclease, is sufficient for generating 3' ssDNA tails. However, in eukaryotes there was no corresponding helicase known to function in resection. Further analysis in yeast revealed that the Sgs1 complex and one of its human homologues, BLM, are also involved in the extensive resection that occurs after MRX and Sae2 protein function [START_REF] Gravel | DNA helicases Sgs1 and BLM promote DNA double-strand break resection[END_REF][START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]103,162). The involvement of Sgs1 and BLM in this process was unexpected since BLM has a well-established later role in resolution of dHJs (152).

One challenge in identifying additional proteins involved in DNA end resection is the visualization of ssDNA. To circumvent this problem, gene conversion can be blocked at an inducible DSB site by either disrupting RAD51 or by eliminating donor sequences needed for strand invasion to occur. Using these approaches, two independent groups found that Sgs1 functions in DNA resection since sgs1∆ cells have a significantly slower rate of ssDNA formation [START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]162). In addition to the helicase activity of Sgs1, the Sgs1-interacting partners, Rmi1 and Top3 are also necessary for end resection suggesting that the entire Sgs1 complex is involved in this step [START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]162).

A breakthrough in our understanding of the resection pathway occurred when it was discovered that sgs1∆ exo1∆ double mutants showed substantially decreased DNA resection activity compared to the single sgs1∆ or exo1∆ strains [START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]162). These results suggest that Sgs1 and Exo1 function in different pathways that each contributes to end resection. Since RecBCD is the main pathway for end resection in bacteria, it was hypothesized that the Sgs1 helicase may also function with a corresponding nuclease during resection. Further analysis revealed that this nuclease is Dna2 (162). This result was very surprising since Dna2 functions in Okazaki fragment processing [START_REF] Bae | RPA governs endonuclease switching during processing of Okazaki fragments in eukaryotes[END_REF].

Interestingly, when a DSB is induced in cells where both Sgs1 and Exo1 resection pathways are blocked, DNA fragments accumulate that are 50-100 bp shorter than the initial cut fragment [START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]162). Subsequent analysis of these ssDNA intermediates revealed that their formation is dependent upon the MRX complex and Sae2 [START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]162). These observations lead to a two-step model for DNA end resection where the ends are first resected by the MRX complex and Sae2 and subsequently resected by either the Sgs1-Dna2 or Exo1 pathway (Figure 3). The combined resection activities of these proteins ensure that enough ssDNA is generated which the ssDNA binding protein RPA then coats.

Inhibition of DNA end resection has profound consequences on the integrity of the DNA damage response. For example, blocking both end-resection pathways leads to increased susceptibility to DNA damaging agents, increased gross chromosomal rearrangements, and the inability to activate the DNA damage checkpoint under DNA damaging conditions [START_REF] Gravel | DNA helicases Sgs1 and BLM promote DNA double-strand break resection[END_REF]. Importantly, these defects are not specific to yeast but are also observed in human cells. For example, co-depleted BLM/EXO1 cells exposed to the DNA damaging agent camptothecin have less activated Chk1, a DNA damage checkpoint protein, decreased RPA2 phosphorylation, and decreased survival rates [START_REF] Gravel | DNA helicases Sgs1 and BLM promote DNA double-strand break resection[END_REF]. BLM/EXO1 co-depleted cells also have fewer co-localizing H2AX foci, a marker of DSBs, and the ssDNA binding protein RPA suggesting that less ssDNA is created when these two pathways are blocked in mammalian cells, which is similar to that observed in yeast [START_REF] Gravel | DNA helicases Sgs1 and BLM promote DNA double-strand break resection[END_REF].

In vitro analysis of purified BLM and human Exo1 nuclease (hExo1B) have also been examined for their resection phenotype on synthetic DNA substrates (103). Unlike the in vivo observations for yeast and human cells, purified BLM and hExo1B collaborate in vitro to resect 5' to 3' dsDNA templates (103). The resection activity of BLM and hExo1B promotes hRad51 joint molecule formation. Importantly, the resection activity is specific to BLM since no other RecQ homologue stimulates resection (103). It remains an open question as to why the in vivo analysis suggesting that Sgs1/BLM function independently of Exo1/EXO1 and the in vitro analysis suggesting that BLM stimulates hExo1B activity do not correspond.

Role of RecQ homologues in the recognition and resolution of secondary DNA structures

Purification and characterization of RecQ proteins from bacteria, yeast, plants and mammals has revealed that RecQ helicases unwind a wide variety of DNA substrates, with a marked preference for Holliday junctions (HJs), G-quadruplexes and D-loops [START_REF] Bennett | Binding specificity determines polarity of DNA unwinding by the Sgs1 protein of S. cerevisiae[END_REF][START_REF] Cejka | The full-length Saccharomyces cerevisiae Sgs1 protein is a vigorous DNA helicase that preferentially unwinds holliday junctions[END_REF][START_REF] Harmon | RecQ helicase, in concert with RecA and SSB proteins, initiates and disrupts DNA recombination[END_REF][START_REF] Mohaghegh | The Bloom's and Werner's syndrome proteins are DNA structure-specific helicases[END_REF]130, 135) (Figure 5). The helicase not only binds ssDNA, it can also bind blunt four-stranded junction structures indicating that it does not always require a free 3' DNA tail [START_REF] Bennett | Binding specificity determines polarity of DNA unwinding by the Sgs1 protein of S. cerevisiae[END_REF][START_REF] Cejka | The full-length Saccharomyces cerevisiae Sgs1 protein is a vigorous DNA helicase that preferentially unwinds holliday junctions[END_REF]. Interestingly, although early work on a truncated purified version of Sgs1 indicated poor processivity of the helicase [START_REF] Bennett | Purification and characterization of the Sgs1 DNA helicase activity of Saccharomyces cerevisiae[END_REF], recently an unprecedented strong helicase activity for the full length Sgs1 protein [START_REF] Cejka | The full-length Saccharomyces cerevisiae Sgs1 protein is a vigorous DNA helicase that preferentially unwinds holliday junctions[END_REF], far beyond that of the BLM and WRN homologues, has been shown [START_REF] Brosh | Replication protein A physically interacts with the Bloom's syndrome protein and stimulates its helicase activity[END_REF]124). In addition, the full-length Sgs1 unwinds a wider variety of substrates with even greater efficiency than the truncated form, although it still has a preference for unwinding HJs [START_REF] Cejka | The full-length Saccharomyces cerevisiae Sgs1 protein is a vigorous DNA helicase that preferentially unwinds holliday junctions[END_REF].

An early task of recombinational repair is homology search and strand invasion, which can be divided into a few key steps (Figure 4). In one of the first steps, Rad51 coats the ssDNA replacing RPA. Subsequently, Rad51 nucleo-protein filaments search for complementary sequences in dsDNA. During strand invasion and pairing, the non-complementary strand of the duplex is displaced creating a displacement loop (D-loop), a process that can occur at collapsed replication forks (Figure 4). In vitro, Rad51 efficiently forms D-loops with either a 5' or a 3' invaded end. However, only the 3' invaded end is proficient for priming new DNA synthesis to allow extension of the D-loop by DNA polymerase. The cross-strand structures formed during this process can also branch migrate. In vitro studies indicate that the RecQ helicases may regulate many steps during strand invasion and exchange. For example, RECQ5 can disrupt the initial step of RAD51 filament formation [START_REF] Hu | RECQL5/Recql5 helicase regulates homologous recombination and suppresses tumor formation via disruption of Rad51 presynaptic filaments[END_REF], similar to the Srs2 protein in yeast [START_REF] Krejci | DNA helicase Srs2 disrupts the Rad51 presynaptic filament[END_REF]137). It has also been shown that several RecQ helicases can disrupt D-loops. For example, C. elegans WRN-1 and A. thaliana RECQ2 unwind D-loops [START_REF] Hyun | Biochemical characterization of the WRN-1 RecQ helicase of Caenorhabditis elegans[END_REF][START_REF] Kobbe | AtRECQ2, a RecQ helicase homologue from Arabidopsis thaliana, is able to disrupt various recombinogenic DNA structures in vitro[END_REF]. In vitro, mammalian BLM and RECQ1 preferentially melt naked D-loops and show an affinity for those with a 5' invaded end. Therefore, these helicases selectively dissociate recombination intermediates whose polarity is unfavorable for polymerase extension [START_REF] Bachrati | Mobile D-loops are a preferred substrate for the Bloom's syndrome helicase[END_REF]135) [START_REF] Bugreev | Novel pro-and anti-recombination activities of the Bloom's syndrome helicase[END_REF]. Interestingly, BLM disruption of D-loops is restricted to filaments containing an inactive ADP-bound form of RAD51, suggesting that the filament remains inactive and susceptible to BLM dissociation until the cell is fully prepared for HR. During the latter steps of the strand exchange reaction, human RECQ1 efficiently promotes 3'→ 5' three-stranded branch migration of the D-loop [START_REF] Bugreev | RECQ1 possesses DNA branch migration activity[END_REF].

For recombination to proceed efficiently, branch migration of the D-loop junction is necessary and the subsequent processing of the HJ determines the outcome of the recombination reaction. In prokaryotes, RecQ or RuvA/RuvB promote ATP-dependent branch migration of HJs. In yeast, replication fork arrest results in accumulation of HJs in the absence of Rqh1, which can either impede sister chromatid segregation or lead to the formation of recombinants through HJ resolution [START_REF] Doe | Partial suppression of the fission yeast rqh1(-) phenotype by expression of a bacterial Holliday junction resolvase[END_REF]. In vitro, BLM and WRN promote the ATP-dependent translocation of HJs and binding of recombinant p53 attenuates their ability to unwind synthetic HJs (157). RECQ1 predominantly branch migrates HJs in an ATP-dependent fashion in human nuclear extracts [START_REF] Leroy | Identification of RecQL1 as a Holliday junction processing enzyme in human cell lines[END_REF].

It has long been suspected that a double Holliday junction (dHJ) could be resolved by a topoisomerase partnered with a helicase by convergent branch migration of the HJs [START_REF] Gilbertson | A test of the double-strand break repair model for meiotic recombination in Saccharomyces cerevisiae[END_REF]102). Genetic analysis of yeast Top3 and Sgs1 supports this hypothesis. Deletion of Sgs1 increases both spontaneous and DSB-induced crossovers, suggesting that Sgs1 with Top3 removes dHJ intermediates from a crossover-producing repair pathway [START_REF] Ira | Srs2 and Sgs1-Top3 suppress crossovers during double-strand break repair in yeast[END_REF]114). In an elegant in vitro system, it was shown that BLM and TOP3α resolve recombination intermediates containing a dHJ through a mechanism called double-junction dissolution, a process that prevents exchange of flanking sequences (152). This mechanism is conserved in flies ( 108), but it is important to note that the in vitro systems only allow the readout of the dissolution reaction, while a dHJ could equally be branch migrated in either direction or apart from one another leading to an increase in the distance between the two junctions. However, the dissolution reaction is highly specific for BLM and depends upon a functional HRDC domain (149). The discovery of BLAP75/RMI1 as a third member of the Sgs1-Top3 (BLM-TOP3α) complex led to the notion of a dissolvasome. Under physiological conditions, dHJ dissolution depends completely on RMI1 to limit DNA crossover formation (112). The conserved N-terminal third of RMI1 mediates complex formation with TOP3α and BLM and acts by recruiting TOP3α to dHJs. Hence, the activity of RMI1 is specific for dissolution catalyzed by TOP3α [START_REF] Bussen | Holliday junction processing activity of the BLM-Topo IIIalpha-BLAP75 complex[END_REF]113,148). Recently, the newest member of this complex, RMI2, was shown to stimulate the dHJ resolution capability (128). G-quadruplex DNAs, which can form into non-Watson-Crick structures within guanine-rich DNA sequences, are another DNA structure that can be preferentially unwound by RecQ helicases (Figure 5). These sequences are often found in telomeric or rDNA repeats. With the exception of RECQ1 (110), the RecQ family of DNA helicases are able to unwind G-quadruplex DNA. The efficient unwinding of G-G paired DNA by Sgs1 is ATP and Mg2+ -dependent and requires a short 3' single-stranded tail. Diminished ability to unwind G-G paired regions may explain the deleterious effect of mutations in Sgs1 on rDNA stability, and the accelerated aging of yeast lacking Sgs1 as well as humans deficient in the WRN helicase (130). In mammals, there is a direct relationship between the helicase activities of BLM and WRN and their G-quadruplex binding capabilities [START_REF] Li | Inhibition of the Bloom's and Werner's syndrome helicases by G-quadruplex interacting ligands[END_REF]. BLM and Sgs1 preferentially unwind G4 DNA relative to HJs. This substrate preference reflects binding affinity and maps to the helicase domain. These observations suggest that, in addition to their roles in promoting recombination to restart a stalled fork, BLM and Sgs1 also function in DNA replication to remove G4 DNA structures, which could hinder fork progression [START_REF] Huber | G4 DNA unwinding by BLM and Sgs1p: substrate specificity and substrate-specific inhibition[END_REF].

Meiotic functions

There are several observations that point to a role for the RecQ family in meiosis. For example, in budding yeast, sgs1∆ mutants exhibit both reduced tetrad formation and spore viability [START_REF] Gangloff | The essential role of yeast topoisomerase III in meiosis depends on recombination[END_REF]146). Human females homozygous for BLM mutations display reduced fertility and males are infertile (reviewed in [START_REF] German | Bloom syndrome: a mendelian prototype of somatic mutational disease[END_REF]). In addition, BLM protein detected by immunofluorescence, frequently colocalizes as discrete foci on synapsed cores with the recombinases RAD51 and DMC1, providing cytological evidence that BLM functions in meiotic recombination as well [START_REF] Moens | Expression and nuclear localization of BLM, a chromosome stability protein mutated in Bloom's syndrome, suggest a role in recombination during meiotic prophase[END_REF]. Furthermore, evidence from other eukaryotes also supports the notion that RecQ family members are involved in meiosis. For example, mutations in the Bloom's homologue in flies (mus309) and worms (him-6) are infertile [START_REF] Grabowski | Bloom syndrome ortholog HIM-6 maintains genomic stability in C. elegans[END_REF][START_REF] Hodgkin | Nondisjunction Mutants of the Nematode CAENORHABDITIS ELEGANS[END_REF][START_REF] Kusano | Sterility of Drosophila with mutations in the Bloom syndrome gene--complementation by Ku70[END_REF].

In budding yeast, the decrease in spore viability in sgs1 mutants was attributed to meiosis I missegregation (146) and precocious separation of sister chromatids (116), while heteroallelic recombination and crossovers were not strongly affected (145). However, further studies indicate that, in the absence of Sgs1, there is a long delay in the appearance of four-spored asci dependent on the initiation of recombination [START_REF] Gangloff | The essential role of yeast topoisomerase III in meiosis depends on recombination[END_REF]. Indeed, disruption of RED1 or RAD17, two checkpoint genes, partially alleviates the poor sporulation of sgs1 mutants. Interestingly, only the region of Sgs1 spanning amino acids 126 to 596 is required for the meiotic function--the helicase function per se is dispensable [START_REF] Miyajima | Sgs1 helicase activity is required for mitotic but apparently not for meiotic functions[END_REF]. However, another study suggests that helicase activity is required in meiosis perhaps reflecting complex interactions between the domains of Sgs1 ( 90). An important breakthrough in understanding Sgs1 meiotic function came from the discovery that the absence of Sgs1 leads to an increase in both the number of interhomologue connections and the number of meiotic crossovers without affecting the frequency of noncrossover events (115). These observations assign a new role for Sgs1 in the negative regulation of meiotic crossovers at an early stage of meiotic prophase. A similar function was later found for both spontaneous and DSB-induced mitotic events [START_REF] Ira | Srs2 and Sgs1-Top3 suppress crossovers during double-strand break repair in yeast[END_REF]114). In subsequent meiotic studies, the sgs1-C795 allele, which truncates the protein after amino acid 795, has been used instead of the complete deletion. Although the sgs1-C795 mutants are indistinguishable from the null mutant with respect to the synapsis and crossover phenotypes, they sporulate like wild-type cells, exhibit significantly improved spore viability compared to sgs1Δ (115) and they grow as well as wild-type cells [START_REF] Mullen | Bipartite structure of the SGS1 DNA helicase in Saccharomyces cerevisiae[END_REF]. It is therefore possible that some meiotic functions of Sgs1 are mediated via interactions with other partners like Top2 or Top3, whose interacting sites are still present in the sgs1-C795 mutant.

The molecular mechanisms by which Sgs1 regulates meiotic crossovers was further revealed when it was found that the SIC/ZMM proteins, responsible for homologous chromosomes synapsis and crossovers, antagonize the anti-crossover activity of Sgs1 [START_REF] Jessop | Meiotic Chromosome Synapsis-Promoting Proteins Antagonize the Anti-Crossover Activity of Sgs1[END_REF]. Elegant genetic and molecular work reached the conclusion that Sgs1 and Mus81/Mms4 can disrupt the formation of aberrant joint molecules resulting from secondary strand-invasion events, therefore enhancing the repair efficiency of breaks [START_REF] Jessop | Mus81/Mms4 endonuclease and Sgs1 helicase collaborate to ensure proper recombination intermediate metabolism during meiosis[END_REF]104). These results suggest that, in meiosis, Sgs1 does not act primarily as a dissolvase (108, 152), but preferentially disrupts D-loop structures [START_REF] Bachrati | Mobile D-loops are a preferred substrate for the Bloom's syndrome helicase[END_REF][START_REF] Bennett | Binding specificity determines polarity of DNA unwinding by the Sgs1 protein of S. cerevisiae[END_REF]105). Interestingly, the role of Sgs1 in meiosis is not conserved. Compelling data from fission yeast indicate that, unlike Sgs1, Rqh1 promotes meiotic recombination [START_REF] Cromie | The fission yeast BLM homolog Rqh1 promotes meiotic recombination[END_REF]. It is tempting to speculate that this difference between RecQ meiotic function in S. cerevisiae and S. pombe is related to the absence of the synaptonemal complex and the lack of crossover interference in fission yeast.

Repair of replicative damage

Many of the activities performed by the RecQ helicases are also important at multiple steps during DNA replication. The RecQ helicases help enable the association of the polymerases with the replication fork, unwind DNA structures that potentially leads to replication fork stalling (i.e. G-quadruplexes and hairpin structures), and resolve hemicatenane-like structures that can form during repair of replicative damage. In the absence of RecQ activity, errors lead to stalled or collapsed replication forks, which need to be repaired to maintain genomic integrity and to prevent DSBs. RecQ proteins may help unwind inappropriately paired nucleic acids during replication to prevent inappropriate HR events and therefore, maintain genomic stability.

One of the first lines of evidence suggesting that the RecQ proteins can function in the repair of replicative damage comes from the observation in yeast that expression of the SGS1 gene is cell cycle regulated and peaks in S phase [START_REF] Frei | The yeast Sgs1p helicase acts upstream of Rad53p in the DNA replication checkpoint and colocalizes with Rad53p in S-phase-specific foci[END_REF]. Similarly, BLM is cell cycle regulated and its concentration peaks during S phase [START_REF] Dutertre | Cell cycle regulation of the endogenous wild type Bloom's syndrome DNA helicase[END_REF][START_REF] Gharibyan | Localization of the Bloom syndrome helicase to punctate nuclear structures and the nuclear matrix and regulation during the cell cycle: comparison with the Werner's syndrome helicase[END_REF], while the other mammalian RecQ homologues show no such regulation. RecQ proteins also interact with many DNA replication proteins. For example, in yeast, Sgs1 physically interacts with topoisomerases I and II and RPA [START_REF] Cobb | DNA polymerase stabilization at stalled replication forks requires Mec1 and the RecQ helicase Sgs1[END_REF][START_REF] Gangloff | The yeast type I topoisomerase Top3 interacts with Sgs1, a DNA helicase homolog: a potential eukaryotic reverse gyrase[END_REF]146). Sgs1 is also found in chromatin immunoprecipitation (ChIP) experiments at unperturbed replication forks [START_REF] Cobb | DNA polymerase stabilization at stalled replication forks requires Mec1 and the RecQ helicase Sgs1[END_REF]. Similarly, the human homologue WRN interacts with hRPA, PCNA, POLδ, and hTOPO1 and copurifies with the DNA replication complex in ES cells [START_REF] Brosh | Functional and physical interaction between WRN helicase and human replication protein A[END_REF][START_REF] Kamath-Loeb | Functional interaction between the Werner Syndrome protein and DNA polymerase delta[END_REF][START_REF] Lebel | A deletion within the murine Werner syndrome helicase induces sensitivity to inhibitors of topoisomerase and loss of cellular proliferative capacity[END_REF][START_REF] Lebel | The Werner syndrome gene product copurifies with the DNA replication complex and interacts with PCNA and topoisomerase I[END_REF]. Indeed, upon hydroxyurea treatment, WRN localizes to discrete nuclear foci that coincide with those formed by RPA, suggesting that WRN prevents aberrant recombination events at sites of stalled replication forks by dissociating recombination intermediates [START_REF] Constantinou | Werner's syndrome protein (WRN) migrates Holliday junctions and co-localizes with RPA upon replication arrest[END_REF][START_REF] Karow | The Bloom's syndrome gene product promotes branch migration of holliday junctions[END_REF]. The BLM proteins interact with p53 and RAD51 at stalled replication forks (122). BLM also forms foci that co-localize with PCNA at stalled replication forks and with the BASC complex (BRCA1associated genome surveillance complex)(144). Finally, RECQ4 is an integral component of the MCM complex, where MCM10 is important for the RECQ4 interaction with the other replisome components, MCM2-7 (155). What role(s) do the RecQ helicases play at the replication fork? Perhaps the topological constraints of DNA replication generate catenane-like structures that require DNA helicases and topoisomerases for resolution. In this scenario, the RecQ proteins act on DNA structures enabling replication to continue efficiently. Without the concerted action of the RecQ helicases with DNA topoisomerases, aberrant replication structures arise. In fact, disruption of RecQ helicases leads to the accumulation of abnormal replication intermediates in both BLM and WRN deficient cells [START_REF] Lonn | An abnormal profile of DNA replication intermediates in Bloom's syndrome[END_REF]109). Surprisingly, in budding yeast, SGS1 disrupted cells progress through S phase faster than wild-type (138). However, not all genomic loci replicate faster since rDNA actually replicates more slowly in sgs1∆ (138). Furthermore, disruption of SGS1 causes contractions at tri-nucleotide repeats [START_REF] Kerrest | SRS2 and SGS1 prevent chromosomal breaks and stabilize triplet repeats by restraining recombination[END_REF]. Both rDNA and tri-nucleotide repeat sequences are capable of forming G-quadruplexes, suggesting that such sequences in these repetitive units require RecQ helicase activity to replicate efficiently. In addition, the reliance on other repair mechanisms, such as sister-chromatid recombination or single-strand annealing in the absence of RecQ helicases may lead to slower processivity during the replication of highly repetitive elements.

The RecQ helicases also function in the repair of replication-induced damage (Figure 4). Our understanding of the RecQ proteins in DNA replication comes mostly from experiments that utilize drugs that stall or collapse replication forks. For example, hydroxyurea (HU) is frequently used to deplete dNTP pools and therefore, initially stall and then subsequently collapse forks. Methyl methanesulfonate (MMS) alkylates DNA and also leads to replication fork stalling. Using these drugs to perturb replication, Sgs1 was shown to contribute to the polymerases ability to efficiently immuno-precipitate with the replication fork [START_REF] Cobb | DNA polymerase stabilization at stalled replication forks requires Mec1 and the RecQ helicase Sgs1[END_REF]. When replication fork damage is induced with MMS, X-shaped molecules form at replication origins, which can be visualized by 2D gel electrophoresis. These X-structures likely contain ssDNA since their formation is sensitive to Mung Bean nuclease [START_REF] Liberi | Rad51dependent DNA structures accumulate at damaged replication forks in sgs1 mutants defective in the yeast ortholog of BLM RecQ helicase[END_REF]. Complete disruption of SGS1 or its helicase domain, leads to the accumulation of these X-structures at damaged forks [START_REF] Bernstein | Sgs1 function in the repair of DNA replication intermediates is separable from its role in homologous recombinational repair[END_REF][START_REF] Liberi | Rad51dependent DNA structures accumulate at damaged replication forks in sgs1 mutants defective in the yeast ortholog of BLM RecQ helicase[END_REF]. Furthermore, X-structure accumulation in sgs1∆ cells is dependent upon the recombination protein Rad51 and a post-replication repair protein Rad18 suggesting that a template-switching mechanism is important for their formation [START_REF] Branzei | SUMOylation regulates Rad18-mediated template switch[END_REF][START_REF] Liberi | Rad51dependent DNA structures accumulate at damaged replication forks in sgs1 mutants defective in the yeast ortholog of BLM RecQ helicase[END_REF]. The Rad18-mediated post-replicative repair pathway requires the SUMO-conjugating enzyme Ubc9 and sumoylated PCNA, suggesting that assembly/disassembly of proteins at the site of replicative damage is an important contributor to X-structure formation [START_REF] Branzei | SUMOylation regulates Rad18-mediated template switch[END_REF]. Sgs1 itself is also an Ubc9-dependent SUMO target (16). Interestingly, it is possible to isolate mutants of SGS1 that encode proteins defective in repair of replicative damage but do not influence recombination at other loci, suggesting that the function of Sgs1 in repair of replicative damage is distinct from its function in resolution of HR intermediates [START_REF] Bernstein | Sgs1 function in the repair of DNA replication intermediates is separable from its role in homologous recombinational repair[END_REF].

When recombination or replication intermediates are not properly resolved during S phase, cells are unable to undergo sister-chromatid disjunction. In this scenario, anaphase bridges (or ultrafine bridges), representing incomplete chromosome segregation, connect the two nuclei. Interestingly, BLM, along with TOP3a and hRMI1, localize to these bridges and is needed for their resolution [START_REF] Chan | BLM is required for faithful chromosome segregation and its localization defines a class of ultrafine anaphase bridges[END_REF]. The anaphase bridges observed also contain the PICH helicase [START_REF] Baumann | PICH, a centromere-associated SNF2 family ATPase, is regulated by Plk1 and required for the spindle checkpoint[END_REF], where PICH is first recruited to the bridges followed by BLM, which then resolves them [START_REF] Chan | BLM is required for faithful chromosome segregation and its localization defines a class of ultrafine anaphase bridges[END_REF]. Intriguingly, FANCD2/I, proteins that localize to DNA damage site and are ubiquitinated, are located at the termini of a subset of BLM-dependent ultra-fine bridges [START_REF] Chan | Replication stress induces sisterchromatid bridging at fragile site loci in mitosis[END_REF].

Disruption of RecQ function during replicative repair also activates the DNA damage checkpoint. The intra-S phase checkpoint is largely mediated by Rad53 in yeast or CHK2 in humans. Rad53 is activated by DNA damage and becomes phosphorylated leading to a signaling cascade enabling the damage signal to be transduced. Sgs1 is important in one pathway used for Rad53 activation (Rad24 being the other in a parallel pathway) [START_REF] Bjergbaek | Mechanistically distinct roles for Sgs1p in checkpoint activation and replication fork maintenance[END_REF]. Sgs1 directly binds Rad53, suggesting that Sgs1 and Rad53 interact at damaged DNA structures for checkpoint activation [START_REF] Bjergbaek | Mechanistically distinct roles for Sgs1p in checkpoint activation and replication fork maintenance[END_REF][START_REF] Frei | The yeast Sgs1p helicase acts upstream of Rad53p in the DNA replication checkpoint and colocalizes with Rad53p in S-phase-specific foci[END_REF]. Sgs1 and Rad53 also form foci that co-localize with the replication factor Orc2 [START_REF] Frei | The yeast Sgs1p helicase acts upstream of Rad53p in the DNA replication checkpoint and colocalizes with Rad53p in S-phase-specific foci[END_REF]. In mammalian cells, ATR, an upstream kinase to CHK2, binds to and phosphorylates BLM [START_REF] Davies | Phosphorylation of the Bloom's syndrome helicase and its role in recovery from S-phase arrest[END_REF]. Furthermore, when replication forks are stalled with HU, BLM foci co-localize with another kinase, CHK1, and 53BP1, a p53 interacting protein in the DNA damage response (123). When CHK1 mRNA is depleted, the formation of BLM and 53BP1 foci at replication forks is disrupted, suggesting that CHK1 recruits BLM to sites of replicative damage (123). In summary, both yeast and mammalian RecQ proteins activate the DNA damage checkpoint in response to replication fork stalling and collapse.

Telomeres

Maintenance of telomere sequences at chromosome ends is critical for genomic stability. Telomeres consist of G-rich repetitive DNA sequences. In the absence of telomerase, telomeres shorten after each cell division until the cell senesces. To bypass senescence, telomeres can be elongated by different mechanisms, for example, one that utilizes telomerase, an RNA-protein complex, or secondly by alternative lengthening of telomeres (ALT), which is predominately DNA recombination mediated. In budding yeast, lengthening of telomeres by ALT requires the recombination protein Rad52. In human tumors, cells often evade senescence by activating either pathway to extend telomere length. The RecQ proteins have been implicated to function in telomere maintenance [START_REF] Bhattacharyya | Unwinding protein complexes in ALTernative telomere maintenance[END_REF]. The WRN RecQ helicase has a well-established role at telomeres in humans. WRN is important for lagging strand synthesis and for efficient replication of G-rich telomeric DNA [START_REF] Crabbe | Defective telomere lagging strand synthesis in cells lacking WRN helicase activity[END_REF]. As mentioned previously, the WRN mutant mouse only recapitulates Werner syndrome when combined with telomerase mutant alleles, suggesting that loss of WRN's function at telomeres is critical in the development of this syndrome.

Similar to processed DSBs, telomere ends have 3' overhangs due to the protrusion of the G strand over the complementary C-strand. In yeast, the length of the single-stranded G-tails is approximately 12-14 nucleotides and these G tails form in mice and humans as well and are considerably longer 75-300 nucleotides [START_REF] Larrivee | The generation of proper constitutive G-tails on yeast telomeres is dependent on the MRX complex[END_REF]131). Studies in yeast have shown that formation of the G-tails is dependent on the MRX complex [START_REF] Larrivee | The generation of proper constitutive G-tails on yeast telomeres is dependent on the MRX complex[END_REF]. Interestingly, disruption of the MRX complex does not completely abolish G-tail formation suggesting that other proteins are also involved in the 5' to 3' processing of telomere ends [START_REF] Larrivee | The generation of proper constitutive G-tails on yeast telomeres is dependent on the MRX complex[END_REF].

One of the defining features of telomeres is their G-rich nature, which potentially enables the formation of G-quadruplexes, which are guanine-guanine interactions stabilized by inter-strand pairings between four DNA strands. As discussed above, several RecQ proteins unwind Gquadruplex DNA in vitro including BLM, WRN, and Sgs1 [START_REF] Li | Inhibition of the Bloom's and Werner's syndrome helicases by G-quadruplex interacting ligands[END_REF]130). In addition, like its role at DSBs [START_REF] Gravel | DNA helicases Sgs1 and BLM promote DNA double-strand break resection[END_REF][START_REF] Mimitou | Sae2, Exo1 and Sgs1 collaborate in DNA doublestrand break processing[END_REF]103,162), Sgs1 is important in resection at telomeres. In budding yeast, an inducible cut site was used to generate a DSB adjacent to the left telomere of chromosome VII to monitor a single telomere for formation of ssDNA and lengthening [START_REF] Bonetti | Multiple pathways regulate 3' overhang generation at S. cerevisiae telomeres[END_REF]. After induction of the DSB, the fragment distal to the break is lost and the short telomeric "seed" sequence is elongated. Wild type cells can elongate this telomere seed sequence, but cells that are unable to form 3' tails do not. Interestingly, using this assay, all the proteins required for resection of DSBs are also necessary for telomeric C-strand degradation and telomere elongation (i.e. Sae2, MRX, Sgs1, Exo1, and Dna2) [START_REF] Bonetti | Multiple pathways regulate 3' overhang generation at S. cerevisiae telomeres[END_REF]. Similar to what occurs at DSBs, Sgs1 and Dna2 function together in a pathway that is parallel to Exo1 in the resection of telomeric DNA [START_REF] Bonetti | Multiple pathways regulate 3' overhang generation at S. cerevisiae telomeres[END_REF]. Surprisingly, the wild type chromosomes observed in multiple mutants blocking both pathways (i.e. exo1∆ sgs1∆, sae2∆ exo1∆), did not exhibit any changes in their telomere lengths even though the cells were largely defective in extending the DSB-induced short telomere [START_REF] Bonetti | Multiple pathways regulate 3' overhang generation at S. cerevisiae telomeres[END_REF]. Together, these results indicate that, similar to DSBs at other sites, resection of telomere ends is also partially mediated by Sgs1. Interestingly, it was recently shown that sumoylation of Srs2 (91) in budding yeast or Rqh1 in fission yeast (117) is important for telomere-telomere recombination. Importantly, Sgs1 sumoylation did not influence recombination at other genomic loci suggesting that the role of Sgs1 at telomeres may be distinct from its role at other loci [START_REF] Lu | Sumoylation of the BLM ortholog, Sgs1, promotes telomere-telomere recombination in budding yeast[END_REF].

Concluding remarks

The RecQ helicases have a diverse role in genome maintenance that, when unregulated in humans, can lead to premature aging and tumorigenesis. Although the diseases associated with mutations in the RecQ helicases are distinct, they are fundamentally characterized by increased cancer incidence, which is likely attributable to RecQ function in DNA repair. Recently, RecQ proteins were shown to function in resection of DSBs. This resection activity is also important for the ALT pathway, which is used during telomere extension in the absence of telomerase. However, it is unknown whether this function is important during the repair of replicative damage or during meiosis. In meiosis, it is likely that the RecQ role in dissolution is the predominate function. The RecQ proteins, in vitro, unwind a diverse set of DNA substrates suggesting that it will be a continuing challenge to dissect out its specific functions at the DNA structures that it encounters. Furthermore, the role of post-translational modification of RecQ, such as sumoylation, may be critical in the regulation of this important helicase family. Finally, insight into precise biochemical function of this helicase family will be revealed by analyzing the specific structures that form from RecQ dysfunction, such as X-structures that arise during DNA replication or the anaphase-bridges found during mitosis.

Future Issues (up to 8)

1) Is there a role for the RecQ proteins in end resection during meiosis or during DNA replication?

2) Are the phenotypes observed in human patients with RecQ disorders attributed to the different functions of the RecQ protein at different processing steps?

3) What is the DNA-protein structure of the anaphase bridges and do they occur in other eukaryotes? 4) Is the role of sumoylation of RecQ proteins only important at telomeres or is it also important for its regulation in general such as during DNA replication or recombination? 5) How are RecQ proteins recruited during repair of different DNA structures? How do they function in the processing of DNA lesions? 6) What is the specificity of the RecQ helicases in organisms with multiple RecQ proteins?

Disclosure Statement

Figure 1. Structural features of RecQ helicases. The RecQ proteins have many structural domains that are conserved from bacteria through humans. The RecQ proteins all have a core helicase domain (red). Most RecQ proteins also contain conserved HRDC (Helicase and RNAse D C-terminal; yellow) and RQC (RecQ C-terminal; turquoise) domains that are thought to mediate interactions with nucleic acid or other proteins respectively. Many RecQ proteins have acidic regions (green) that enable protein-protein interactions while some of the RecQ proteins have nuclear localization sequences (NLS; orange). WRN and FFA-1 protein are unique in that they also contain an exonuclease domain (EXO; purple). The number of amino acids for each protein are indicated on the right. The Rad52 group of proteins recruits Rad51 and displaces RPA leading to Rad51 filament formation. Rad51 filaments perform homology search and strand invasion leading to Dloop formation followed by branch migration. Rad51 coated DNA can invade using 5' or 3' DNA ends; however, only the 3' invading end is proficient for homologous recombination. The RecQ proteins can unwind the 5' end and thus abort the unproductive reaction but also the 3' end after it is extended to promote synthesis dependent strand annealing (not shown). Alternatively, second end capture of the homologous chromosome can lead to double Holliday junction formation (dHJ). The RecQ proteins function by promoting translocation and branch migration of dHJs. Resolution: Dissolution of dHJs utilize the Sgs1-Top3-Rmi1/BLM-TOP3a-RMI1(BLAP75) complex. In the figure the yeast proteins are shown bound to each HJ and if they move toward each other dissolution can occur. However, the precise biochemical reaction is not known. During DNA replication, hemicatenenes are thought to form behind the replication fork [START_REF] Branzei | SUMOylation regulates Rad18-mediated template switch[END_REF]. In vitro, maximal decatenation of this structure is achieved when Rmi1 and Rmi2 are added to the reaction.

Figure 2 .

 2 Figure 2. Conserved interaction between DNA repair and recombination proteins with Sgs1 and BLM. In yeast, Sgs1 physically interacts with many different repair and recombination proteins as indicated such as Top3 and Rmi1. Many of these interactions are evolutionarily conserved and are shown with the BLM protein. BLM also interacts with one of the other RecQ helicases, WRN. Mlh1 has an interaction site in the C-terminal region of both proteins (not shown). The colors for Sgs1 and BLM are the same as in Figure 1.

Figure 3 .

 3 Figure 3. Model for RecQ function during end resection. After a DSB, the DNA ends are recognized by Mre11-Rad50-Xrs2 (MRX) in yeast or MRE11-RAD50-NBS1 (MRN) in mammals. The DNA ends are partially resected by Mre11/MRE11 nucleases, in collaboration with Sae2/CtIP endonucleases, leaving short 3' single-stranded DNA tails. These DNA ends can be further resected by utilizing Sgs1/BLM helicases and Dna2/DNA2 nucleases or via a parallel pathway that uses Exo1/EXO1 nucleases. The ssDNA created is coated by RPA.

Figure 4 .

 4 Figure 4. Model for RecQ function during junction processing and resolution. Junction processing:The Rad52 group of proteins recruits Rad51 and displaces RPA leading to Rad51 filament formation. Rad51 filaments perform homology search and strand invasion leading to Dloop formation followed by branch migration. Rad51 coated DNA can invade using 5' or 3' DNA ends; however, only the 3' invading end is proficient for homologous recombination. The RecQ proteins can unwind the 5' end and thus abort the unproductive reaction but also the 3' end after it is extended to promote synthesis dependent strand annealing (not shown). Alternatively, second end capture of the homologous chromosome can lead to double Holliday junction formation (dHJ). The RecQ proteins function by promoting translocation and branch migration

Figure 5 .

 5 Figure 5. DNA structures unwound by one or multiple RecQ helicases. The RecQ proteins unwind a diverse set of DNA structures in vitro such as blunt ended DNA (however, not the preferred substrate), 3' overhangs, forked substrates (such as those that arise during DNA replication), displacement-loops (D-loops, that arise during strand invasion), 4-way junctions (similar to a Holliday junction, HJ), synthetic dHJs (mimicking a recombination intermediate), or structures capable of forming G-quadruplex DNA (for example, predicted in rDNA and telomere sequences).

  Figure 5

Table 1 .

 1 Clinical features of RecQ disorders Syndrome (gene) Dwarfism, beaked nose, narrow face, pigmentation, redness, and dilated blood vessels in skin, mental retardation, type-II diabetes, immunodeficiency, lung problems, low or no fertility

		Main Clinical Features	Cancer Predisposition
	Blooms syndrome		Early onset with
	(BLM)		normal distribution of
			tissue and type
	Werner syndrome	Bilateral cataracts, hoarseness, skin alterations,	Early onset of
	(WRN)	thin limbs, premature gray/loss of hair, pinched	primary sarcomas and
		facial features, short stature, osteoporosis,	mesenchymal tumors
		hypogonadism, diabetes, soft tissue calcification
	Rothmund-	Poikiloderma, juvenile cataracts, growth	Early onset of
	Thomson	retardation, skeletal dysplasia, sparse scalp hair,	osteosarcomas
	syndrome	hypogonadism
	(RECQ4)
	RAPADILINO	Growth retardation, bone malformation such as	Lymphoma and
	syndrome	limbs, radial defects such as hypoplasia and	osteosarcoma
	(RECQ4)	aplasia of thumbs and radius, cleft or highly
		arched palate
	Baller-Gerold	Craniosynostosis, radial aplasia and hypoplasia,	N.A.
	syndrome	poikiloderma, growth retardation
	(RECQ4)

The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review.

Acknowledgments

We thank Peter Thorpe and Michael Chang for helpful comments and careful reading of the manuscript. This study was supported by ANR-07-BLAN-0350-01 (SG) and by National Institute Health grants GM50237 (RR), GM078840 (KAB), GM088413 (KAB).

Rad51


domain: math stat

text:
Patrick Tardivel

Comment on the subdifferential formula given in the article "Algorithmic Analysis and Statistical Estimation of SLOPE via Approximate Message Passing"

. We believe that expressing the sorted 1 norm as the maximum of linear functions, as suggested by the authors, is an appropriate approach to derive its subdifferential. However the formula provided in this article contains many flaws and we hope that authors would take into account this note in order to rewrite and prove their formula.

However this inclusion is wrong as soon as some components of s are negative. To conclude, instead to use implicitly the permutation group, we suggest to authors to use the signed permutation group G (see e.g. [8] or [10, Definition 22]) and to rewrite the sorted 1 has a maximum of linear functions: J λ (s) = max{g(λ) T s : g ∈ G}.

3 The weighted 1 norm is differentiable at s since, by assumption, s does not have any null component. 4 This formula is also wrong when s = 0 but this particular case is discarded by the authors.

We remind that the sorted 1 norm is defined as follows

J λ (x) = p i=1 λ i |x| (i) ,
where λ = (λ 1 , . . . , λ p ) ∈ R p with λ 1 > 0 and λ 1 ≥ • • • ≥ λ p ≥ 0 is a sequence of penalty parameters and |x| (1) ≥ • • • ≥ |x| (p) are non-increasing components of x in absolute value. Fact V3 in the article of Bu et al., [START_REF] Bu | Algorithmic analysis and statistical estimation of slope via approximate message passing[END_REF] provides a formula for the subdifferential of J λ reported hereafter 1 :

∂J λ (s) =    v ∈ R p : for each equivalent class I,    if s I = 0 =⇒ v I ∈ P([ Π-1 s (λ)] I )sgn(s I ) if s I = 0 =⇒ v I ∈ P 0 ([ Π-1 s (λ)] I )    . (1)
In the above, P, P 0 are polytope-related mappings: P(u) = {y : y = Au for some doubly stochastic matrix A} P 0 (u) = {y : y = Au for some doubly sub-stochastic matrix A} Hereafter, we are going to discuss the notation Π-1 s given in (1), the polytope mappings as well as sketch of proof for this formula. First, before commenting (1), we remind that for a given norm • whose dual norm is • * , the subdifferential at s satisfies (see e.g. [START_REF] Hiriart-Urruty | Fundamentals of convex analysis[END_REF])

∂ • (s) = {v ∈ R p : v * ≤ 1 and v T s = s }.

In particular

• The subdifferential at 0 is the unit ball of the dual norm.

• If v is an arbitrary subgradient of • at s ∈ R p , namely v ∈ ∂ • (s), then v * ≤ 1.
Note that the dual sorted 1 norm has the following explicit expression (see e.g. [START_REF] Negrinho | Orbit regularization[END_REF])

J * λ (x) = max |x| (1) λ 1 , . . . , |x| (1) + |x| (2) λ 1 + λ 2 , . . . , |x| (1) + • • • + |x| (p) λ 1 + • • • + λ p .
Mappings Πx and Π-1

x

The mapping Πx : R p → {maximal atoms} and its pseudo-inverse Π-1

x are not properly defined; instead authors only provide the following example for these notations. If x = (5, 2, -3, -5) then Πx (x) = ({5, -5}, {5, -5}, -3, 2) and Π-1

x (λ) = ({λ 1 , λ 2 }, λ 4 , λ 3 , {λ 1 , λ 2 }).
As pointed out by the authors, there exists λ ∈ Π-1

x (λ) such that J λ (x) = λ, |x|2 . We agree with this fact, indeed

J λ (x) = λ 1 |x 1 | + λ 4 |x 2 | + λ 3 |x 3 | + λ 2 |x 4 | = λ 2 |x 1 | + λ 4 |x 2 | + λ 3 |x 3 | + λ 1 |x 4 |. Therefore, J λ (x) = λ, |x| as soon as λ ∈ {(λ 1 , λ 4 , λ 3 , λ 2 ), (λ 2 , λ 4 , λ 3 , λ 1 )}. This fact suggests that Π-1 x (λ) is a Cartesian product, namely Π-1 x (λ) = {(λ 1 , λ 4 , λ 3 , λ 1 ), (λ 1 , λ 4 , λ 3 , λ 2 ), (λ 2 , λ 4 , λ 3 , λ 1 ), (λ 2 , λ 4 , λ 3 , λ 2 )}.
However, if Π-1

x (λ) is Cartesian product then the formula given in (1) is wrong since (λ 1 , λ 4 , λ 3 , λ 1 ) / ∈ ∂J λ (x) (indeed J * λ ((λ 1 , λ 4 , λ 3 , λ 1 )) > 1). Overall we believe that the notations Πx and Π-1

x are very complicated and not useful to derive a formula for the subdifferential of J λ . Instead, one may probably replace Π-1 s (λ), in [START_REF] Ma Lgorzata Bogdan | Pattern recovery by slope[END_REF], by λ = (λ π -1 (1) , . . . , λ π -1 (p) ) where π -1 is the inverse of π an arbitrary permutation in {1, . . . , p} for which (|x π(1) |, . . . , |x π(p) |) = (|x| (1) , . . . , |x| (p) ).

Polytope mappings

We agree with the authors, when components of s are all equal (and positive) then ∂J λ (s) is the permutoèdre: conv{(λ π(1) , . . . , λ π(p) ) : where π is a permutation on {1, . . . , p}}. The permutoèdre is closely related to the Birkhoff polytope (the set of doubly stochastic matrices); indeed, P(λ) = conv{(λ π(1) , . . . , λ π(p) ) : where π is a permutation on {1, . . . , p}}.

On the other hand, the link between the unit ball of the dual norm J * λ (the permutoèdre signé) and the set of the sub-stochastic matrices is unclear. We conjecture the following statement

P 0 (λ) = {x ∈ [0, +∞) p : J * λ (x) ≤ 1}.
However, if this conjecture is wrong it would be impossible to recover the permutoèdre signé: ∂J λ (0), based on P 0 .

Sketch of proof for the formula

Authors claim that a rigorous proof of Fact V3 is given in [START_REF] Tyrrell | Variational analysis[END_REF]Exercise 8.31]. Actually, this exercise only provides a well known formula for the subdifferential of the maximum of a finite family of convex smooth functions (this fact is also proved in the book of Hiriart-Urruty and Lemaréchal [6, pp. 182-183,187-188]). So, currently fact V3 is not yet proven. Concerning the sketch of proof, authors "rewrite J λ (s) as a finite max function

J λ (s) = max{λ T f 1 (s), . . . , λ T f m (s)}, (2)
where {f i (s)} 1≤i≤m is the collection of all possible permutations for the entries of |s|". To our understanding expression ( 2) is unclear, indeed:

1. If f i (s) = (|s π(1) |, . . . , |s π(p) |)
for some permutation π on {1, . . . , p} then the formula (2) is true.

However, λ T f i (s) is a weighted 1 norm thus not a smooth function, the gradient 3 ∇ s λ T f i (s) depends on sgn(s) ∈ {-1, 1} p and the notation f -1 i (λ) does not make sense.

2. If f i (s) = (s π(1) , . . . , s π(p) ) then the gradient satisfies ∇ s λ T f i (s) = f -1 i (λ). However, the formula (2) is wrong as soon as some components of s are negative.

Authors claims that when components of s are all equal then ∂J λ (s) = conv{(λ π(1) , . . . , λ π(p) ) : where π is a permutation on {1, . . . , p}}. This equality is true when components of s are all equal and positive (see e.g [START_REF] Dupuis | Proximal operator for the sorted 1 norm: Application to testing procedures based on slope[END_REF][START_REF] Schneider | The geometry of uniqueness, sparsity and clustering in penalized estimation[END_REF]). However, this formula is no longer true when components of s are all equal and negative 4 . Finally, we believe that the formula ∂J λ (s) = conv{f -1 i (λ) : i ∈ A(s)} is misleading. Indeed, if f -1 i (λ) is just a permutation of components of λ then we would have the following inclusion ∂J λ (s) = conv{f -1 i (λ) : i ∈ A(s)} ⊂ conv{(λ π(1) , . . . , λ π(p) ) : where π is a permutation on {1, . . . , p}}.

This formula also appears in supplementary material of the article[START_REF] Bu | Algorithmic analysis and statistical estimation of slope via approximate message passing[END_REF]; derivation for the subdifferential of the sorted 1 norm are very similar.

This statement is not formulated this way; in the article there is a confusion between x and b.

This formula might be very useful to derive the subdifferental of J λ .


ICTMS 2022 : IMPROVED WAVEFRONT RECONSTRUCTION FOR MASK BASED PHASE-CONTRAST TOMOGRAPHY

INTRODUCTION HARTMANN SENSOR

A Hartmann sensor consists of a mask drilled with a micrometric holes placed in front of a detector, that defines an array of beamlets. The phase-related information is contained in the deflection of the individual beamlets. Different Hartmann configurations were tested in our setup to improve deflection sensitivity, spatial resolution and SNR.

Phase-contrast imaging (PCI) is a promising technique that became practical in laboratory setups thanks to high-power microfocus X-Ray sources [1]. Coupled with high-resolution (HR) detectors, HR-PCI can be achieved in a single exposure using Hartmann masks, which captures the sample-induced deformation of the x-ray wavefront (WF) through the local deflections of X-rays. The reconstructed wavefront then provides information on the complex index of refraction of the sample [2,3]. With accurate measurement of the projected phase shifts, a phase tomogram can be reconstructed to obtain localized information on the sample material.

WAVEFRONT RECONSTRUCTION

Algorithms dedicated to reconstruct wavefront (WF) acquired using Hartmann sensors have been largely described in literature. The most common is described in [4] as an iterative reconstruction algorithm (IR-WF).

To improve the homogeneity between the projections during IR-WF, we developed a 3D-driven algorithm that converges on the volume rather than the projections. An IR-WF iteration is applied to the current volume projection, and then compared to the raw projection to compute the error to back-propagate. This method allows to retrieve a more homogeneous result with both better contrast-to-noise and signal-to-noise ratios than the consecutive application of IR-WF and IR-CT in both sample datasets. Since only the order of the operations differs, the computation time for the two methods is similar. Plot. 1 : Gray level along the lines of the example layers, for both sequential and simultaneous reconstructions.

  Acknowledgements: this study was done within the context of the XPulse project, funded by the Nouvelle-Aquitaine region and the ERDF. Alberto Bravin, et al. "X-ray phase-contrast imaging: from pre-clinical applications towards clinics.". Physics in medicine and biology 58 1. (2013): R1-35 . [2] Begani Provinciali, Ginevra et al. "High-Sensitivity X-ray Phase Imaging System Based on a Hartmann Wavefront Sensor". Condensed Matter 7. (2021). [3] La Rochefoucauld, Ombeline et al. "EUV and Hard X-ray Hartmann Wavefront Sensing for Optical Metrology, Alignment and Phase Imaging". Sensors 21. 3(2021). [4] W.H. Southwell, . "Wave-front estimation from wave-front slope measurements". J. Opt. Soc. Am. 70. 8(1980): 998-1006.

Fig. 1 :

 1 Fig. 1 : Diagram of our acquisition setup.

Fig. 2 :

 2 Fig. 2 : Examples of horizontal deflections extracted from the raw image acquired with this setup on two samples. (a) Shell of a juvenile oyster from Institut Fresnel, Marseille. (b) Tube filled with glass silicate microspheres.

Fig. 4 :

 4 Fig. 4 : Diagram of the simultaneous WF and CT reconstructions. Both reconstructions converge simultaneously, ensuring that any single wavefront has to be coherent with all others.

  Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, F-33400 Talence, France 2 ALPhANOV, Rue François Mitterrand, 33400, Talence, France 3 INSERM LAMC U1029, Allée Geoffroy Saint Hilaire, 33615 Pessac Cedex, France 4 Imagine Optics, Rue François Mitterrand, 33400, Talence, France

			PSNR local	Sequential 11,016	Simultaneou s 12,107	Tab. 1 : Metrics measured from the example layers. Local metrics are obtained
			PSNR full	11,685	15,519	by manually selecting the
			SNR local	0,634	1,279	signal and noise regions
			SNR full	0,863	0,924	of interest, while the full
	Sequential	Simultaneous	CNR local CNR full	11,016 10,088	27,062 14,333	metrics are obtained on the complete image without segmentation.
				Sequential	Simultaneou s
			PSNR local	6,265	9,643
			PSNR full	9,242	9,406
			SNR local	1,055	2,315
			SNR full	1,075	1,259
			CNR local	6,100	19,128
	Sequential	Simultaneous	CNR full	9,916	11,789

1


Emile Barjou

Francesca Mastropietro

Benjamin Barbrel

Ombeline De

La Rochefoucauld

Aboubakr Bakkali

Benoît Recur

Pascal Desbarats

Simultaneous Wavefront and 3D Tomographic Reconstructions for Phase Imaging Using Hartmann Sensor

published or not. The documents may come   L'archive ouverte pluridisciplinaire

CONCLUSIONS REFERENCES

Phase-contrast imaging (PCI) is a promising technique that became practical using high-power micro-focus X-ray sources.

The Hartmann method captures the deflections of individual X-ray beamlets to obtain contrast, relying on variations of the imaginary part of the sample complex refractive index δ. This is interesting for clinical imagery since δ becomes larger than the absorption index β at high energy for soft tissues [1].

Algorithms dedicated to reconstruct wavefronts (WF) acquired using Hartmann sensors have been largely described in the literature. A common one is described in [3] as an iterative reconstruction algorithm (IR-WF).

In order to improve the homogeneity between the projections during IR-WF, we developed a 3D-driven algorithm that converges on the reconstructed volume rather than the individual projections. To do so, the IR-WF algorithm is built into the iterative tomographic reconstruction (IR-CT).

We measured the SNR, PSNR and CNR on the three different dataset using both methods to assert the quality of the 3D

reconstruction. The values of these metrics are reported in Fig. 7, as well as the evolution of the SNR vs iteration # on dataset (A) in Fig. 8.

This method allows to obtain a more homogeneous result w i t h b e t t e r S N R a n d C N R t h a n t h e c o n s e c u t i v e application of IR-WF and IR-CT.

Barjou Emile a,b , Mastropietro Francesca b , Barbrel Barbrel b , De La Rochefoucauld Ombeline c , Bakkali Aboubakr b , Recur Benoit d , Desbarats Pascal a By doing both reconstructions at the same time all wavefronts are constrained to converge to the same result. This attenuates the artifacts caused by the IR-WF.

Our simultaneous IR-WF and IR-CT algorithm provides superior results compared to the existing algorithm when provided with a Hartmann PCI tomographic dataset by using the information of all projections in the iterative process.

Although the computational complexity are equal, our method tends to converge more slowly due to the 3D homogeneity constraint. Existing algorithms lead to low-frequency artifacts when confronted with noisy images, resulting in incoherent information of each projection. The Hartmann mask is placed between the sample and the detector.

Dataset

Fig. 6 : Slices from the reconstructed objects using the sequential (top) and simultaneous (bottom) methods. The simultaneous method offers a more homogeneous result and is able to resolve some details that are not visible with the sequential method. We c a n s e e t h a t u n l i k e t h e s e q u e n t i a l m e t h o d , o u r simultaneous method is able to converge further and can support more iterations without introducing a quality loss.

  , A. et al.X-ray phase-contrast imaging: from pre-clinical applications towards clinics.," Physics in medicine and biology 58 1, R1-35 (2013) 2. Hagen, C. K., Munro, P. R. T., Endrizzi, M., Diemoz, P. C., and Olivo, A., "Low-dose phase contrast tomography with conventional xray sources," Med. Phys. 41, 070701 (July 2014). 3. Southwell, W., "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (Aug 1980).

Fig. 7 :

 7 Fig.7: SNR, PSNR and CNR extracted from layers illustrated in Fig.6. The simultaneous method shows a better result than the sequential method in almost all cases.

Fig. 8 :

 8 Fig. 8 : Evolution of the SNR of the reconstruction of dataset (A) as a function of IR-WF iterations number.

Fig. 3 :

 3 Fig. 3 : Example of an integrated WF using traditionnal method. Low-frequency artifact are clearly visible.

  Fig. 5 : Photos of the samples A (left) and C (right).