Caroline Schluth-Bolard

Bruno Delobel

Damien Sanlaville

Odile Boute

Jean-Marie Cuisset

Sylvie Sukno

Audrey Labalme

Bénédicte Duban-Bedu

Ghislaine Plessis

Sylvie Jaillard

Christèle Dubourg

Catherine Henri

Josette Lucas

Sylvie Odent

Laurent Pasquier

Henri Copin

Philippe Latour

Marie-Pierre Cordier

Gwenaël Nadeau

Marianne Till

Patrick Edery

Joris Andrieux
email: andrieux@chru-lille.fr

Cryptic genomic imbalances in de novo and inherited apparently

Keywords: array CGH, apparently balanced translocations, abnormal phenotype

Introduction

It is estimated that standard karyotype displayed chromosome aberrations in 3 to 15 % of patients affected with mental retardation [START_REF] Rauch | Diagnostic yield of various genetic approaches in patients with unexplained developmental delay or mental retardation[END_REF][START_REF] Stankiewicz | Use of array CGH in the evaluation of dysmorphology, malformations, developmental delay, and idiopathic mental retardation[END_REF][START_REF] Van Karnebeek | Diagnostic investigations in individuals with mental retardation: a systematic literature review of their usefulness[END_REF]. Most of them are unbalanced by either numerical (trisomy, monosomy) or structural (deletion, duplication…) anomalies. However, apparently balanced structural rearrangements are present in 0.6 % of mentally retarded patients [START_REF] Rauch | Diagnostic yield of various genetic approaches in patients with unexplained developmental delay or mental retardation[END_REF]. About 6 % of de novo apparently balanced translocations [START_REF] Warburton | De novo balanced chromosome rearrangements and extra marker chromosomes identified at prenatal diagnosis: clinical significance and distribution of breakpoints[END_REF] and 23 % of apparently balanced complex chromosomal rearrangements (CCR) defined by three or more breakpoints [START_REF] Madan | Recombination in a balanced complex translocation of a mother leading to a balanced reciprocal translocation in the child, Review of 60 cases of balanced complex translocations[END_REF] are associated with an abnormal phenotype. These balanced rearrangements were demonstrated to be responsible for the phenotype by different mechanisms such as gene disruption at the breakpoints [START_REF] Kalscheuer | Disruption of the serine/threonine kinase 9 gene causes severe X-linked infantile spasms and mental retardation[END_REF][START_REF] Kenwrick | Molecular analysis of the Duchenne muscular dystrophy region using pulsed field gel electrophoresis[END_REF], position effect [START_REF] Fantes | Aniridia-associated cytogenetic rearrangements suggest that a position effect may cause the mutant phenotype[END_REF][START_REF] Kleinjan | Position effect in human genetic disease[END_REF][START_REF] Krebs | Translocation breakpoint maps 5 kb 3' from inserm-00405484, version 1 -25 Aug 2009 TWIST in a patient affected with Saethre-Chotzen syndrome[END_REF] or disturbance of parental imprinting [START_REF] Dupont | Familial reciprocal translocation t(7;16) associated with maternal uniparental disomy 7 in a Silver-Russell patient[END_REF]. Development of Fluorescent In Situ Hybridization (FISH) or Comparative Genomic Hybridization (CGH) on chromosomes showed that a proportion of these rearrangements was in fact associated with cryptic imbalances [START_REF] Astbury | Detection of deletions in de novo "balanced" chromosome rearrangements: further evidence for their role in phenotypic abnormalities[END_REF][START_REF] Ciccone | Reciprocal translocations: a trap for cytogenetists?[END_REF][START_REF] Higgins | Characterization of apparently balanced chromosomal rearrangements from the developmental genome anatomy project[END_REF][START_REF] Kirchhoff | High resolution comparative genomic hybridisation analysis reveals imbalances in dyschromosomal patients with normal or apparently balanced conventional karyotypes[END_REF][START_REF] Kumar | Molecular characterization and delineation of subtle deletions in de novo "balanced" chromosomal rearrangements[END_REF][START_REF] Patsalis | Fluorescence in situ hybridization characterization of apparently balanced translocation reveals cryptic complex chromosomal rearrangements with unexpected level of complexity[END_REF]. More recently, array CGH technology [START_REF] Solinas-Toldo | Matrix-based comparative genomic hybridization: biochips to screen for genomic imbalances[END_REF] has been used to investigate apparently balanced translocations associated with an abnormal phenotype and has found cryptic deletion in about 30 to 50 % of them [START_REF] Baptista | Breakpoint mapping and array CGH in translocations: comparison of a phenotypically normal and an abnormal cohort[END_REF][START_REF] Gregori | Cryptic deletions are a common finding in "balanced" reciprocal and complex chromosome rearrangements: a study of 59 patients[END_REF][START_REF] Gribble | The complex nature of constitutional de novo apparently balanced translocations in patients presenting with abnormal phenotypes[END_REF].

Here, we explored 47 patients presenting with mental retardation and carrying an apparently balanced chromosomal rearrangement with high-resolution oligonucleotide array in order to detect cryptic imbalances accounting for the phenotype. These rearrangements were either de novo (33 patients) or inherited (14 patients) and included reciprocal translocations, peri-and paracentric inversions or CCR. We estimated their frequency and defined the place of this technology in a diagnostic setting. inserm-00405484, version 1 -25 Aug 2009

Material and methods

Patients

Forty-seven patients (26 males and 21 females) with mental retardation and/or multiple congenital malformations have been included in the study after fully informed consent was obtained. All patients had been assessed by a clinical geneticist. Phenotype range was very wide and included variable degree of mental retardation with or without malformations and facial dysmorphism. For all of them, standard karyotype (RHG, 500 bands) showed an apparently balanced rearrangement including 28 reciprocal translocations, 12 inversions and 7 CCR. Thirty-three balanced rearrangements occurred de novo (21 translocations, 7 inversions and 5 CCR) and 14 were inherited from a healthy parent (7 translocations, 5 inversions and 2 CCR) (Table 1). There was no other evident cause for their phenotype. Patients' karyotypes are summed up in Table 1. Parents' blood sample was required to assess if the imbalances detected by array CGH were de novo or inherited.

Array CGH

Agilent® oligonucleotide arrays were used according to the manufacturer instruction (Agilent Human Genome CGH Microarray kit 244A® and 44K®). The overall median probe spacing was 43 kb for 44K array and 8.9 kb for 244A array. Thirty eight patients DNA were analyzed with a 44,000 oligonucleotides array and 9 patients DNA with a 244,000 oligonucleotides array (#1, #2, #3, #29, #30, #31, #32, #41, #42). Patient's DNA as well as a reference DNA were digested with RsaI and AluI. Each digested DNA product was labelled by random priming using either Cy5-dUTP or Cy3-dUTP. After columns-purification, probes were denaturated and pre-annealed with 50 µg of human Cot-1 DNA (Invitrogen®, California). Hybridization was performed at 65°C during 40 hours. After washing, the array was scanned and analyzed with Feature Extraction® 9.1 software. Control DNA consisted inserm-00405484, version 1 -25 Aug 2009 either of a sex-matched pool of genomic DNA commercially available (Promega®, USA) or of two other patients DNA, according to the loop model [START_REF] Menten | Emerging patterns of cryptic chromosomal imbalance in patients with idiopathic mental retardation and multiple congenital anomalies: a new series of 140 patients and review of published reports[END_REF]. Results were interpreted with CGH analytics® 4.5 software by two investigators. A copy number variation was considered if at least 3 contiguous oligonucleotides presented an abnormal log ratio (> + 0,66 or < -0,75).

Results were compared to data recorded in the database of genomic variants.

Fluorescent in situ hybridization (FISH)

FISH analyses on patient metaphases were performed in order to confirm the results of array CGH. Each time a microdeletion was confirmed, FISH was performed on parents' sample in order to check if the genomic imbalance was de novo or inherited. BACs were chosen on UCSC and Ensembl databases. FISH using BAC clones was performed as described by Romana et al [START_REF] Rauch | Diagnostic yield of various genetic approaches in patients with unexplained developmental delay or mental retardation[END_REF]. DNA was fluoresceine or rhodamine labeled by nicktranslation. Probes were coprecipitated with human Cot-1 DNA (Invitrogen®, California) and then resuspended in hybridization buffer (50 % formamide). After denaturation, overnight hybridization and post-hybridization wash, slides were DAPI counterstained and were read using a fluorescent microscope equipped with a CCD camera. All details about BAC clones used are available on request. Germany), 1.5 µM of each primer and 10 ng of genomic DNA. The thermal cycling conditions comprised a 15 min polymerase activation at 95°C followed by 35 cycles of 15 s at 95°C, 30 s at 60°C and 15s at 72°C. Experiments need to have a coefficient of variation for triplicate samples inferior to 0.1. PCR efficiency is calculated as followed: 10 -1/slope . Efficiency of qPCR is equal to 100% when 10 -1/slope = 2 meaning that quantity of DNA is multiplied by 2 at each cycle of the PCR. We consider that PCR efficiency do be superior to 98% to assure good results.

Results

Overall, array CGH demonstrated cryptic imbalances in 20 of the 47 patients (42.6%).

It consisted of 21 deletions ranging from 60 kb to 15.37 Mb. Nine of the 21 imbalances were located in regions not involved in the balanced rearrangement. Two of these cryptic imbalances were inherited from a healthy parent. The proportion of imbalances detected in de novo (16/33, 48.5 %) and in inherited rearrangements (4/14, 28.6%) was not statistically different (p<0.34). Results and phenotypes of these patients are described in detail in Table 2.

De novo rearrangements inserm-00405484, version 1 -25 Aug 2009

Microdeletions were detected in 16 of the 33 de novo structural rearrangements (48.5%). They ranged from 60 kb to 15.37 Mb and were all de novo. Nine of them were at distance from initial breakpoints. One patient (#42) presented two deletions.

Reciprocal translocations: 38.1 % (8/21) of apparently balanced translocations showed an associated deletion ranging from 60 kb to 15.37 Mb. Three of them were located at distance from translocation breakpoints (#1, #22, #27).

Inversions: Four of the seven (57.1 %) de novo inversions were imbalanced.

Microdeletions ranged from 1.06 Mb to 8.87 Mb. Three of them were located on a different chromosome than the chromosome carrying the inversion (#29, #34, #36).

Complex chromosomal rearrangements: Four of the five de novo CCR were imbalanced (80 %) with deletions ranging from 690 kb to 4.9 Mb. Case #42 showed two deletions, one on a chromosome 2 at distance from the breakpoint and one on a chromosome 6 at the breakpoint.

Inherited rearrangements

Cryptic rearrangements were detected in 4 of the 14 inherited structural rearrangements (28.6%). These were only deletions ranging from 80 kb to 3.64 Mb. Two of them were inherited from a healthy parent (#9, #31). Two of them were at distance from initial breakpoints (#9, #31).

Reciprocal translocations: One of the seven (14.3 %) apparently balanced translocations showed a 1.21 Mb deletion at distance from the breakpoints (#9). It was inherited from the healthy father who also carries the balanced translocation. Results according to the array resolution Thirty-eight cases were studied with 44K array. It displayed 15 microdeletions ranging from 300 kb to 15.37 Mb (mean = 4.24 Mb). Nine cases were investigated with a 244K array (#1, #2, #3, #29, #30, #31, #32, #41, #42). Six microdeletions in five patients were found ranging from 60 kb to 8.87 Mb (mean: 3.16 Mb). In two cases (#1, #31) in whom the deletion was of small size (less than 100 kb), it could not be concluded if the deletion accounted for the phenotype really.

Discussion

Development of more and more accurate molecular cytogenetics techniques such as FISH, CGH on chromosomes and array CGH allowed to dissect apparently balanced chromosomal rearrangements in patients with abnormal phenotype. These techniques displayed the complexity of reciprocal translocations that could in fact involve up to 5 chromosomes in a combination of translocations, insertions and inversions [START_REF] Astbury | Detection of deletions in de novo "balanced" chromosome rearrangements: further evidence for their role in phenotypic abnormalities[END_REF][START_REF] Ciccone | Reciprocal translocations: a trap for cytogenetists?[END_REF][START_REF] Gribble | The complex nature of constitutional de novo apparently balanced translocations in patients presenting with abnormal phenotypes[END_REF][START_REF] Patsalis | Fluorescence in situ hybridization characterization of apparently balanced translocation reveals cryptic complex chromosomal rearrangements with unexpected level of complexity[END_REF]. They also showed presence of cryptic imbalances either at the chromosomal breakpoint or at distance [START_REF] Astbury | Detection of deletions in de novo "balanced" chromosome rearrangements: further evidence for their role in phenotypic abnormalities[END_REF][START_REF] Ciccone | Reciprocal translocations: a trap for cytogenetists?[END_REF][START_REF] Gribble | The complex nature of constitutional de novo apparently balanced translocations in patients presenting with abnormal phenotypes[END_REF][START_REF] Higgins | Characterization of apparently balanced chromosomal rearrangements from the developmental genome anatomy project[END_REF][START_REF] Kirchhoff | High resolution comparative genomic hybridisation analysis reveals imbalances in dyschromosomal patients with normal or apparently balanced conventional karyotypes[END_REF][START_REF] Kumar | Molecular characterization and delineation of subtle deletions in de novo "balanced" chromosomal rearrangements[END_REF][START_REF] Patsalis | Fluorescence in situ hybridization characterization of apparently balanced translocation reveals cryptic complex chromosomal rearrangements with unexpected level of complexity[END_REF]. Characterization by FISH of 40 apparently balanced chromosomal rearrangements from the Developmental Genome Anatomy Project revealed imbalances in 37 % of them (15/40 cases) [START_REF] Higgins | Characterization of apparently balanced chromosomal rearrangements from the developmental genome anatomy project[END_REF]. Array CGH is the most recent technology used to characterize this type of rearrangements and has the advantage over FISH approach to investigate the entire genome and not only breakpoint regions.

inserm-00405484, version 1 -25 Aug 2009

Cryptic imbalances in apparently balanced de novo rearrangements Beside several isolated case reports [START_REF] Della Monica | A case of autism with an interstitial 1q deletion (1q23.3-24.2) and a de novo translocation of chromosomes 1q and 5q[END_REF][START_REF] Hayashi | Fortuitous detection of a submicroscopic deletion at 1q25 in a girl with Cornelia-de Lange syndrome carrying t(5;13)(p13.1;q12.1) by array-based comparative genomic hybridization[END_REF], larger studies using array CGH estimated the proportion of imbalances in apparently balanced de novo translocations (Table 3) [START_REF] Baptista | Breakpoint mapping and array CGH in translocations: comparison of a phenotypically normal and an abnormal cohort[END_REF][START_REF] Gregori | Cryptic deletions are a common finding in "balanced" reciprocal and complex chromosome rearrangements: a study of 59 patients[END_REF][START_REF] Gribble | The complex nature of constitutional de novo apparently balanced translocations in patients presenting with abnormal phenotypes[END_REF].

Gribble et al. studied 10 patients using a BAC/PAC array and found 5/10 imbalances from 1.2 to 6.2 Mb [START_REF] Gribble | The complex nature of constitutional de novo apparently balanced translocations in patients presenting with abnormal phenotypes[END_REF]. De Gregori et al investigated 59 patients including de novo reciprocal translocations and CCR. They showed i) that 40 % of apparently balanced translocations with abnormal phenotype are associated with a cryptic deletion, ii) that 18 % of them are in fact more complex and iii) that almost all CCR with abnormal phenotype are imbalanced [START_REF] Gregori | Cryptic deletions are a common finding in "balanced" reciprocal and complex chromosome rearrangements: a study of 59 patients[END_REF].

More recently, Baptista et al found four imbalances in 14 patients (28.6 %) [START_REF] Baptista | Breakpoint mapping and array CGH in translocations: comparison of a phenotypically normal and an abnormal cohort[END_REF]. In the present study, we found cryptic deletion in 48.5 % of cases (16/33) of apparently balanced de novo rearrangements associated with an abnormal phenotype including 8 translocations, 4 inversions and 4 CCR. Twenty-seven percent of them revealed more complex as initially thought. In 15 of these cases, the phenotype could be related to the cryptic imbalance according to its de novo nature, its size and its gene content [START_REF] Lee | Copy number variations and clinical cytogenetic diagnosis of constitutional disorders[END_REF]. For example, case #43 showed a de novo 690 kb deletion involving the TWIST gene that accounted for his Saethre-Chotzen phenotype and was described elsewhere [START_REF] Schluth-Bolard | TWIST microdeletion identified by array CGH in a patient presenting Saethre-Chotzen phenotype and a complex rearrangement involving chromosomes 2 and 7[END_REF]. These results are consistent with the previous studies leading us to conclude that about 40 % of apparently balanced de novo rearrangements with abnormal phenotype are associated with a cryptic imbalance. The yield of array CGH in MCA/MR patients with normal standard karyotype is about 10 to 17 % [START_REF] Lu | Genomic imbalances in neonates with birth defects: high detection rates by using chromosomal microarray analysis[END_REF][START_REF] Shaffer | The identification of microdeletion syndromes and other chromosome abnormalities: cytogenetic methods of the past, new technologies for the future[END_REF]. So it seems that genomic imbalances are more likely to be found in MCA/MR patients with structural chromosome rearrangements than in patients without. Interestingly, no case of our cohort had copy-number gains, which is also consistent with the previous studies [START_REF] Baptista | Breakpoint mapping and array CGH in translocations: comparison of a phenotypically normal and an abnormal cohort[END_REF][START_REF] Gregori | Cryptic deletions are a common finding in "balanced" reciprocal and complex chromosome rearrangements: a study of 59 patients[END_REF][START_REF] Gribble | The complex nature of constitutional de novo apparently balanced translocations in patients presenting with abnormal phenotypes[END_REF]. This could be the fact of a particular mechanism generating preferentially loss of material. But gains of material could also be associated with milder phenotype or a different phenotype than MCA/MR and may not have been recruited. Finally, microdeletions unrelated inserm-00405484, version 1 -25 Aug 2009 to the breakpoints involve about 20 % of cases [START_REF] Gregori | Cryptic deletions are a common finding in "balanced" reciprocal and complex chromosome rearrangements: a study of 59 patients[END_REF]. However, their significance is still unclear.

They may either be part of a complex rearrangement involving multiple breakpoints and fusions at different part of the genome or be associated to the balanced rearrangement fortuitously.

Cryptic imbalances in apparently balanced inherited rearrangements

Four out of 14 inherited cases of chromosomal rearrangements were imbalanced: one translocation, 2 inversions and 1 CCR (cases #9, #31, #40 and #45). In two cases the cryptic imbalance occurred de novo and could be causally related to the phenotype of the patients. In two other cases (#9 and #31) the cryptic imbalance was inherited from the healthy parent who also transmitted the balanced rearrangement. So it cannot be concluded if these deletions were new benign variations not reported in databases yet or if they contributed to the phenotype in a complex manner like variable expression, unmasking of recessive mutation on the other allele, disturbance of parental imprinting or combination of multiple genetic defects. So, we believe that array CGH is also useful to explore patients with an abnormal phenotype carrying an inherited chromosomal rearrangement.

Diagnostic yield according to array resolution

Diagnostic yield of 244K arrays was not statistically different from 44K arrays in the present study. Although 244K array identified deletions less than 100 kb in two cases (cases #1 and #31), it was not possible to conclude about their pathological significance. Indeed, these deletions included a single gene, neither referenced in databases of genomic variants nor morbid databases (OMIM). Investigations to confirm the role of these genes in the phenotype of patients are time-consuming and go beyond the means of a diagnostic laboratory. The smallest deletion detected by 44K was 300 kb in this series (case #22). Moreover, it has inserm-00405484, version 1 -25 Aug 2009 already been demonstrated that 44K array detected as much as pathological imbalances than 244K array but detected less copy number polymorphisms [START_REF] Fan | Detection of pathogenic gene copy number variations in patients with mental retardation by genomewide oligonucleotide array comparative genomic hybridization[END_REF]. So, the use of 44K arrays seems compatible in a high-throughput diagnostic setting since it provides a good diagnostic yield and avoids too many false positive cases and time-consuming verifications.

Conclusion

In conclusion, we studied 47 cases of MCA/MR patients presenting an apparently balanced chromosomal rearrangement either de novo or inherited by array CGH. Genomic imbalances were identified in 48.5 % of de novo cases and 28.6 % of inherited cases. These results support previous studies showing that 40 % of patients with MCA/MR and an apparently balanced translocation carry a cryptic imbalance that can account for the phenotype. We suggest that the management of MCA/MR patients with an apparently balanced chromosome rearrangement should include a systematic investigation by array CGH, whatever the type of rearrangements (translocation, inversion or CCR) and whatever the inheritance (de novo or familial). If array CGH fails to detect any imbalance, breakpoints should be investigated to look for position effect [START_REF] Fantes | Aniridia-associated cytogenetic rearrangements suggest that a position effect may cause the mutant phenotype[END_REF][START_REF] Kleinjan | Position effect in human genetic disease[END_REF][START_REF] Krebs | Translocation breakpoint maps 5 kb 3' from inserm-00405484, version 1 -25 Aug 2009 TWIST in a patient affected with Saethre-Chotzen syndrome[END_REF] or gene disruption [START_REF] Kalscheuer | Disruption of the serine/threonine kinase 9 gene causes severe X-linked infantile spasms and mental retardation[END_REF][START_REF] Kenwrick | Molecular analysis of the Duchenne muscular dystrophy region using pulsed field gel electrophoresis[END_REF] that occurs in 35% to 50% of balanced rearrangements [START_REF] Baptista | Breakpoint mapping and array CGH in translocations: comparison of a phenotypically normal and an abnormal cohort[END_REF][START_REF] Fantes | FISH mapping of de novo apparently balanced chromosome rearrangements identifies characteristics associated with phenotypic abnormality[END_REF]. Of course, a fortuitous association between a balanced rearrangement and MCA/MR of another etiology cannot be excluded. In prenatal diagnosis, array CGH should be proposed to fetuses presented an apparently balanced de novo chromosomal rearrangement associated to malformations according to the literature [START_REF] Gregori | Cryptic deletions are a common finding in "balanced" reciprocal and complex chromosome rearrangements: a study of 59 patients[END_REF]. Table 1: Conventional karyotypes of the 47 patients

Legends to Tables

dn 44K T R A N S L O C A T I O N S I N V E R S I O N S C C R

2. 4 .

 4 Quantitative PCR (qPCR) When FISH was not possible, the confirmation of allelic imbalance in the target chromosome region was analyzed using SYBR Green I based quantitative real time PCR with Light-Cycler® (Roche Diagnostics, GmbH, Mannheim, Germany). The protocol involved amplification of a target gene and a reference gene (ADORA2B, HGNC:264) (primers sequences available on request). Quantitative PCR protocol was conducted in triplicate in a 20 µL final volume containing 10 µL of SYBR PCR Master Mix (2X) (Qiagen®, GmbH, Hilden, inserm-00405484, version 1 -25 Aug 2009

A

  melting curve step was used to examine each sample for purity and specificity and the size of the amplicons was checked by electrophoresis. The calculation is based on the Ct values (minimal number of PCR cycles necessary to detect a fluorescence issued by the SYBR Green I) obtained by the Light Cycler software. A series of 5-fold dilutions of human genomic DNA corresponding to 0.5 to 8 ng/µL was included in each experiments in order to generate an external standard curve (Ct = A x log [Concentration DNA] + B) that allowed to estimate DNA concentration for each sample. Relative copy number is then calculated as the [target gene]/[reference gene] ratio.

Inversions:

  Two of the five (40 %) inversions were imbalanced. Deletion size was respectively of 80 kb and 1.23 Mb. One of these imbalances was located on a different inserm-00405484, version 1 -25 Aug 2009 chromosome than the chromosome carrying the inversion and was inherited from the father who also transmitted the inversion (#31). Complex chromosomal rearrangements: One of the two CCR (50 %) presented a 3.64 Mb de novo deletion.

Table 2 :

 2 Array CGH results in patients carrying an imbalance and corresponding phenotype

Table 3 :

 3 Review of the literature and comparison with the present study inserm-00405484, version 1 -25 Aug 2009

Table 1 :

 1 Conventional karyotypes of the 47 patients

	Case	Karyotype	Inheritance Array resolution
	1	46,XY,t(1;18)(q11.1;q12.1)	dn	244K
	2	46,XX,t(1;18)(p36;q21)	dn	244K
	3	46,XY,t(4;22)(q21;q12)	dn	244K
	4	46,XY,t(3;5)(q24;q21)	pat	44K
	5	46,XX,t(10;11)(p14;p15)	dn	44K
	6	46,XY,t(4;11)(q27;q22;3)	dn	44K
	7	46,XY,t(12;14)(q21;q31)	dn	44K
	8	46,XY,t(7;10)(q3?5;q25?)	dn	44K
	9	46,XY,t(2;6)(q36;q26)	pat	44K
	10	46,XY,t(2;12)(p16;q14)	dn	44K
	11	46,X,t(Y;2)(q12;p24)	dn	44K
	12	46,XX,t(8;18)(q21;q22)	dn	44K
	13	46,XX,t(5;14)(q34;q31)	dn	44K
	14	46,XX,t(4;11)(q3?2;q25)	dn	44K
	15	46,XY,t(1;4)(q43;q22)	mat	44K
	16	46,XY,t(2;9)(q37.2;p23)	pat	44K
	17	46,XY,t(2;9)(q32;q13)	dn	44K
	18	46,XY,t(5;12)(q34;q23)	dn	44K
	19	46,XY,t(7;14)(p14;q21)	mat	44K
	20	46,XX,t(2;5)(p22;q12)	dn	44K
	21	46,XY,t(9;12)(p23;q21)	dn	44K
	22	46,XX,t(2;18)(p15;q21)	dn	44K
	23	46,XX,t(1;18)(p31;q12.3)	mat	44K
	24	46,XX,t(1;11)(q12;q13)	mat	44K
	25	46,XX,t(1;14)(q31;q12)	dn	44K
	26	46,XY,t(2;8)(q22;q24.2)	dn	44K
	27	46,XY,t(7;12)(p11;p11)	dn	44K
	28	46,XY,t(1;6)(q4?1;q1?4)	dn	44K
	29	46,XX,inv(8)(p22q12.2)	dn	244K
	30	46,XY,inv(11)(p15q13)	mat	244K
	31	46,XY,inv(4)(p13q22)	pat	244K
	32	46,XX,inv(8)(q21q24.2)	pat	244K
	33	46,XX,inv(1)(q42q44)	dn	44K
	34	46,XX,inv(4)(p16q32)	dn	44K
	35	46,XX,inv(13)(q12.13q34)	dn	44K
	36	46,XY,inv(7)(p13q21)	dn	44K
	37	46,XY,inv(2)(p13q13)	dn	44K
	38	46,X,inv(X)(p21.1q21.1)	dn	44K
	39	46,XY,inv(7)(p14q21.1)	mat	44K
	40	46,XX,inv(1)(p21q13)	mat	44K
	41	46,XY,t(1;7;11)(p35;q33;q12)	dn	244K
	42	46,XX,t(2;3;6)(q21;q22;p26.1)	dn	244K
	43	46,XY,t(2;7)(p24;p21),ins(7)(p21.3q21.3q22)	dn	44K
	44	46,XY,inv(5)(p14q23)t(1;inv(5))(p21;q23)	pat	44K
	45	46,XX,ins(7;4)(q31;q27q32)	mat	44K
		46,XX,t(2;5;10)(2pter®2q22::2q34®2qter;
	46	5pter®5q21::2q22®2q33::10p14®10pter;10qter
		®10p14::2q33®2q34::5q21®5qter)

Table (

 (

	s)
	46,XX,t(1;2;9)(1pter®1q31::9p12®9pter;
	2pter®2q24::1q41®1qter;9qter®9p12:	dn	44K
	:1q31®1q41::2q24®2qter),t(11;14)(q11;q23)
	dn: de novo ; pat: paternal; mat: maternal
	inserm-00405484, version 1 -25 Aug 2009 inserm-00405484, version 1 -25 Aug 2009

Table 2 :

 2 Array CGH results in patients carrying an imbalance and corresponding phenotype a) de novo rearrangement group

	Table(s)
			Case	Karyotype	Rearranged region	Inheritance	Size Mb	Phenotype
			1*	46,XY,t(1;18)(q11.1;q12.1)	del(14)(q32.2q32.2)	dn	0.06	Moderate mental retardation, macrosomia, leukodystrophy, hexadactyly
			3	46,XY,t(4;22)(q21;q12)	del(4)(q21.22q21.22)	dn	0.77	Moderate mental retardation, facial dysmorphism
		T R	8	46,XY,t(7;10)(q3?5;q25?)	del(7)(q35q36.1)	dn	5.13	Severe mental retardation, autistic troubles, seizures, facial dysmorphism
		A N	17	46,XY,t(2;9)(q32;q13)	del(9)(q21.13q21.31)	dn	6.49	Mild mental retardation, speech delay, facial dysmorphism, hirsutism
		S L	21	46,XY,t(9;12)(p23;q21)	del(9)(p24.2p23)	dn	11.61	Severe mental retardation, speech delay, aggressivity, muscular hypotonia, hydronephrosis, cryptorchidism, diabetes
	inserm-00405484, version 1 -25 Aug 2009	O C I N V C C R	22* 25 27* 29* 34* 35 36* 43 46 47 42*	46,XX,t(2;18)(p15;q21) 46,XX,t(1;14)(q31;q12) 46,XY,t(7;12)(p11;p11) 46,XX,inv(8)(p22q12.2) 46,XX,inv(4)(p16q32) 46,XX,inv(13)(q12.13q34) 46,XY,inv(7)(p13q21) 46,XY,t(2;7)(p24;p21),ins(7)(p21.3q21.3q22) 46,XX,t(2;5;10) 46,XX,t(1;2;9),t(11;14)(q11;q23) 46,XX,t(2;3;6)(q21;q22;p26.1)	del(2)(p21p21) del(1)(q25.2q31.2) del(2)(q33.1q33.1) del(1)(q24.1q24.2) del(13)(q12.3q13.1) del(13)(q12.3q13.1) del(14)(q22.1q22.1) del(2)q34q34) del(6q25.1q25.2) del(7)(p21.3p21.3) del(2)(q33.3q33.3) del(1)(q23.3q24.2)	dn dn dn dn dn dn dn dn dn dn dn dn	0.30 15.37 2.02 8.87 3.52 3.85 1.06 4.3 4.9 0.69 3.64 3.57	Mental retardation, speech delay, hyperactivity, facial dysmorphism, cleft lip and palate, congenital cardiac defect, syndactyly Moderate mental retardation, hypotonia, growth retardation, facial dysmorphism, trigonocephaly Severe mental retardation, autistic troubles, growth retardation, facial dysmorphism, microcephaly, dental anomalies Mild mental retardation, seizures, growth retardation, facial dysmorphism Moderate mental retardation, speech delay, obesity, facial dysmorphism, camptodactyly Severe mental retardation, microcephaly, muscular hypertonia, growth retardation, liver steatosis Mild mental retardation, spasticity, poor motor coordination Mild mental retardation, craniosynostosis, syndactyly (Saethre-Chotzen syndrome), cryptorchidism, kidney hypoplasia Facial dysmorphism, congenital cardiac defect, brain malforamtion, hepatosplenomegaly, cryptorchidism Mental retardation, muscular hypotonia, growth retardation, facial dysmorphism, corpus callosum hypoplasia, renal hypoplasia, anal anteposition, sacrococcygeal dimple Moderate mental retardation , seizures, facial dysmorphism, fingers hyperlaxity
			b) inherited rearrangement group
			Case	Karyotype	Rearranged region	Inheritance	Size Mb	Phenotype
			9*	46,XY,t(2;6)(q36;q26)pat	del(6)(q24.2q24.3)	pat	1.21	Autistic troubles
			31*	46,XY,inv(4)(p13q22)pat	del(15)(q21.3q21.3)	pat	0.08	Mild mental retardation, seizures, growth retardation, facial dysmophism, brachymesophalangia
			40	46,XX,inv(1)(p21q13)mat	del(1)(p21.2p21.2)	dn	1.23	Severe mental retardation, microcephaly, facial dysmorphism
			45	46,XX,ins(7;4)(q31;q27q32)mat	del(4)(q31.3q32.1)	dn	4.03	Moderate mental retardation, seizures, scoliosis

Transloc: translocation; Inv: inversion: CCR: complex chromosomal rearrangement; dn: de novo; pat: paternal; mat: maternal; Mb: megabases Patients carrying a deletion unrelated to the balanced rearrangement breakpoint are marked by an asterix.

Table 3 :

 3 Review of the litterature and comparison with the present study

Gribble et al.[10] De Gregori et al.[4] Baptista et al.[2]

	Table(s)
					Present study
	Array	BAC/PAC	Oligonucleotides	BAC/PAC	Oligonucleotides
	Resolution	3,500 clones	44K/244K	30,000 clones	44K/244K
	Rearrangements	t/CCR	t/CCR	t	t/inv/CCR
	de novo /inherited	de novo	de novo	de novo	de novo	inherited
	Number of patients	10	59	14	33	14
	Rate imbalance	50% (5/10)	45.7% (24/59)	28.6 %(4/14)	48.5 % (16/33)	28.6% (4/14)
	Imbalance size (Mb)	2.2-6.2	0.5-8.4	0.17-2.5	0.06-15.37	0.08-3.64
	Imbalance at distance from breakpoint	60% (3/5)	41.6% (10/24)	25% (1/4)	56.2% (9/16)	50% (2/4)
	t: translocation; CCR: complex chromosomal rearrangement; inv: inversion

inserm-00405484, version 1 -25 Aug 2009

Acknowledgements:

We thank the family members for their continued interest and cooperation.

inserm-00405484, version 1 -25 Aug 2009

This works was partially supported with grants of the University Claude Bernard Lyon 1, faculté Lyon Nord and the Hospices Civils de Lyon.

We thank Dr Delphine Maucort-Boulch (Service de Biostatistiques, Hospices Civils de Lyon) for her help in statistical analyses.

We thank the DHOS (Direction de l'Hospitalisation et de l'Organisation des Soins) for their support in the development of several array CGH platforms in France.

inserm-00405484, version 1 -25 Aug 2009

WEB RESSOURCES Database of Genomic Variants: http://projects.tcag.ca/variation/ UCSC Genome Bioinformatics: http://genome.ucsc.edu/ Ensembl: http://www.ensembl.org/index.html OMIM: http://www.ncbi.nlm.nih.gov/sites/entrez?db=omim


A Yassin
email: aliyassin@etu.u-bourgogne.fr

H Cherifi

H Seba

O Togni

Keywords: Complex Networks, Backbone Filtering Techniques, Network Compression, Graph Summarization, Sparsification

Filtering Real World Networks: A Correlation Analysis of Statistical Backbone Techniques

Ali Yassin • Hocine Cherifi • Hamida Seba • Olivier Togni Received: date / Accepted: date Abstract Networks are an invaluable tool for representing and understanding complex systems. They offer a wide range of applications, including identifying crucial nodes, uncovering communities, and exploring network formation. However, when dealing with large networks, the computational challenge can be overwhelming. Fortunately, researchers have developed several techniques to address this issue by reducing network size while preserving its fundamental properties [1][2][START_REF] Ghalmane | 9th International Conference on Complex Networks and Their Applications[END_REF][START_REF] Gemmetto | [END_REF][START_REF] Ghalmane | [END_REF][START_REF] Rajeh | Network Science: 7th International Winter Conference, NetSci-X 2022[END_REF][START_REF] Yassin | IEEE Workshop on Complexity in Engineering (COMPENG)[END_REF][START_REF] Yassin | Complex Networks and Their Applications XI: Proceedings of The Eleventh International Conference on Complex Networks and their Applications: COMPLEX NETWORKS[END_REF][START_REF] Dai | [END_REF] . To achieve this goal, two main approaches have emerged: structural and statistical methods. Structural methods aim to keep a set of topological features of the network while reducing its size. In contrast, statistical methods eliminate noise by filtering out nodes or links that could obscure the network's structure, utilizing advanced statistical models.

In a previous work [START_REF] Yassin | Air transport network: A comparison of statistical backbone filtering techniques[END_REF] we compared a set of seven statistical backbone filtering techniques in the World Air Transportation network. Results show that the Marginal Likelihood Filter, Disparity Filter, and LANS Filter give more importance to high-weight edges. The other techniques emphasize both small and high-weighted edges.

This study extends the previous research on seven statistical filtering techniques, namely Disparity, Polya Urn, Noise Corrected, Marginal Likelihood, LANS, ECM, and GloSS filters, through the analysis of 39 real-world networks of diverse origins. These networks range in size from 18 to 13,000 nodes and include character, web, biological, economic, infrastructural, and offline/online social networks. In the first experiment, we aim to evaluate and compare the similarities between the seven statistical filtering techniques. Each method assigns a probability value, called a p-value, to each edge. To compare the methods, we use these p-values to conduct correlation analysis. Specifically, we compute the Pearson correlation between each pair of techniques' p-value edges. However, it is important to note that Pearson correlation examines linear relationships, whereas Jaccard similarity compares the similarities of two sets. Therefore, we use Jaccard similarity to compare the fraction of shared edges in each backbone. In a second experiment, we investigate the relationship between edge significance and edge properties. To do this, we compute the Pearson correlation between the p-values and edge properties, including weight, edge degree, and edge betweenness. The heatmaps present the mean and standard deviation of Pearson correlation between filtering technique pairs across all networks. The couples (LANS, Disparity filter) and (Noise Corrected, ECM ) are well correlated (0.8). Conversely, the Polya Urn filter does not exhibit a noticeable correlation with any other filtering method. The standard deviation heat map shows a low standard deviation validating these findings.

The middle graphs illustrate the typical behaviors of how the mean Jaccard score changes as a function of the top fraction of edges sorted by various backbone filtering techniques. The top left panel shows a low Jaccard score between the Polya Urn filter and the Noise Corrected filter. The other techniques also have a low Jaccard score between the Polya Urn filter. The top right panel shows that the GloSS filter shares at least 20% of its edges with the Marginal Likelihood filter. The other techniques have the same behavior as the Marginal Likelihood filter with the GloSS filter except for the Polya Urn filter. The bottom right panel shows that the set of edges obtained by the Disparity filter shares on average at least 50% of its edges with the LANS filter. The ECM Filter and Marginal Likelihood Filter (ECM-MLF) and ECM Filter and Noise Corrected Filter (ECM-NC) behave similarly. Finally, in the bottom left panel the set of edges obtained by the Marginal Likelihood filter shares on average at least 70% of its edges with the Noise Corrected filter. On the other hand, the couples DF-NC, DF-ECM, DF-MLF, LANS-ECM, LANS-NC, and LANS-MLF behave the same, sharing at least around 30% of the edges. However, they have a high standard deviation.

The boxplots illustrate the Pearson correlation coefficient between edge pvalues and edge weights, degrees, and betweenness across all networks. Results indicate a greater demonstration of the distinct behavior of the Polya Urn filter. The edge p-values were found to be uncorrelated with edge weights, degree, and betweenness, with a very low standard deviation. In contrast, the top panel shows that the edge p-values obtained through the Disparity filter and Marginal Likelihood filter were correlated with weights, with average correlation higher than 0.6. This indicates that these techniques prioritize edges with high weights. In the middle panel, the Noise Corrected filter and ECM filter have an average correlation higher than 0.6. This means that these methods give importance to edges that connect hubs, as these edges have a high edge degree, which is used indirectly by these methods to determine edge significance. Finally, the bottom panel shows that the edge p-values from all techniques have no correlation with edge betweenness, indicating that none of the methods prioritize edges that play a significant role in communication between nodes through the shortest paths.

In conclusion, correlation analysis is crucial in highlighting similarities and differences between backbone edge filtering techniques, identifying areas for improvement, and advancing knowledge in this field. This study can help to identify areas where improvements can be made in the development of new techniques or in the refinement of existing ones.

  Fig 1 illustrates these results.

Fig. 1

 1 Fig. 1 At the left, the mean and standard deviation heatmap of Pearson Correlation between pairs of filtering techniques p-values across all networks. In the middle the typical behaviors of the mean Jaccard score between the set of edges of pairs of different filtering techniques as a function of fraction of edges preserved across all networks. In the right, the boxplots of Pearson correlation coefficient between edge p-values and edge weights, degrees, and betweenness across all networks. The MLF is the Marginal Likelihood Filter, DF is the Disparity Filter, LANS is the Local Adaptive Network Sparsification, PF is the Polya Urn Filter, NC is the Noise Corrected Filter, and GloSS is Global Statistical Significance Filter. Note that we took the absolute value of the Pearson correlation.

This material is based upon work supported by the Agence Nationale de Recherche under grant ANR-20-CE23-0002.