Khaoula Rochdi
email: khaoula.rochdi-etu@etu.univh2c.ma

Mathieu Cerino

Nathalie Da Silva

Valérie Delague

Aymane Bouzidi

Halima Nahili

Ghizlane Zouiri

Yamna Kriouile

Svetlana Gorokhova

Marc Bartoli

Valerie Delague

Rachid Saïle

Abdelhamid Barakat

Martin Krahn

Identification of novel mutations by targeted NGS in Moroccan families clinically diagnosed with a neuromuscular disorder

Keywords:

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Introduction

Neuromuscular disorders (NMD) as a group, encompass a wide range of diseases that affect peripheral nerves or muscle [START_REF] Morrison | Neuromuscular diseases[END_REF], they are linked by anatomy, with overlapping but distinct phenotypes, as well as different pathogenic mechanisms, clinical expression, and disease progression [START_REF] Bhatt | The Epidemiology of Neuromuscular Diseases[END_REF]. Symptoms vary depending on the speed of onset of the respiratory muscle weakness [START_REF] Hutchinson | Neuromuscular disease and respiratory failure[END_REF]. The position of damage can be in the cell bodies, neuromuscular junction, axons, Schwann cells, muscle, or any combination of these sections [START_REF] Morrison | Neuromuscular diseases[END_REF]. NMD are difficult to diagnose due to the abundance of possible sites of injury. Clinical presentation of NMD differs largely; many diseases of the peripheral nervous system (PNS) will manifest with muscle atrophy, distal sensory loss, and/or reduced tendon reflexes. Most NMD are hereditary [START_REF] Laing | Genetics of neuromuscular disorders[END_REF], and only a few mutations have been identified in this context, especially in northern African countries, where inbreeding is at a high rate and access to diagnosis and health care is limited [START_REF] Khaoula | First characterization of congenital myasthenic syndrome type 5 in North Africa[END_REF][START_REF] Al-Gazali | Genetic disorders in the Arab world[END_REF]. In the following sections we will detail the two hereditary diseases found in our patients previously diagnosed with muscle damage suggestive of a neuromuscular disease.

Marinesco-Sjögren syndrome (MSS) (MIM# 248800)

It's a rare autosomal recessive multisystem disorder. Cerebellar ataxia, bilateral cataracts, hypergonadotropic hypogonadism, mild to moderate mental retardation, chronic myopathy, short stature, and skeletal abnormalities comprise the cardinal features of the disease. Mutations in the SIL1 gene on chromosome 5q31, which encodes an endoplasmic reticulum resident co-chaperone, were identified as the principal cause of Marinesco-Sjögren syndrome [START_REF] Krieger | SIL1 mutations and clinical spectrum in patients with Marinesco-Sjögren syndrome[END_REF][START_REF] Yis | Heterogeneity of Marinesco-Sjögren syndrome: report of two cases[END_REF]. SIL1 (also called BAP) encodes a nucleotide exchange factor for the protein chaperone HSPA5, which is a key regulator of the main functions of the endoplasmic reticulum. The main endoplasmic reticulum (ER) chaperone and the primary sensor of ER stress is SIL1 a nucleotide exchange factor for BiP. In the endoplasmic reticulum cell membrane and secretory proteins are synthesized and a network of molecular chaperones and folding factors assure correct protein folding and export to post-ER compartments. in case of rupture of this process, the accumulation of unfolded/ misfolded proteins, ER stress, and activation of the unfolded protein response (UPR) will take place, a complex signaling pathway aimed at restoring ER homeostasis, whose failure eventually leads to cell death [START_REF] Chiesa | Protein misfolding diseases -The rare case of Marinesco-Sjögren syndrome[END_REF][START_REF] De Michele | Other autosomal recessive and childhood ataxias[END_REF].

Autosomal recessive hereditary Spastic Paraplegia (HSP) (MIM# 611026)

The disease describes a heterogeneous group of 27 autosomal recessive neurodegenerative disorders, in which the predominant clinical features are a lower extremity weakness and spasticity [START_REF] Fink | Hereditary spastic paraplegia: clinico-pathologic features and emerging molecular mechanisms[END_REF][START_REF] Aguirre-Rodríguez | Novel FA2H mutation in a girl with familial spastic paraplegia[END_REF]. The genetics of HSPs is complex and has been reported with all modes of inheritance pattern, the autosomal recessive form of diseases are often common in consanguineous populations such as Middle East and North African population, with a prevalence of 0.6/100,000 identified in the Norway population. Thus, a remarkable prevalence was found in the Tunisian population is 5.75/100,000 the overall prevalence of all HSPs ranges between 4,3 and 9.8/100,000 [START_REF] Aguirre-Rodríguez | Novel FA2H mutation in a girl with familial spastic paraplegia[END_REF][START_REF] Finsterer | Hereditary spastic paraplegias with autosomal dominant, recessive, X-linked, or maternal trait of inheritance[END_REF]. The most common autosomal recessive HSP identified is the SPG11 subtype associated with mutation in the SPG11, followed by SPG15 associated to mutations in the ZFYVE26. One more kind of connection among autosomal-recessive HSPs is exemplified by studies recognizing changes in the FA2H gene at 16q21-q23 chromosome, across a disorder range including SPG35, leukodystrophy, and neurodegeneration with brain iron aggregation (NBIA) [START_REF] Blackstone | Hereditary spastic paraplegia[END_REF]. SPG35 is defined by childhood-onset (6-11 years) and variable neurologic features in which the cardinal pathological feature is upper motor neuron degeneration leading to progressive spasticity and weakness of the lower limbs, with extrapyramidal features. Other variable neurologic features are dystonia, optic atrophy, and seizures may also occur [START_REF] Fink | Hereditary spastic paraplegia: clinico-pathologic features and emerging molecular mechanisms[END_REF][START_REF] Mari | Clinical and neuroimaging features of autosomal recessive spastic paraplegia 35 (SPG35): case reports, new mutations, and brief literature review[END_REF][START_REF] Dick | Mutation of FA2H underlies a complicated form of hereditary spastic paraplegia (SPG35)[END_REF]. 2-Hydroxy fatty acids (hFA) have been found present in additional tissues and cell types such as tumors. hFA are necessary components of a subset of mammalian sphingolipids. Their presence in sphingolipids is described in the nervous system, epidermis, and kidney. However, Biosynthesis of hFA-sphingolipids requires fatty acid 2-hydroxylase, This protein is an NADPH-dependent monooxygenase that catalyzes the synthesis of free fatty acids to 2-hydroxy fatty acids. These are then incorporated into myelin galactolipids containing hydroxy fatty acid as the N-acyl chain, which helps maintain the myelin sheath [START_REF] Blackstone | Hereditary spastic paraplegia[END_REF][START_REF] Hama | Fatty Acid 2-Hydroxylation in Mammalian Sphingolipid Biology[END_REF].

In the present study, Next-Generation sequencing allowed us to identify variants associated with rare neuromuscular disorders in a 2 Moroccan family. To this date 24 pathogenic and likely pathogenic SIL1 variants have been reported in LOVD and Clinvar. While, only 22 pathogenic and likely pathogenic FA2H variants were reported in the same specific locus databases. The rarity of the identified cases and the diversity of the clinical characteristics of these diseases constitutes a barrier in terms of identification and harmonization of the phenotypic spectrum, from where the need for further exploration, essentially in the North African and Middle Eastern populations having a rather important consanguinity rate.

Material and methods

Ethics approval

The study was approved by the ethics committee for biomedical research in Rabat and written informed consent was collected from all volunteers.

Molecular genetic analysis

Genomic DNA was extracted from peripheral leukocytes with Qiagen Kit, QIAamp DNA Blood Mini Kits. The enriched libraries utilizing the HaloPlex Target (Agilent, CA, USA) Enrichment System for Illumina sequencing later sequenced using Next Generation Sequencing (NGS). The Panel gene approach was conducted using the NextSeq 550 (Illumina, CA, USA).

Data analysis

Therefore, targeted NGS sequencing was performed for 306 neuromuscular genes [START_REF] Gorokhova | Comparing targeted exome and whole exome approaches for genetic diagnosis of neuromuscular disorders[END_REF]. The list must essentially cover the initial "Limb-Girdle Muscular Dystrophies" clinical entry-diagnosis group defined by the FILNEMUS network guidelines except for a few newly involved genes added very recently to the list of the corresponding genes [START_REF] Krahn | A National French consensus on gene lists for the diagnosis of myopathies using next-generation sequencing[END_REF]. Clean reads were aligned to UCSC hg19 human reference genome. Annotated VCF files including all variants were analyzed to prioritize mutations using VarAFT software. VarAFT Interactive filtration features provide the progressive reduction of the list of candidate mutations by combining the various annotations [START_REF] Desvignes | VarAFT: a variant annotation and filtration system for human next generation sequencing data[END_REF]. The identification of the disease-causing mutations from the 2 index patients VCF corresponding to diseases transmitted in an autosomal recessive pattern. It was performed in many steps using data from the variant annotations and the phenotype layers, excluding all variants types except splicing and exonic, removing variant with a Minor Allele Frequency (MAF) > 0.01 in the GnomAD database [START_REF] Karczewski | The mutational constraint spectrum quantified from variation in 141,456 humans[END_REF], polymorphism, and probable polymorphism were also excluded. The remaining variants were classified according to the ACMG classification system [START_REF] Richards | Standards and Guidelines for the Interpretation of Sequence Variants: A Joint Consensus Recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology[END_REF]. Following gene assessment and variant classification according to the American College of Medical Genetics and Genomics (ACMG) guidance for variant classification, integration of results with patients' phenotype was performed to provide a clinically relevant interpretation of the findings [START_REF] Richards | Standards and Guidelines for the Interpretation of Sequence Variants: A Joint Consensus Recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology[END_REF].

Sanger verification

Exon 6 and 4 of the SIL1 and FA2H genes respectively, were amplified by a polymerase chain reaction from the DNAs of affected and unaffected individuals of families, of each index patient. The amplicons were subsequently sequenced by the Sanger method using ABI Big-Dye terminator v3.1 sequencing + reaction Kit (Applied Biosystems) and analyzed on an ABI 3130 Genetic analyzer (Applied Biosystems). All the sequences were analyzed with the ChromasPro software.

Results

The sequence analysis of the SIL1 gene revealed the novel mutation NM_001037633: c.453 + 5G > A (hg19) chromosome5: 138378304, associated with Marinesco-Sjogren Syndrome for the first patient. All the mutations reported in the literature and responsible for the same disease are gathered in Table 1. Thus, the homozygous status of the mutation that we have identified is consistent with the parental consanguinity. This variant may most probably affect splicing, as predicted by Human Splice Finder (HSF) [START_REF] Desmet | Human Splicing Finder: an online bioinformatics tool to predict splicing signals[END_REF]. Also, the patient phenotype observed sticks with the clinical features described in OMIM (# 248800).

Moreover, the second patient harbored the variant NM_024306: 2). The two variants reported in this study were novel and never have been reported in any locus databases, and several prediction programs were used to assess the pathogenicity (SIFT [START_REF] Ng | SIFT: predicting amino acid changes that affect protein function[END_REF], REVEL [START_REF] Ioannidis | REVEL: An Ensemble Method for Predicting the Pathogenicity of Rare Missense Variants[END_REF], MetaLR [START_REF] Dong | Comparison and integration of deleteriousness prediction methods for nonsynonymous SNVs in whole exome sequencing studies[END_REF]), the novel missense variants were found to have severe predicted pathogenic effects (Table 3), regarding the Human Splice Finder (HSF [START_REF] Desmet | Human Splicing Finder: an online bioinformatics tool to predict splicing signals[END_REF])) predictions, the first variant in the SIL1 was considered to have an effect of alteration of the WT donor site which is most probably affecting splicing, the same program predicted an alteration of the exonic splicing enhancer site and a potential alteration of splicing for the second FA2H variant. In addition, according to the ACMG [START_REF] Richards | Standards and Guidelines for the Interpretation of Sequence Variants: A Joint Consensus Recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology[END_REF] classification, the SIL1 variant has been predicted as uncertain significance, studies have shown that this type of mutation is consistent with splicing errors, and often leads to open reading frame alterations due mainly to incorrect deletion of introns [START_REF] Anna | Splicing mutations in human genetic disorders: examples, detection, and confirmation[END_REF]. A previous study found this type of intronic splicing mutations in individuals with MSS, which result from a disruption of donor splice sites, the same study proved that SIL1 mutations are the main cause of MSS [START_REF] Senderek | Mutations in SIL1 cause Marinesco-Sjögren syndrome, a cerebellar ataxia with cataract and myopathy[END_REF]. As well, the FA2H variant reported in this study has a pathogenic verdict according to the ACMG [START_REF] Richards | Standards and Guidelines for the Interpretation of Sequence Variants: A Joint Consensus Recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology[END_REF] classification, a study also reported the involvement of FA2H loss-of-function mutations in three Israeli families [START_REF] Dick | Mutation of FA2H underlies a complicated form of hereditary spastic paraplegia (SPG35)[END_REF]. All of the above evidence supported the involvement of these variants in the diseases diagnosed in both patients, including predictions of pathogenicity, the absence of these variants from generic databases (1000G and Gno-mAD), the similarity of the phenotype in the patient to phenotypes described in the literature, and the potential impact on splice sites. All variants identified by the Illumina NextSeq 550 sequencer were confirmed by Sanger sequencing (Fig. 1). After family segregation analyses, the first patient harboring mutation in the SIL1 gene, the exon 6 mutation was found in a heterozygous state in a non-affected brother. Moreover, the mutation was found in the parents as a heterozygous state (Fig. 1.A). The second patient carried the novel homozygous frameshift deletion in the FA2H gene, the family segregation allowed the identification of the variant in a heterozygous state in the parents (Fig. 1.B).

Discussion

In this study, we identified another example of an instance where NGS using a panel approach established the genetic cause of disease in two recessive families (Table 4). Using a panel approach, we identified two novel mutations. The first mutation was responsible for Marinesco-Sjogren syndrome, the second for Autosomal Recessive Spastic Paraplegia 35 (SPG35), these variants have never been reported neither in the gnomAD database, or scientific literature. The clinical phenotype helped to lead the diagnosis, the differential diagnosis for NMD broad. Hence, we opted to use the massive parallel sequencing using the panel approach of 306 neuromuscular genes to identify the specific genetic defects leading to the diseases. The VarAFT software was used to prioritize causative variants, using filters with different annotation and prediction tools, as well as the patient's phenotype, we only kept the exonic and splicing variants and the variants with an allelic frequency lower than 1% in the gnomAD database. In addition, we excluded variants suspected to be polymorphisms or likely polymorphisms. Biocomputational analyses of these mutations did not spare the pathogenic status of the variants, using the different prediction tools, as well as the ACMG classification and the HSF program prediction allowed the support of the involvement of these variants in the diseases found in the patients. After using these different levels of filtering, we kept the variants that correlate with the patient's phenotypes for further molecular analysis.

The clinical diagnosis of the first patient presented neonatal hypotonia, the 8-year-old patient had first-degree consanguineous parents, as well as walking deficit. The patient is described with clinical and pathological features of a neuromuscular disorder, accompanied by cerebellar dysfunction, possibly the result of cerebellar atrophy, a myogenic involvement has also been mentioned in this context. The patient does not fulfill the clinical diagnostic criteria for MSS, as myopathy and cataracts are absent in him. In addition, the disease was present earlier in the child. As well, SIL1 mutations were reported to be

4.2933

The table provides information about the three Index Cases (ICs) and prediction by several tools. SNV: Single nucleotide Variant. NA: Not available (SIFT, REVEL, DANN do not provide prediction for variants creating a stop or a frameshift). ACMG [START_REF]Standards and Guidelines for the Interpretation of Sequence Variants: A Joint Consensus Recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology[END_REF]: American College of Medical Genetics SIFT [START_REF] Ng | SIFT: predicting amino acid changes that affect protein function[END_REF]: Sort Intolerant From Tolerant; REVEL [START_REF] Ioannidis | REVEL: An Ensemble Method for Predicting the Pathogenicity of Rare Missense Variants[END_REF]: Rare Exome Variant Ensemble Learner; DANN [START_REF] Quang | DANN: a deep learning approach for annotating the pathogenicity of genetic variants[END_REF]: Deleterious Annotation of genetic variants using Neural Networks, HSF [START_REF] Dong | Comparison and integration of deleteriousness prediction methods for nonsynonymous SNVs in whole exome sequencing studies[END_REF]: Human Splicing Finder; GERP [START_REF] Cooper | Single-nucleotide evolutionary constraint scores highlight disease-causing mutations[END_REF]: Genomic Evolutionary Rate Profiling. rare (2.7 %) in MSS patients [START_REF] Krieger | SIL1 mutations and clinical spectrum in patients with Marinesco-Sjögren syndrome[END_REF]. The patient harbored a novel mutation in the SIL1 gene (Nucleotide Exchange Factor protein; *608005), associated with the Marinesco-Sjogren syndrome. Thus, the parent's consanguinity demonstrates the homozygous status of this variant. Moreover, the Sanger verification demonstrated the heterozygous status of this variant in the parent's analysis. In addition, family segregation presented a heterozygous status of the variant in the patient's brother. Therefore, we suggest that screening of SIL1 mutations should be considered in patients with neonatal hypotonia, cerebellar atrophy, and myogenic damage, even without other associated features. This second novel mutation harbored by the second patient in the FA2H (Fatty acid 2-hydroxylase *611026) gene, the frameshift mutation seems to be associated with autosomal recessive Spastic Paraplegia 35 (SPG35). The 4-years-old patient diagnosis presented normal brain CT, besides early welding of inters temporoparietal and metopic sites, epileptic seizures were also present. The available phenotype correlated with the clinical features already reported in the databases, in addition to the bioinformatics prioritization of causative variants, lead us to conclude that the variant was linked with the Spastic Paraplegia 35 (SPG35) in an autosomal recessive mode of inheritance. Molecular analysis of the various relatives made it possible to confirm the homozygous status of the mutation found in the patient, explained by the consanguinity of the parents, as well as the heterozygous status of this mutation in the latter. Generally these diseases represent involuntary cramps (dystonia), in association or not with problems in coordination and balance (ataxia). The evolution of regression of movements is progressive and can eventually require in some cases the wheelchair assistance. These muscular impairments, as well as the age of onset of the disease, suggest at first a neuromuscular disease diagnosis. The new generation sequencing and with the use of the gene panel approach, has allowed to reveal an impairment of the nervous system (neurodegeneration), the condition belongs rather to the class of diseases called neurodegeneration with brain iron accumulation (NBIA).

Conclusion

These results should be taken into consideration in order to expand scientific research to properly illustrate these diseases and improve the phenotypic barriers of such conditions that may have symptoms or phenotypes that intersect. Finally, these rare conditions could lead to a false diagnosis when they are underdiagnosed or underrated, which causes a misidentification of the causative disease. One of the major problems with this type of rare diseases is that the phenotypic spectrum as well as the age of onset, which vary considerably from a case to another. Increasing awareness of this clinically and genetically diverse group of diseases is particularly important for patients and researchers, as progress in this field is rapid with the advent of next-generation sequencing. Thus further improvement and exploration in this area will open up promising prospects for treatment and harmonization of diagnosis, especially in populations with a high rate of inbreeding that leads to the diversification of inherited genetic diseases.

CRediT authorship contribution statement

Declaration of Competing Interest

The authors declare that they have no known competing financial The table provides several information about the disorder, Protein affected, phenotype and prevalence for each Index Cade (IC). AR: Autosomal recessive.

interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .

 1 Fig. 1. Pedigree and Electropherogram corresponding to the Sanger sequencing of the Index Cases (IC), and members of the families. (A), corresponds to pedigree the electropherogram of the IC1 family. The parents, brother, and the patient were analyzed in this case. (B), corresponds to the pedigree and Electropherogram of the IC2 family. The patient and his parents were analyzed.

Khaoula Rochdi:

  Methodology, Software, Writingoriginal draft. Mathieu Cerino: Methodology, Software, Validation, Writingreview & editing. Nathalie Da Silva: Methodology. Valerie Delague: Conceptualization, Validation, Resources. Aymane Bouzidi: Methodology. Halima Nahili: Investigation. Ghizlane Zouiri: Investigation. Yamna Kriouile: Investigation. Svetlana Gorokhova: Validation, Writingreview & editing. Marc Bartoli: Conceptualization, Validation, Resources, Writingreview & editing, Supervision. Rachid Saïle: Conceptualization, Validation, Writingreview & editing, Supervision. Abdelhamid Barakat: Conceptualization, Validation, Writingreview & editing, Supervision. Martin Krahn: Conceptualization, Validation, Resources, Writingreview & editing, Supervision.

Table 1

 1 SIL1 mutations in patients with Marinesco-Sjögren syndrome autosomal recessive, identified in this study and earlier reports. FA2H mutation leading to a frameshift of the reading frame. In the literature, only few cases have been reported with HSP type 35 (Table

	Nucleotide change	Effect on coding sequence

Table 2

 2 FA2H mutations in patients with Hereditary spastic paraplegias (HSPs) type 35 (SPG35), identified in this study and earlier reports.

	Nucleotide change	Effect on coding sequence	Number of patients	Geographic origin	Reference
	c.130C > T	p. Pro44Ser	1	Turkey	[42]
	c.388C > T / c.506 + 6C > G	p.L130F / affect the splicing of the FA2H mRNA	1	Chinese	[43]
	c.230 T > G	p.Leu77Arg	1	Chinese	[43]
	C.688G > A; c.968C > A ; c.976G > A	p.E230K ; p.P323Q ; p.G326S	2	Chinese	[44]
	c.786 + 1G > A	Skipping of exons 5 and 6	2	Arab-Muslim	[45]
	c.103G > T	p.D35Y	1	Arab-Muslim	[45]
	c.703C > T	p.R235C	1	Omani	[16,46]
	c.157_174 del	p.R53_I58del	1	Pakistani	[16,46]
	c.460C > T	p.R154C	2	Italian/ NR	[47,48]
	c.509_510delAC	p.Y170X	1	Albanian	[47]
	c.270 + 3A > T	Loss of exons 2-7	-	NR	[49]
	c.707 T > C	p. F236S	-	NR	[50]
	c.209C > T; c.968C > T	p.S70L; p.P323L	-	Filipino/ Vietnamese	[51]
	c.509A > G	Y170C	-	NR	[52]
	c.527G > A	p.Trp176*	2	Serbian / NR	[5348]
	c.131C > A	p.Pro44Gln	2	German / NR	[5348]
	c.133G > T	p.Gly45Trp	2	German/ NR	[5348]
	c.785A > C	p.Lys262Thr	2	Spanish / NR	[5348]
	C.265C > T	p.Q89*	1	Egypt	[54]
	chr16:74760208C > G	p.Trp176Cys	1	Sudan	[54]
	chr16:74750478C > A	p.Arg269Leu	1	Yemen	[54]
	c.169_170insGCGGGCCAGG	p.Asp57Glyfs*66	1	NR	[55]
	c.117C > A	p.Phe39Leu
	c.620C > T ; c.460C > T	p.T207M ; p.R154C	1	Italy/UK	[56]
	c.1051A > C ; c.486G > C	p.S351R; p.E162D	1	UK	[56]
	c.798C > G ; c.782dupA	p.D266E ; p.H261Qfs*	1	Ireland/UK	[56]
	c.157_174del	p.Arg53_Ile58del	1	Pakistan	[56]
	c.509_510delAC	p.Y170X	4	Montenegro/ Albanian/NR	[47,48,57]
	c.160_169dup	p.D57Gfs*66	1	Turkey	[58]
	c.21delC	p.A8Pfs*91	1	NR	[48]
	c.160_169del GCGGGCCAGG	p.A54Tfs*42	2	NR	[48]
	c.205C > T	p.H69Y	1	NR	[48]
	c.232G > A	p.E78K	2	NR	[48]
	c.262G > T	p.E88*	1	NR	[48]
	c.443C > T	p.P148L	1	NR	[48]
	c.503_506del TCTG	p.V168Gfs*72	1	NR	[48]
	c.704G > A	p.R235H	2	NR	[48]
	c.859 T > C	p.C287R	1	NR	[48]
	c.908G > T	p.G303V	1	NR	[48]
	c.956A > G	p.H319R	1	NR	[48]
	c.968C > T	p.P323L	2	NR	[48]
	c.805C > T ; c.1501A > G	p.R269C ; p.S351G	1	Italian	[15]
	c.193C > T	p.P65S	1	NR	[15]
	c.1055C > T ; [c.340_363del24][c.363 + 1_8del8]	p.T352I	1	Brazilian	[15]
	c.445G > T ; c.780C > A	p.Val149Leu; p.His260Gln	1	Japanese	[59]
	c.806G > A	p.R269H	2	Moroccan	[60]
	c.1006C > A	p.H336N	3	Saudi Arabia	[60]
	c.130C > T	p.Pro44Ser	1	Czech	[61]
	c.137G > A	p.Gly46Asp	1	Moroccan	[62]
	c.101A > G ; c.620C > T	p.Tyr34Cys ; p.Thr207Met	1	NR	[62]
	c.677G > A	p.Trp226*	1	NR	[62]
	c.581delG	G194Afs*47	1	Moroccan	This study

Table 3

 3 Mutational data of the two patients.

	Patient	RefSeq Transcript	HGVS	HGVS Protein	Variant	Location	Coding	ACMG	SIFT	REVEL	DANN	HSF[26]	GERP
			coding		type		impact	classification	[24]	[25]	[65]		[66]
					[63]		[63]	[64]
	IC1	NM_001037633.1	c.453 +	-	SNV	intron 5	-	Uncertain	NA	NA	0.7779	Alteration	4.11
			5G > A			of 9		Significance				of the WT
						position 5						donor site,
						of 15,627						Most
						(splicing,						probably
						intronic)						affecting
												splicing.
	IC2	NM_024306.4	c.581delG	G194Afs*47 (p.	Deletion	exon 4 of	Frameshift	Pathogenic	NA	NA	NA	Alteration
				Gly194AlafsTer47)		7 position						of an
						75 of 107						exonic
						(coding,						ESE site.
						NMD)						Potential
												alteration
												of
												splicing.

Table 4

 4 Disorders data of the two Index Cases.

	Patient	Disorder[67]	Protein name	Locus/	Cellular functions	Disease clinical features	Inheritance	Prevalence	Treatment[69]
				Gene	[68]	[67]		[69]
	IC1	Marinesco-Sjogren	SIL1	5q31.2	SIL1 is a resident	Characterized primarily	AR	Prevalence:	Treatment is
		syndrome	Nucleotide		endoplasmic	by congenital cataracts,		<1/1000000	symptomatic.
		# 248,800	Exchange Factor		reticulum (ER)	cerebellar ataxia,		(Worldwide)	Cataracts often
			OMIM: *608005		glycoprotein that	progressive muscle			require surgical
			UniProtKB:		interacts with the	weakness due to			removal to preserve
			Q9H173		ATPase domain of	myopathy, and delayed			vision. Hormonal
			Ensembl:		BIP (HSPA5;	psychomotor			replacement therapy
			ENSG00000120725		138120) and	development. Other			may be needed if
					enhances	features include short			hypogonadism is
					nucleotide	stature,			present. Physical and
					exchange.	hypergonadotropic			occupational therapy
						hypogonadism, and			are crucial.
						skeletal deformities due
						to muscle weakness.
	IC2	-Spastic Paraplegia	FA2H	16q23.1	Myelin lipid	seizures, ataxia, urgency	AR	Prevalence:	At the present time,
		35, Autosomal	Fatty acid 2-		hydroxylation	of micturition		<1/1000000	therapy is
		Recessive (SPG35)	hydroxylase					(Worldwide)	predominantly
		-Fatty Acid	OMIM : *611026						symptomatic
		Hydroxylase-	UniProtKB: Q7L5A8						Physical therapy,
		Associated	Ensembl:						stretching, and
		Neurodegeneration	ENSG00000103089						activity
		(FAHN)							are mainstays of
		# 612,319							treatment, seeking to
									maintain mobility
									and avoid
									complications from
									inactivity or falls

Acknowledgments

We thank the families and their relatives for participating in this study.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


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François Carpentier

Group 12 and 13 Metal-Alkenyl Promoted Generation of Long-Chain Branching in Metallocene-Based Polyethylene

In situ synthesis of topologically modified linear polyethylenes (PEs) using singlesite polymerization catalysis is a challenging task that enables the production of advanced materials with tailored properties. We describe here our investigations aimed at an efficient generation of long-chain branches (LCB) in linear PEs using discrete B-, Al-and Zn-alkenyl co-reagents in combination with homogeneous rac-{EBTHI}ZrCl 2 (1)/ or (nBuCp)ZrCl 2

(2)/MAO catalytic systems. As corroborated by extensive rheological studies and 13 C NMR spectroscopy, Al-and Zn-based reagents promote LCB formation via a two-step mechanism involving both vinylic group insertion and MZr transmetallation steps. In striking contrast, the B-alkenyl species was found to form hydrolytically stable B-centred cross-linked PE structures. The Mg-based reagent appeared to be reluctant towards MgZr transmetallation reaction, providing only the products of vinylic group insertion, which after hydrolysis afforded short-chain branched (SCB) PEs. The experimental observations were rationalized by DFT computations.

Introduction

The production of polyethylene (PE) with high molecular weight and narrow polydispersity has been largely enabled thanks to the development of single-site catalyst technology. [START_REF] Alt | Effect of the Nature of Metallocene Complexes of Group IV Metals on Their Performance in Catalytic Ethylene and Propylene Polymerization[END_REF] Although these characteristics confer excellent mechanical properties, such polymers suffer from poor processability due to their low elasticity and melt viscosity. Since the processing behaviour of PE is strongly dependent on its intrinsic properties such as molecular weight (M w ), polydispersity (M w /M n ) and, more generally, its molecular architecture (linear, branched or cross-linked), it can be improved by introducing long-chain branching (LCB) to the linear PE structures. [START_REF] Lai | Elastic substantially linear olefin polymers[END_REF][START_REF] Brant | M Long chain branched polymers and a process to make long chain branched polymers[END_REF][START_REF] Kim | Melt rheological and thermodynamic properties of polyethylene homopolymers and poly(ethylene/α-olefin) copolymers with respect to molecular composition and structure[END_REF] Several post-reactor technologies have been reported to produce LCBpolymers: high-energy electron beam irradiation, [START_REF] Rätzsch | Reaction mechanism to Long-Chain Branched PP[END_REF] peroxide curing [START_REF] Parent | Structure-rheology relationships of long-chain branched polypropylene: Comparative analysis of acrylic and allylic coagent chemistry[END_REF][START_REF] Wang | Chemical modification of polypropylene with peroxide/pentaerythritol triacrylate by reactive extrusion[END_REF][START_REF] Tian | The preparation and rheology characterization of long chain branching polypropylene[END_REF] and grafting. [START_REF] Lu | Synthesis of Long Chain Branched Polypropylene with Relatively Well-Defined Molecular Structure[END_REF] However, due to the radical mechanisms involved in these treatments, ample control over LCB formation appeared to be impossible, and polymers exhibiting complex structures are obtained in those cases. Also, in-reactor technologies have been developed including copolymerization of ethylene with either in situ-formed or previously isolated macromonomers [START_REF] Chum | Materials Properties Derived from INSITE Metallocene Catalysts[END_REF][START_REF] Weng | Synthesis of Long-Chain Branched Propylene Polymers via Macromonomer Incorporation[END_REF] or with a non-conjugated α,ω-diene. [START_REF] Kokko | Long-chain-branched polyethene by the copolymerization of ethene and nonconjugated α,ω-dienes[END_REF][START_REF] Pietikäinem | Copolymerization of ethylene and nonconjugated dienes with Cp 2 ZrCl 2 /MAO catalyst system[END_REF][START_REF] Pietikäinem | Copolymerization of ethylene and non-conjugated dienes with Cp 2 ZrCl 2 /MAO catalyst system: effect of polymerization temperature on the copolymer structure[END_REF][START_REF] Naga | Copolymerization of Ethylene and 1,7-Octadiene, 1,9-Decadiene with Zirconocene Catalysts[END_REF][START_REF] Williamson | Alternating Copolymers of Ethylene and Diolefins Containing Pendent Functional Groups[END_REF] For copolymerization techniques, only a limited number of catalysts have been found to efficiently generate and incorporate macromonomers. The second approach is limited by the rather scarce availability of α,ω-dienes and by the uneven distribution of LCB in the resulting polymers [START_REF] Das | Controlled Synthesis, Characterization, and Flow Properties of Ethylene-Diene Copolymers[END_REF].

In recent studies, the Al-alkenyl compound iBuAl(oct-7-en-1-yl) 2 (Al-1) [START_REF] Holtcamp | Aluminum alkyls with pendant olefins for polyolefin reactions[END_REF] has been successfully used as an LCB-promoter in the polymerization of ethylene catalyzed by homogeneous rac-{EBTHI}ZrCl 2 (Zr-1)/MAO and (nBuCp) 2 ZrCl 2 (Zr-2)/MAO or their heterogeneous MAO on silica-supported-Zr-1 or Zr-2/TIBAL versions (EBTHI = ethylenebis(tetrahydroindenyl)). [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF][START_REF] Santoro | Alkenyl-Induced Formation of Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using (nBuCp) 2 ZrCl 2 /MAO Systems: An Experimental and Theoretical Study[END_REF] Both experimental and computational techniques have identified the crucial role of Al-1 co-reagent in the generation of LCB. In particular, it has been corroborated that the two-step mechanism involves (1,2-) insertion of a pending oct-7-enyl moiety into the ZrC Polymeryl bond, followed by AlZr transmetallation, eventually generating a growing polymer side-chain (Scheme 1). On the contrary, (incidental or final) protonolysis of the intermediate species would lead to the formation of n-hexyl short-chain branches (SCB). Although the discrimination between LCB and SCB in the final polymer could not be performed by means of 13 C NMR spectroscopy, [START_REF] Stadler | Influence of Type and Content of Various Comonomers on Long-Chain Branching of Ethene/α-Olefin Copolymers[END_REF][START_REF] Stadler | Detecting very low levels of long-chain branching in metallocenecatalyzed polyethylenes[END_REF][START_REF] Takeh | Analytical Rheology of Metallocene-Catalyzed Polyethylenes[END_REF] the use of this Alvinyl transfer agent (AVTA) resulted in a marked change in the rheological behavior of the PEs, unambiguously consistent with LCB generation. Scheme 1. Proposed pathway involving transmetallation and vinylic insertion steps, and 13 C NMR spectroscopic characterisation of short-(SCB) and long-chain branching (LCB) obtained in the presence of Malkenyl co-reactants. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF] To the best of our knowledge, this methodology remains widely unexplored and the reports in the open literature concerning the use of either Al-based reagents or other Malkenyl compounds remain very scarce. [START_REF] Lee | Synthesis of Long-Chain Branched Polyolefins by Coordinative Chain Transfer Polymerization[END_REF][START_REF] López-Barrón | One-Pot Synthesis of High-Melt-Strength Isotactic Polypropylene Ionomers[END_REF] Herein, we report on the synthesis of LCB-PEs mediated by discrete B-, Al-, Mg-and Zn-alkenyl co-reagents, namely B(pent-4-enyl) 3 (B-2), Al(pent-4-enyl) 3 (Al-2), Mg(pent-4-enyl) 2 (Mg-2) and Zn(oct-7-enyl) 2 (Zn-1). The shorter alkenyl group (pent-4-enyl) was selected to allow for the unambiguous detection of LCB by 13 C NMR spectroscopy. In fact, the resonance for the tertiary carbon at the branching point of LCB and those of the pendant alkyl groups arising from the insertion/protonolysis of the co-reagents could be hence easily discriminated, which was not possible in prior investigations. Additional information concerning the level of branching/cross-linking of the PE samples was achieved by means of melt rheology analysis. In turn, B-2 proved to have a tremendous impact on the flow properties of the corresponding polymers.

Results and discussion

Synthesis of M-alkenyl reagents. Mg-, B-and Al-alkenyl reagents were prepared using modified literature protocols (Scheme 2). Zn(oct-7-enyl) 2 (Zn-1) was synthesised by chain-transfer from its parent boron analogue. [START_REF] Chen | Synthesis of bis(7-octenyl)zinc via heterogeneous Ni catalysts[END_REF] Mg(pent-4-enyl) 2 (Mg-2) and B(pent-4enyl) 3 (B-2) were synthesised from the corresponding Grignard reagent by displacement of the Schlenk equilibrium with excess 1,4-dioxane and Mg-to-B transmetallation, respectively. [START_REF] Belaid | Dialkenylmagnesium Compounds in Coordinative Chain Transfer Polymerization of Ethylene. Reversible Chain Transfer Agents and Tools To Probe Catalyst Selectivities toward Ring Formation[END_REF][START_REF] Lyle | The Preparation and Properties of a Series of Ethereal and Unsaturated Boranes[END_REF] Al(pent-4-enyl) 3 (Al-2) was obtained by chain-transfer from the parent B-2 onto trimethylaluminum. [START_REF] Koster | Organic Aluminum Heterocycles[END_REF][START_REF] Dolzine | Intramolecular Metal-Double Bond Interactions. VI. Metal--Electron Interactions Observed in Trialkenylaluminum and -Gallium Derivatives[END_REF] Scheme 2. Synthesis of putative LCB-promoting co-reagents B(pent-4-enyl) 3 (B-2), Al(pent-4-enyl) 3 (Al-2), Mg(pent-4-enyl) 2 (Mg-2) and Zn(oct-7-enyl) 2 (Zn-1).[2729]

Polymerization of ethylene catalyzed by homogeneous rac-{EBTHI}ZrCl 2 and

(nBuCp) 2 ZrCl 2 /MAO/M-alkenyl systems. Table 1 summarizes the ethylene polymerization experiments carried out using metallocene/MAO systems in the presence of the M-alkenyl coreagents. The Zr-based pre-catalysts reported in Chart 1, namely rac-ethylenebis (4,5,6,7-tetrahydro-1-indenyl)]zirconium dichloride (Zr-1) and bis(n-butylcyclopentadienyl)zirconium dichloride (Zr-2), were employed in order to make a direct comparison with our previous works. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF] Such metallocenes were selected due to their opposite behaviour towards LCB formation. In fact, while Zr-1 proved more prone to afford branched PEs by macromonomer insertion, Zr-2 is known to lead mainly to purely linear polymers [START_REF] Kokko | Influence of the catalyst and polymerization conditions on the long-chain branching of metallocenecatalyzed polyethenes[END_REF].

Chart 1. Structures of rac-{EBTHI}ZrCl 2 (Zr-1) and (nBuCp) 2 ZrCl 2 (Zr-2).

For each catalytic system, reference reactions in the absence of M-alkenyl co-reactants (Table 1, entries 1 and 12) and in the presence of the previously investigated Al-1 (Table 1, entries 2 and 13) were reported. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF] Compared to these benchmark runs, a positive effect on the polymerization productivity was observed upon introducing Zn-1, Mg-2 and Al-2. With the Zr-1/MAO system, a slight improvement of productivity was observed also in the case of B-2 for B/Zr molar ratios of 50 and 200 (Table 1, entries 9 and 10); contrastingly, a significant drop was occurred when 500 equiv of co-reagent were employed (Table 1, entry 11). We assume that such a decrease could be due to monomer diffusion issues arising from the gelation of the reaction medium in the presence of high concentration of the co-reagent.

On the other hand, when B-2 was used in combination with Zr-2/MAO, no variation of productivity was observed (Table 1, entries 2022). In all cases, the polymers showed lower melting temperatures and broader molecular weight distributions compared to the reference materials PE1 and PE12. [START_REF] Van Meurs | Polyethylene Chain Growth on Zinc Catalyzed by Olefin Polymerization Catalysts: A Comparative Investigation of Highly Active Catalyst Systems across the Transition Series[END_REF][START_REF]L. R. Aufbaureaktion Redux: Scalable Production of Precision Hydrocarbons from AlR 3 (R=Et or iBu) by Dialkyl Zinc Mediated Ternary Living Coordinative Chain-Transfer Polymerization[END_REF] In order to assess the possible formation of LCB, the samples produced with Al-2 (PE8 and PE19) were analysed by 13 The LCB content calculated from the area of those signals was found to be 1.9 and 2.5/10,000C for PE10 and PE22, respectively. Several other unassigned signals, probably corresponding to more complex branched structures involving B-alkyl linkers, were also detected (vide infra). , where ΔH m is the heat of fusion of the sample (in J/g) determined by DSC and ΔH 0 m is the theoretical heat of fusion for 100% crystalline PE (293 J/g); [START_REF] Wang | Liquid-liquid phase separation in a polyethylene blend monitored by crystallization kinetics and crystal-decorated phase morphologies[END_REF] f Data from ref. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF]; g Only n-propyl branches were detected; h Potential LCB calculated from area of the CH 2 () and CH 2 () signals; i Data from ref. [START_REF] Santoro | Alkenyl-Induced Formation of Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using (nBuCp) 2 ZrCl 2 /MAO Systems: An Experimental and Theoretical Study[END_REF] .

T m b [°C] T c b [°C] M w c [10 3 ] M w/ M n c LCB d Crystallinity e [wt.%] 1 f PE1 Zr-1 none 8,
The effect of the M-alkenyl co-reactants on the rheological properties of the PEs was next investigated. The van Gurp-Palmen plots of the samples prepared with the Zr-1/MAO system were all indicative of LCB-PEs (Figure 1). In fact, all curves tend (at low |G*|) to phase angles (δ) lower than 90 °, that is the values found for purely linear polymers. [START_REF] Trinkle | Van Gurp-Palmen-plot: a way to characterize polydispersity of linear polymers[END_REF][START_REF] Trinkle | Van Gurp-Palmen Plot IIclassification of long chain branched polymers by their topology[END_REF][START_REF] Ahmadi | Complex interplay of short-and long-chain branching on thermal and rheological properties of ethylene/α-olefin copolymers made by metallocene catalysts with oscillating ligand structure[END_REF] PE3, isolated in the presence of 50 equiv of Zn-1, described a curve almost superimposable to that of PE2, the benchmark sample obtained with a greater concentration of Al-1 (500 equiv).

A significant drop of phase angle, indicative of higher LCB-density, was also observed with PE4 (200 equiv of Zn-1). However, the extent of branching drastically dropped for higher Zn-1/Zr ratios (PE5). (that occurs during final hydrolytic workup), BC cleavage does not readily occur under acidic conditions. [START_REF] Smith | Hydroboration of C=C and CC[END_REF][START_REF] Snyder | Organoboron Compounds, and the Study of Reaction Mechanisms. Primary Aliphatic Boronic Acids[END_REF][START_REF] Mirviss | It has to be noted that BC bonds, although hydrolytically stable, proved reactive towards atmospheric oxygen[END_REF] In order to corroborate this last hypothesis, PE10 sample, synthesized with Zr-1/MAO system in the presence of 200 equiv. of B-2 (Table 1, entry 10), was treated with an aqueous base under harsh conditions in attempting to promote effective hydrolysis of BC polymeryl bonds allegedly present in the PE structure (see the Supporting Information).

Scheme 3. Hypothetic pathway towards LCB-PEs containing B-alkyl moieties.

Compared to the parent material, higher melting and crystallization temperature values were obtained (133 vs 130 °C and 119 vs 116 °C, respectively). In addition, an interesting change in the rheological behaviour was also observed. In fact, the curve on the van Gurp-Palmen plot for the base-treated PE tends to a higher phase angle than that of the starting polymer (45 ° and 25 °, respectively) and similar to that of PE2, prepared with 500 equiv of Al-1 (Figure 3). Moreover, the alkali-treated polymer exhibited lower viscosity al low frequency and lesser pronounced shear thinning than the parent sample (Figure S8). These observations are compatible with the drop of LCB-content caused by the base-treatment of the polymer and reinforce the hypothesis of the presence of branched or even cross-linked structures involving Balkyl linkers. S1). The focus of the DFT study is separated into three main aspects that allow insight into the nature of the bonding between co-reagent and catalyst systems: the coordination affinities to the catalyst system, the ability of this to influence subsequent ethylene insertions, and the possible insertion pathways generated by introduction of such co-reagents.

DFT studies on the LCB formation with

Previous investigations reported have eluded the way in which an Al-alkenyl moiety (Al-1) coordinates to catalyst systems [Zr-1,2R] + (derived either from the neutral Zr-1 or Zr-2), and the subsequent influences on the mechanisms of insertion by presenting a competitive coordination environment. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF] The following study thus began by examining the coordination affinities when computed M-alkenyl bridged heterobimetallic complexes are formed. This is compared initially with the coordination of ethylene monomer and both B-2, Mg(oct-7-enyl) 2 (Mg-1), and Zn-1 species to the [Zr-1R] + catalyst system (Table 2). The coordination energies reported demonstrate two key points: Experimentally, an Zr-1/MAO/M(Al and Zn)-alkenyl environment appeared to promote LCB formation via the proposed insertion/transmetallation mechanism. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF] Computationally we observed a clear agreement with our reference Zr-1/MAO/Al-1 polymerization condition, which has been reported as a beneficial mixture for LCB. [START_REF] Santoro | Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using rac-{EBTHI}ZrCl 2 /MAO/Al-alkenyl Combinations: An Experimental and Theoretical Study[END_REF][START_REF] Santoro | Alkenyl-Induced Formation of Long-Chain Branched Polyethylene via Coordinative Tandem Insertion and Chain-Transfer Polymerization Using (nBuCp) 2 ZrCl 2 /MAO Systems: An Experimental and Theoretical Study[END_REF] The two Zn-1 and B-2 co-reagents may promote the formation of LCB but, via the aforementioned investigations into their coordination affinity with the [Zr-1R] + system, this may highlight a difference in the action to which a branched structure is formed. The Zn-1 coreagent follows a similar coordination trend to that of the reference Al-1 co-reagent studied previously, highlighting a competitive coordination environment for either Zn-1 or ethylene monomer about the [Zr-1R] + catalyst. In contrast, the B-2 co-reagent offers no initial competition to the monomer through an alkenyl-bridged coordination, suggesting an 'exclusive' preference to coordinate and insert a terminally located vinyl group on the cocatalyst ligand chain. This step would indicate a competition directly to form a branched polymer.

In agreement with experimental results, the ability of the B-2 co-reagent to infer some competition toward a monomer coordination remains true regardless of increasing chain length on the [Zr-1R] + catalyst. To examine how this affects the various mechanisms of insertions, a comparison can therefore be investigated through the insertion of a monomeric species to favour a linear chain growth vs. the insertion of a vinyl group on the B-2 co-reagent which may allow the generation of LCB (Figure 4). The reactivity profile demonstrates the preference of the B-2 system to coordinate through the vinyl group species (stabilizing the [Zr-1pentyl] + catalyst by 4.2 kcal•mol 1 ) rather than an alkenyl bridge (+15.8 kcal•mol 1 ).

This profile then nicely demonstrates the kinetic ability of this B-2 co-reagent to generate a competitive insertion environment about the catalyst to form a B-cross-linked PE product.

Note that the transition states calculated between both co-reagent and monomer are almost identical (6.0 and 6.1 kcal•mol 1 , respectively). The formation of cross-links in this B-2/Zr-1 environment is therefore considered highly plausible computationally. Recalling Figure 2 and samples PE13/PE20, the presence of the B-2 co-reagent promotes the presence of branched or even cross-linked structures involving B-alkyl linkers. Through our DFT analysis, the formation of a stabilizing adduct at longer chain lengths, as well as a competitive insertion barrier with ethylene monomer, strongly supports the notion that the B-2 co-reagent is capable of promoting branched or even cross-linked structures through aggregated vinyl group coordination and insertion steps in Zr-1-catalyzed environments. The same analysis, conducted on a Zn-1 co-reagent system, presents the same observable trends: a stabilizing adduct and competitive insertion barrier to that of a monomer insertion (Figure 5). Thus, computationally, it is evident that this co-catalyst system would induce LCB formations. Recalling the rheology patterns observed in Figure 1 The Mg-1 compound offers a stabilizing coordination interaction to the Zr-1 catalyst compared to ethylene monomer (2.4 (monomer) vs 17.9 kcal•mol 1 ). The stability of this coordination originates from the fact that the coordination itself is not a 'four-centered' heterobimetallic complex as we have previously observed in the other Zr/M-alkenyl systems.

Instead, the Mg-1 donates an oct-7-en-1-yl chain to the catalyst. The extent to which this coordination influences subsequent propagations was thus investigated considering a 20 transmetallation step and compared to a more general monomer coordination and insertion (Figure 6). The stability of the alkylation was considered via a monomer insertion into a ZrC alkenyl bond, presenting a kinetic barrier of 24.9 kcal•mol 1 . This highlights the ability of propagation to continue at longer chain lengths after one step. The figure presented compares both an insertion pathway after a transmetallation event or dissociation of the Mg-1 coreagent, demonstrating the competitive kinetic environment between either insertion pathway or product formed. Interestingly, the insertion product after a transmetalation step seems to be thermodynamically favorable. This may offer an insight toward the reduced effects of LCB promotions: recalling samples PE6 and PE7 compared to that of the reference PE1 (Table 1), whereby a Mg-1 co-reagent has no effect on LCB rheologies; without hindering ethylene polymerization. LCB PE is thought to be produced via a vinyl group coordination and insertion from the co-reagent present in the reaction medium. For the PEs obtained in the presence of Zn-1, the extent of branching appeared to be reduced drastically at higher Zn/Zr-1 ratios. On the other hand, Mg-based co-reagents appeared to be completely ineffective in combination with the given catalytic systems, likely due to the inability to promote the transmetallation step.

Conclusions

From a theoretical point of view, the observed trends computed are in agreement with the existence of a stabilizing interaction through the coordination of the co-reagent and monomer along with a kinetic insertion barrier that possibly could influence a monomer insertion (moving away from a classic linear polymer formation). The computations also highlighted the fact that changing the nature of the co-reagent indeed influences the mechanisms of insertion. M-alkenyl co-reagents generate LCB products through the initial formation of heterobimetallic adducts between the catalyst and co-reagent. Such an interaction allows the formation of a competitive environment about the catalyst, making an otherwise facile monomer insertion more dependent on the co-reagent presence and thus changing the propagative behavior. The B-2 species both experimentally and computationally appears to promote B-centered cross-linked rather than LCB structures. This could be accounted to the failure of the BZr transmetallation due to the instability of the corresponding heterobimetallic B/Zr adducts.

Further synthetic and computational studies are currently under way to understand and use the potential of such co-reagents for the preparation of various tailor-made polymer architectures.

2 (

 2 C NMR spectroscopy. No signals compatible with LCB were detected but a significant amount of n-propyl branches (11.0 and 5.3 /10,000C for PE8 and PE19, respectively) was found (FiguresS1-S3). For PE samples prepared with B-PE10 and PE22),13 C NMR spectroscopy analysis could not allow unambiguous identification of the signal from the CH group at the branching point (overlapping with other minor signals), but rather intense resonances assignable to the CH 2 fragments at the and position of the LCB branching point were clearly observed (Figures S4 and S5, respectively).

Figure 1 .

 1 Figure 1. Van Gurp-Palmen plots for the PEs synthesised in the presence of M-alkenyl coreactants with the catalytic system Zr-1/MAO (PE1 and PE2 reference samples).[19] Shear strain (γ) 10%, angular frequencies (ω) from 0.1 to 250 rad⋅s -1 , T = 190 °C, N 2 atmosphere.

Figure 2 .

 2 Figure 2. Van Gurp-Palmen plots for the PEs prepared in the presence of M-alkenyl coreagents with the catalytic system Zr-2/MAO (PE12 and PE13 reference samples).[19] Shear strain (γ) 10%, angular frequencies (ω) from 0.1 to 250 rad⋅s -1 , T = 190 °C, N 2 atmosphere.

Figure 3 .

 3 Figure 3. Comparison between the van Gurp-Palmen plots of PE1, PE2 and PE5 (before and

Zr- 1

 1 system in the presence of M-1,2 coreagents. We next aimed at rationalizing the mechanism of formation of long-chain branches during polymerization of ethylene with Zr-1 system, in the presence of M-alkenyl compounds (M = Al, B, Zn and Mg), by theoretical computations of the first, second and third insertion steps. The purpose of this study was to analyze the various coordinated co-catalystcatalyst species and examine the change in structure as subsequent insertions of ethylene continue.

( 1 )

 1 the addition of the M-alkenyl (M = Al or Zn) species tends to introduce a competitive coordination environment to the monomer (notice 2.4 vs. 4.8 and 1.7 kcal•mol 1 ); (2) the B-2 co-reagent seems to be destabilizing in the sense a heterobimetallic coordination through an alkenyl bridge and is unlikely here, contrasted by the strong stability offered by the Mg-1 co-catalyst (17.9 kcal•mol 1 ). Understanding the coordination affinity between Malkenyl and [Zr-1R] + catalyst provides key insights toward the ability of these co-reagents to influence the possible mechanisms of propagation. To clarify the extent to which either Al-1, Zn-1 or B-2 moieties impact the polymerization, investigations into the insertion mechanisms were next conducted.

Figure 4 .

 4 Figure 4. A comparison between the third coordination of either (a) the co-catalyst (red), (b) ethylene monomer (blue) or (c) the vinyl group from the co-catalyst pent-4-en-1-yl chain.

also demonstrated that the Zn- 1 /

 1 Zr-1 environments almost superimposed the same rheological fingerprint as the Al-1/Zr-1 ratio at higher Al-1 loadings, which would suggest a similar action of LCB formation. The profile below thus demonstrates a similar reactivity to promote LCB formations observed in Al-1 environments.

Figure 5 .

 5 Figure 5. A comparison between the third coordination and insertion of either (a) the vinyl group from the Zn-1 co-catalyst (black) and (b) ethylene monomer (blue).

Figure 6 .

 6 Figure 6. The coordination of Mg-1 to [Zr-1Me] + , followed by the first insertion of ethylene via either cleavage of the MgC alkenyl or MgC alkyl bonds. This profile illustrates the kinetic competition that is generated by the ability of a Mg-1 co-catalyst to facilitate a transmetalation product after one insertion step.

  Discrete B-, Al-, Mg-and Zn-alkenyls have been synthesized and employed as LCBpromoters in the polymerization of ethylene catalyzed by Zr-1 or Zr-2/MAO catalytic systems. The use of Al-and B-based co-reagents induced a clear change of the rheological behavior of the PEs compatible with LCB formation. This was much more evident for the samples prepared with the Zr-1/MAO system. On the other hand, the data collected for the Bderived branched PEs are in agreement with cross-linked structures incorporating hydrolytically stable B-centered branches, whose presence could be corroborated by13 C NMR spectroscopy.

Table 1 .

 1 Polymerization

	Entry	Sample ID	Complex	M-alkenyl [M/Zr, mol/mol]	Productivity [kg pol /kg cat ]

of ethylene with Zr-1 or Zr-2/MAO/Al-1,2 -Mg-2, B-2 or Zn-1 systems. a

Table 2 .

 2 The various coordination affinities of the co-reagents to the [Zr-1R] + catalyst resulting in heterobimetallic Zr/M species.

	[Zr-1R] +		Coordination Energies (kcal•mol 1 )
	R	Ethylene	Al-1	Mg-1	B-2	Zn-1
	Methyl	2.4	4.8	17.9	11.3	1.7
	Propyl	2.6	5.0	19.2	13.8	3.0
	Pentyl	1.0	3.0	7.9	15.8	1.2

  Table 3 summarizes the coordination energies for the vinyl group on the various co-reagent systems toward the [Zr-1R] + catalyst. Samples PE6 and PE7 indicate that, regardless of Mg-alkenyl concentrations, this co-reagent has little to no effect on LCB promotions. Computationally, this would rationalize an unfavored vinyl group coordination and insertion mechanism (+12.9, +13.2 and +3.4 kcal•mol 1 ).

Table 3 .

 3 The various vinyl coordination energies (in enthalpy) from an octenyl, or pentenyl chain from the co-reagent to the catalyst -R-moiety. Note that for the Mg, Al and Zn coreagents, these are relative to the heterobimetallic species.

	[Zr-1R] +		Vinyl Coordination Energies (kcal•mol -1 )
	R	Ethylene	Al-1	Mg-1	Zn-1	B-2
	Methyl	2.4	0.2	12.9	3.0	5.1
	Propyl	2.6	0.4	13.2	2.9	6.6
	Pentyl	1.0	0.1	3.4	3.0	4.2

Acknowledgements: LM is a senior member of the Institut Universitaire de France. CalMip is acknowledged for a generous grant of computing time.

Funding sources: This work was gratefully supported by TotalEnergies One Tech Belgium (postdoctoral and PhD fellowships to OS, LP and KMC).

Appendix A: Supplementary data

Supporting information to this article (NMR spectroscopy and rheological analyses of polymers, computational details, Cartesian coordinates) can be found online at DOI: