Carla Marini
email: carla.marini@meyer.it

Alessandro Porro

Agnès Rastetter

Carine Dalle

Ilaria Rivolta

Daniel Bauer

Renske Oegema

Caroline Nava

Elena Parrini

Davide Mei

Catherine Mercer

Radhika Dhamija

Chelsea Chambers

Christine Coubes

Julien Thévenon

Paul Kuentz

Sophie Julia

Laurent Pasquier

Christèle Dubourg

Wilfrid Carré

Anna Rosati

Federico Melani

Tiziana Pisano

Maria Giardino

A Micheil Innes

Yves Alembik

Sophie Scheidecker

Manuela Santos

Sonia Figueiroa

Cristina Garrido

Carlo Fusco

Daniele Frattini

Carlotta Spagnoli

Anna Binda

Tiziana Granata

Francesca Ragona

Elena Freri

Silvana Franceschetti

Laura Canafoglia

Barbara Castellotti

Cinzia Gellera

Raffaella Milanesi

Maria Margherita Mancardi

Damien R Clark

Fernando Kok

Katherine L Helbig

Shoji Ichikawa

Laurie Sadler

Jana Neupauerová

Petra Laššuthova

Katalin Štěrbová

Annick Laridon

Eva Brilstra

Bobby Koeleman

Johannes R Lemke

Federico Zara

Pasquale Striano

Soblet

Smits

Nicolas Deconinck

Andrea Barbuti

Dario Difrancesco

Eric Leguern

Renzo Guerrini

Bina Santoro

Kay Hamacher

Gerhard Thiel

Anna Moroni

Jacopo C Difrancesco

Christel Depienne
email: christel.depienne@uni-due.de

# Affiliations

HCN1 mutation spectrum: from neonatal epileptic encephalopathy to benign generalized epilepsy and beyond

ABSTRACT

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels control neuronal excitability and their dysfunction has been linked to epileptogenesis but very few individuals with neurological disorders related to variants altering HCN channels have been reported so far. In 2014, we described five individuals with epileptic encephalopathy due to de novo HCN1 variants.

To further delineate HCN1-related disorders and investigate genotype-phenotype correlations, we assembled a cohort of 33 unpublished patients with novel pathogenic or likely pathogenic variants: 19 probands carrying 14 different de novo mutations and 4 families with dominantly-inherited variants segregating with epilepsy in 14 individuals, but not penetrant in six additional individuals. Sporadic patients had epilepsy with median onset at age 7 months and in 36% the first seizure occurred during a febrile illness. Overall, considering familial and sporadic patients, the predominant phenotypes were mild, including genetic generalized epilepsies and genetic epilepsy with febrile seizures plus (GEFS+) spectrum. About 20% manifested neonatal/infantile onset otherwise unclassified epileptic encephalopathy. The study also included eight patients with variants of unknown significance: one adopted patient had two HCN1 variants, four probands had intellectual disability without seizures, and three individuals had missense variants inherited from an asymptomatic parent. Of the 18 novel pathogenic missense variants identified, 12 were associated with severe phenotypes and clustered within or close to transmembrane domains, while variants segregating with milder phenotypes were located outside transmembrane domains, in the intracellular N-and C-terminal parts of the channel. Five recurrent variants were associated with similar phenotypes. Using whole-cell patch-clamp, we showed that the impact of 12 selected variants ranged from complete loss-of-function to significant shifts in activation kinetics and/or voltage dependence. Functional analysis of three different substitutions altering Glycine 391 revealed that these variants had different consequences on channel biophysical properties. The Gly391Asp variant, associated with the most severe, neonatal phenotype, also had the most severe impact on channel function. Molecular dynamics simulation on channel structure showed that homotetramers were not conducting ions because the permeation path was blocked by cation(s) strongly complexed to the aspartate residue, while heterotetramers showed an instantaneous current component possibly linked to deformation of the channel pore.

In conclusion, our results considerably expand the clinical spectrum related to HCN1 variants to include common generalized epilepsy phenotypes and further illustrate how HCN1 has a pivotal function in brain development and control of neuronal excitability.

Introduction

Hyperpolarization-activated, Cyclic Nucleotide-gated (HCN) channels constitute a unique class of voltage-gated ion channels comprising four different paralogous subtypes encoded by different genes (HCN1-4) in human [START_REF] Ludwig | A family of hyperpolarizationactivated mammalian cation channels[END_REF][START_REF] Santoro | Identification of a gene encoding a hyperpolarization-activated pacemaker channel of brain[END_REF].

Composed of four homomeric or heteromeric subunits, HCN channels are permeable to potassium and, to a lesser extent, to sodium. HCN channels are activated upon hyperpolarization, remain open at negative voltages and their opening is potentiated by binding of cAMP [START_REF] Biel | Hyperpolarization-activated cation channels: from genes to function[END_REF]. They conduct an inward, depolarizing current named If ("funny" current) in the heart and Ih ("hyperpolarization-activated" current) in the brain [START_REF] Postea | Exploring HCN channels as novel drug targets[END_REF][START_REF] Difrancesco | Dysfunctional HCN ion channels in neurological diseases[END_REF]. The generation of this depolarizing current drives the membrane potential back toward the threshold for calcium and sodium channel activation, thereby allowing action potential firing.

In the brain, HCN channels are involved in multiple regulatory functions including the stabilization of resting membrane potential, the integration of synaptic inputs, the modulation of rhythmic oscillatory activity in individual neurons and neuronal networks and they are therefore essential for the control of neuronal excitability [START_REF] Poolos | Pharmacological upregulation of h-channels reduces the excitability of pyramidal neuron dendrites[END_REF][START_REF] Poolos | Hyperpolarization-Activated Cyclic Nucleotide-Gated (HCN) Ion Channelopathy in Epilepsy[END_REF][START_REF] Benarroch | HCN channels: function and clinical implications[END_REF]. All four HCN subtypes are expressed in the mammalian brain but their expression greatly varies from one brain region to the other, HCN1 being the predominant isoform expressed in the cortex [START_REF] Moosmang | Differential distribution of four hyperpolarization-activated cation channels in mouse brain[END_REF][START_REF] Monteggia | Cloning and localization of the hyperpolarization-activated cyclic nucleotide-gated channel family in rat brain[END_REF]. Furthermore, HCN subtypes have distinct electrophysiological properties, HCN1

showing the most positive threshold for activation, the fastest activation kinetics, and the lowest sensitivity to cAMP [START_REF] Chen | Properties of hyperpolarization-activated pacemaker current defined by coassembly of HCN1 and HCN2 subunits and basal modulation by cyclic nucleotide[END_REF].

Increasing evidence over the last decade indicated that long-term deregulation of Ih current properties, due to abnormal HCN channel expression or cellular distribution, are early and probably key events of epileptogenic processes in rodent models with acquired seizures [START_REF] Noam | Towards an integrated view of HCN channel role in epilepsy[END_REF]. Interestingly, both the upregulation and downregulation of HCN channels have been associated with epileptic activity in different animal models [START_REF] Noam | Towards an integrated view of HCN channel role in epilepsy[END_REF]. An increase of HCN1 channels has also been observed in brain tissue of patients with temporal lobe epilepsy after exeresis [START_REF] Bender | Enhanced expression of a specific hyperpolarization-activated cyclic nucleotide-gated cation channel (HCN) in surviving dentate gyrus granule cells of human and experimental epileptic hippocampus[END_REF]. In 2014, we reported that de novo HCN1 missense variants cause an early infantile epileptic encephalopathy (EIEE) sharing common features with Dravet syndrome (Nava et al., 2014a).

Herein, we report on clinical, electrophysiological, genetic and functional data of novel patients with de novo or inherited HCN1 variants. The cohort includes sporadic and familial patients in whom analysis of clinical manifestations uncovered a large spectrum of phenotypes ranging from the very mild and benign febrile seizures (FS), febrile seizures plus (FS+), and genetic generalized epilepsy (GGE) to moderately severe forms of genetic generalized epilepsy with febrile seizure plus (GEFS+), focal or unclassified epilepsy and to catastrophic neonatal or infantile epileptic encephalopathy. Interestingly, the cohort further includes four patients with intellectual disability (ID) and autism spectrum disorder (ASD) without seizures. We also characterized the biophysical properties of mutant channels for 12 out of the 18 novel variants identified, and investigated possible genotypephenotype correlations.

Material and methods

Patients

We collected electroclinical and genetic data of 19 patients carrying de novo variants in the HCN1 gene from highly heterogeneous cohorts of patients with paediatric epilepsies, either refractory or benign and with a supposed genetic aetiology. In addition, we studied four families in which HCN1 variants segregated with epilepsy in at least two affected members.

Patients and families were recruited from epilepsy and genetic centres around Europe (Italy, France, Netherlands, Germany, United Kingdom, Czech Republic, Portugal, Switzerland and Belgium), Brazil, USA, Canada and Australia. Patients 11 and 36 were recruited though Decipher (ID: 260229 and 357848) [START_REF] Firth | DECIPHER: Database of Chromosomal Imbalance and Phenotype in Humans Using Ensembl Resources[END_REF]. Collection and analysis of retrospective clinical, EEG, neuropsychological and neuroimaging data were assessed using a specific format filled by the treating specialist aiming to obtain accurate and homogenous information. We classified seizure types and epilepsy/syndromes according the ILAE guidelines [START_REF] Fisher | ILAE official report: a practical clinical definition of epilepsy[END_REF]. We also included eight patients with variants altering HCN1 but classified as variants of unknown significance (VUS) based on unusual inheritance or phenotype: two patients with ID but no epilepsy carrying de novo HCN1 variants, two patients with ID or ASD with a heterozygous deletion encompassing exon 4 of HCN1 identified by microarrays, an adopted child with two heterozygous HCN1 variants, and three probands with HCN1 missense variants inherited from healthy parents.

Patient 37 was briefly previously reported (Nava et al., 2014a;Nava et al., 2014b); all other patients are novel.

Genetic studies

Genetic studies were independently performed in diagnostic or research laboratories using next generation sequencing. Details on the methods used to detect the HCN1 variants in each patient are indicated in Supplementary Table 1. Sanger traces confirming variant existence were collected for 25/29 index patients. Sanger sequencing was not performed in patient 3 for whom variant accuracy was supported by a high sequencing depth (>850X).

For the remaining three patients (patients 10, 13 and 41), we obtained the written report of the genetic tests performed by private laboratories but could not directly access to sequence data. Variants identified in patients 2 and 12 were previously reported [START_REF] Parrini | Diagnostic Targeted Resequencing in 349 Patients with Drug-Resistant Pediatric Epilepsies Identifies Causative Mutations in 30 Different Genes[END_REF].

The ACMG criteria and the Intervar interface (http://wintervar.wglab.org/) were used to filter and classify HCN1 variants [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][START_REF] Li | InterVar: Clinical Interpretation of Genetic Variants by the 2015 ACMG-AMP Guidelines[END_REF]. The consequences of HCN1 variants were interpreted on isoform NM_021072.3 using Alamut 2.10 (Interactive Biosoftware, France).

Patch-Clamp experiments

The plasmid containing the human HCN1 cDNA differing from the HCN1 reference sequence (NM_021072.3) by a deletion of 3 bp encoding one of the 12 glycine residues starting from residue 63 (known polymorphism) was kindly provided by Dr. Juliane Stieber (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany). The properties of the HCN1 channel with this in-frame variant were comparable to that of HCN1 corresponding to the reference sequence. Ten of the novel identified variants (M153I, M243R, K261E, M305L, G391C, G391D, G391S, I397L, S399P and R590Q) were introduced into this HCN1 cDNA with the QuikChange Site-Directed Mutagenesis Kit (Stratagene). All constructs were sequenced to ensure that no additional variants were introduced. Whole-cell patch-clamp experiments were performed at room temperature in CHO-K1 cells transiently cotransfected with 1 µg of plasmid expressing the wild-type (WT) or a mutant human HCN1 (hHCN1) channel plus pEGFP (at a ratio of 50(pHCN1):1(pEGFP)), using the NeonTM transfection system (Invitrogen), and whole-cell patch clamp experiments were performed at room temperature 24 hours after transfection, as previously described (Nava et al., 2014a). For coexpression experiments, an equal amount of WT and M153I constructs (0.5 µg of each plasmid) was transfected in the same conditions.

The biophysical properties of M305L, G391C, G391D, G391S and I397L were further studied in HEK293T cells transiently transfected with WT and/or mutant constructs using Turbofect transfection reagent (Thermo Fisher). 1 µg or 0.5 µg of the HCN1-containing vector (pcDNA3) and 0.3 µg of GFP-containing plasmid (pmaxGFP, AmaxaBiosystems) were transfected. In coexpression studies, 0.5 µg each HCN1 plasmid was cotransfected.

Green-fluorescent cells were recorded by whole-cell patch-clamp at room temperature 24 hours after transfection, as previously described [START_REF] Lolicato | Cyclic dinucleotides bind the C-linker of HCN4 to control channel cAMP responsiveness[END_REF].

Finally, the C329S and V414M variants were introduced in pIRES-GFP-hHCN1-WT (GenBank: AF488549.1). CHO cells were transiently transfected with 1.5 µg of WT or mutant in pIRES-GFP-hHCN1 plasmid using the jetPRIME reagent (Polyplus Transfection, Euroclone). Whole-cell patch clamp experiments were performed at room temperature 48 hours after transfection, as previously described [START_REF] Gravante | Interaction of the pacemaker channel HCN1 with filamin A[END_REF].

Data Analysis

To analyse current density, the steady-state current amplitude was measured at the end of each test potential and normalized to cell capacitance. Mean activation curves were obtained by fitting maximal tail current amplitude, plotted against the voltage step applied, with the Boltzmann equation It=It(max)/(1+exp(V-V1/2)/k where It is the current amplitude of the tail current recorded for a given pre-pulse and It(max) is the maximum current amplitude of the tail current, V is the voltage of the prepulse, V1/2 is the half-activation potential and k is the inverse slope factor in mV using Originpro software (Originlab, Northampton, MA, USA). All data are presented as mean ± S.E.M.

Molecular dynamics (MD) simulations

Residues 94 to 403 of the crystal structure of HCN1 (PDB: 5U6P) [START_REF] Lee | Structures of the Human HCN1 Hyperpolarization-Activated Channel[END_REF] were used as starting point of MD simulations. Missing residues were added and insilico point variants were introduced using Modeller 9.19 [START_REF] Fiser | Modeling of loops in protein structures[END_REF], followed by protonation of titratable side chains according to their estimated pKa value (PROPKA3) [START_REF] Olsson | PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical pKa Predictions[END_REF]. The proteins were embedded into an equilibrated palmitoyloleoylphosphatidyl-cholin (POPC) bilayer consisting of 512 lipids using g_membed [START_REF] Wolf | g_membed: Efficient insertion of a membrane protein into an equilibrated lipid bilayer with minimal perturbation[END_REF]. K + ions were placed in the SF at binding site S4 and in the central cavity (Scav). Finally, the internal cavity was solvated with VOIDOO/FLOOD (Kleywegt and Jones, 1994). The resulting system consisted of the protein, 494 POPC, 41911 TIPS3P water, 126 K + and 114 Cl -(≈ 0.15 mol l-1) for the heterozygous mutation, 441941 TIPS3P water, 122 K + and 114 Cl -for the WT channel and 41970 TIPS3P water, 124 K + and 114 Cl -for the heterozygous mutation, respectively. Simulations employed the GROMACS software package (2018) [START_REF] Van Der Spoel | GROMACS: fast, flexible, and free[END_REF][START_REF] Pronk | GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit[END_REF] and CHARMM36m forcefield [START_REF] Huang | CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data[END_REF]. The integration time step was set to 2fs. Van der Waals forces were switched to zero between 0.8 and 1.2 nm. Electrostatic interactions were represented using the fast smooth particle-mesh Ewald (PME) method with a Coulomb cut-off of 1.2 nm [START_REF] Essman | A smooth particle mesh Ewald method[END_REF]. Hydrogen bonds were kept constant using the LINCS algorithm [START_REF] Hess | LINCS: A linear constraint solver for molecular simulations[END_REF]. The velocity-rescale thermostat [START_REF] Bussi | Canonical sampling through velocity rescaling[END_REF] with a coupling time constant of 0.1 ps was used to keep the simulation temperature at 298 K. The pressure was kept at 1 bar using the Parrinello-Rahman barostat algorithm [START_REF] Parrinello | Polymorphic transitions in single crystals: A new molecular dynamics method[END_REF] with a coupling constant of 5 ps. Prior to 100 ns production simulation, the system was energy minimized (5,000 steps steepest descend) and equilibrated (10 ns NPT simulation). During equilibration, protein heavy atoms were restrained to their initial position by a force constant of 1,000 kJ mol -1 nm -2 .

The raw data that support the findings of this study are available from the corresponding authors, upon request.

Results

We collected the data of 33 affected individuals carrying 18 different novel HCN1 missense variants classified as pathogenic or likely pathogenic using the ACMG criteria, all absent from the GnomAD database (Fig. 1, Supplementary Table 1). Overall, 14 different variants occurred de novo in 19 sporadic patients (Table 1). Four variants segregated with epilepsy in at least two affected family members of four families (Table 2). All 18 variants led to missense substitutions altering amino acids highly conserved in orthologs and/or paralogs (Supplementary Fig. 1). Five amino acid substitutions (Met153Ile, Met243Arg, Met305Leu, Gly391Ser and Gly391Asp) were each observed twice, Met305Leu and Met153Ile resulting from different nucleotides substitutions. Three different base changes altering glycine 391 (Gly391Ser, Gly391Cys and Gly391Asp) were observed in five patients.

The spectrum of phenotypic manifestations related to the occurrence of pathogenic and likely pathogenic HCN1 variants is illustrated in Fig. 2A. To display results in a clear and effective way, sporadic and familial cases were analysed separately.

Sporadic epilepsy phenotypes related to de novo, pathogenic HCN1 variants

At the time of the study, the 19 probands harbouring de novo HCN1 variants (11 females and 8 males) had a median age of 12.0 years (mean age: 13.2, ranging from 1 to 42 years).

Table 1 summarizes the main clinical features of sporadic patients and additional details are provided in Supplementary Table 2. Median age at seizure onset was 7 months (mean age: 11.8 months, ranging from 30 hours to 72 months). At onset, seizure types were heterogeneous including mainly generalized episodes, triggered by febrile illness in seven patients (36.8%; patients 2, 4-7, 14, 18). Yet, only two of them were reported to have had prolonged FS and hemiclonic component in one. Six patients (31.5%; patients 1, 3, 10, 11, 16, 19) had generalized seizures including absences, eyelid myoclonia and afebrile tonicclonic seizures (TCS). In five probands (26.3%; patients 8, 9, 12, 13, 15), initial seizures were classified as possibly focal with a variable combination of symptoms including hypotonia, hypomotor behavior, apnea and cyanosis, tonic posturing, clonic jerking with or without secondary generalization. In patient 17, characterization of the first seizure was difficult and left as unclassified.

At follow up, all 19 patients had had subsequent polymorphic seizures, either focal or generalized, occurring with variable frequency, from multiple per day (patients 1, 2, 9, 12, 13, 16-19) to weekly (patient 3) to monthly (patients 7 and 11) or rare (patients 5, 6, 8, 10, 14, 15) events. A 42 year-old patient (patient 4) has been seizure-free and off antiepileptic drugs (AEDs) for over 20 years. Patients 12 and 13 respectively deceased at 14 and 15 months, due to cardiopulmonary failure, and while living, both had a very severe and drug resistant epilepsy with dozens of daily seizures. Both patients presented worsening of seizure frequency while treated with phenytoin and lacosamide. Overall, at least 10 out of the 17 living patients (58.8%) with seizures at the time of the study, had a drug resistant epilepsy not responding to combination of several conventional AEDs. The remaining patient with FS (patient 6) is currently 2 years and 6 months old and she has seizures only during febrile illnesses.

Following the ILAE guidelines for epilepsy classification (Fisher et al., 2014), three probands (15.7%;patients 4, 16, 19) were considered as having GGE including CAE with typical 3 Hz spike and waves (Fig. 2B), or GGE with TCS and epilepsy with eyelid myoclonia; 5 probands (26.3%; patients 5-7, 14, 15) were classified within the GEFS+ spectrum; 7 probands (36.8%; patients 1, 2, 11-13, 17, 18 ) had a neonatal/infantile onset otherwise unclassified EE. The remaining 4 patients (21%) had infantile onset focal (patient 9), or infantile onset unclassified epilepsy (patients 3, 9, 10).

All patients underwent periodic EEG recordings from seizure onset to current age.

According to their epilepsy phenotype, EEG recordings showed either focal, multifocal or generalized paroxysmal activity. Brain MRI was normal or showed non-specific brain abnormalities including parietal, occipital or fronto-temporal atrophy (two patients), thin corpus callosum and mild diffuse withe matter hyperintensity (one patient each). Patients 10-12 had acquired microcephaly (Supplementary Fig. 2). Patient 12 underwent several video-EEG monitoring from birth up to age 14 months and numerous focal seizures with an ictal discharge shifting from one hemisphere to the other in the same event were recorded (Fig. 2C). Due to these peculiar migrating seizures, an initial diagnosis of malignant migrating partial seizures of infancy (MMPSI) was suspected, but KCNT1 mutation was ruled out.

Motor and cognitive development were normal in six patients (31.5%; patients 3, 6-8, 14, 19) with only mild language developmental delay in two, whereas 13 probands (68.4%) had a variable degree of ID ranging from mild in four patients (21%; patients 3, 4, 10, 15), to moderate in three (15.7%; patients 5, 9, 16) and to severe ID in the remaining six (31.5%; patients 1, 11-13, 17, 18), with autistic traits in two.

Families with inherited, likely pathogenic HCN1 variants

We identified HCN1 variants segregating with epilepsy in four families (Table 2, Fig. 3A), for a total of 20 individuals (7 males and 13 females), 14 of whom exhibited an epilepsy phenotype while six were not known to have had seizures. Thus, the milder outcome and epilepsy phenotypes, including afebrile tonic-clonic seizures and absences with predominant FS, observed in these four families were consistent with GEFS+ conditions. Extended HCN1 spectrum: variants of unknown significance (VUS)

We also collected electroclinical and genetic data of eight probands with VUS in HCN1 (Supplementary Table 3, Supplementary Fig. 3).

A 9 year-old adopted male (patient 34) with severe EIEE had two predicted damaging variants, one missense (Lys261Glu) in domain S4, and one G>A transition abolishing the donor splice site of intron 5 (c.1377+1G>A). We could not determine whether these variants were located on the same allele (cis) or on different parental alleles (trans) due to absence of DNA from biological parents and unavailability of patient's material.

Two patients with no history of seizures had de novo HCN1 variants identified by WES or medical exome sequencing. Patient 35 was an 8-year-old-male with moderate intellectual disability and acquired microcephaly carrying a de novo nonsense mutation (Tyr138*).

Patient 36 had severe ID and language delay associated with the de novo Met379Arg variant in the S6 transmembrane (TM) domain.

Two sporadic female patients had intragenic deletions encompassing exon 4 (encoding the pore of the channel and segment S6), inherited in both cases from their asymptomatic father. Patient 37 had moderate ID, severe behavioural disturbances (agitation, auto-and hetero-aggressive behaviours) and ASD. Patient 38 had global developmental delay, behavioural disturbances with intolerance to frustration, and peculiar facial features (long face, arched eyebrows, marked but short philtrum, and epicanthus). This latter patient had a HCN1 deletion extending to exon 5 and also carried a de novo 339kb 17q12 duplication (arr[hg19] 17q12(37332899_37672040)) of unknown significance.

Finally, three sporadic patients (patients 39-41) with mild GGE and GEFS+ phenotypes carried HCN1 missense variants inherited from an asymptomatic parent. Proband 39 had the Glu85Ala variant, inherited from his asymptomatic mother, and exhibited GGE with tonic-clonic seizures at age 11 years and generalized spike wave discharges enhanced during intermittent photic stimulation. He also manifested cortical tremor with giant evoked potentials and positive C-reflex. Similarly, a 15-year-old female (proband 41) carrying the Arg715Gly variant inherited from her asymptomatic father, exhibited absence seizures with 3 Hz spike-wave discharges on EEG recordings at age 7 years leading to a diagnosis of childhood absence epilepsy. The remaining proband had infantile onset of febrile and afebrile TCS suggestive of a GEFS+ phenotype and carried the Tyr411Cys variant (proband 40), inherited from his asymptomatic father.

Genotype-phenotype correlations

We further investigated the correlations existing between variants and their associated phenotypes. Twelve of the 14 de novo pathogenic missense variants clustered in TM domains of HCN1 including S1, S4, S5 and S6 segments or were located in close proximity to domains S3/S6 (Fig. 1A and1B), whereas the four missense variants identified in families were all located outside TM segments, either in extracellular loops (S1-S2: T171R; S5-P: C329S) or in the intracellular C-terminal domain (p.V414M, S680Y). Of the two de novo variants located outside TM domains, one (R590Q) affected a residue of the cyclic nucleotide-binding domain (CNBD) critical for cAMP binding [START_REF] Zagotta | Structural basis for modulation and agonist specificity of HCN pacemaker channels[END_REF][START_REF] Lolicato | Tetramerization dynamics of C-terminal domain underlies isoform-specific cAMP gating in hyperpolarization-activated cyclic nucleotide-gated channels[END_REF] and was associated with a mild generalized epilepsy phenotype. All four VUS identified in patients with mild phenotypes, although predicted to be damaging, were also located outside TM domains, either in the N or C-terminal regions. Altogether, these observations suggested that variants located in TM segments or domains required for formation of the pore structure are generally associated with more severe phenotypes than variants located in extracellular loops or N/C-terminal domains.

Patients with identical de novo variants strikingly had concordant phenotypes, indicating that the phenotype was largely determined by the mutation itself: patients 2 and 3 (M153I) both exhibited an infantile onset epilepsy, although patient 2, who was older, also had seizures increased during febrile illness and mild ID; patients 5 and 6 (M243R) had feverrelated seizures; patients 14 and 15 (G391S) both had infantile onset of febrile and afebrile seizures; patients 12 and 13 with G391D showed neonatal epileptic encephalopathy with severe, intractable seizures and profound cognitive and motor delay leading to death at ages 14 and 15 months. The only exception was Met305Leu, caused by two different base changes, in patients 10 and 11 who had apparently dissimilar phenotypes, although patient 10 was an infant whereas patient 11 was an adolescent. Yet, both patients had similar postnatal microcephaly (Supplementary Fig. 2).

Functional impact of inherited, likely pathogenic variants

To determine the functional impact on the biophysical properties of the channel, we performed whole-cell patch-clamp recordings in CHO cells for two of the four inherited, likely pathogenic HCN1 variants. HCN1 C329S exhibited a smaller current density compared with the WT channel (Fig. 3B-C), but comparable voltage-dependence of activation (Fig. 3D). The activation and deactivation kinetics were not altered (Fig. 3E).

Conversely, HCN1 V414M showed a current density similar to the WT channel (Fig. 3B-C) but the half-activation voltage (V1/2) was shifted to the right by ~5mV with faster activation kinetics at all tested voltages (Fig. 3D-E). These results suggest that these two familial variants behave as mild loss-of-function (LoF) or gain-of-function (GoF) of homotetrameric HCN1 channels, respectively.

Functional impact of de novo pathogenic variants

We then carried out whole-cell patch-clamp recordings in CHO cells transiently transfected with WT HCN1 or mutant HCN1 channels corresponding to ten selected de novo HCN1 variants. No Ih current was recorded from cells transfected with M305L, G391D and S399P and rarely from cells transfected with K261E (Fig. 4A-C), indicating a probable LoF for these mutants. Recordings were inconstant in CHO cells for G391C, G391S and I397L, preventing a detailed analysis (Fig. 4E). All mutant channels leading to a LoF were expressed and reached the plasma membrane although their quantity was highly decreased for all except G391C, with the lowest amounts observed for K261E and M305L (Supplementary Fig. 4). On the contrary, voltage-dependent, slowly activating inward currents were recorded upon hyperpolarization in cells transfected with WT, M153I, M243R and R590Q channels, consistent with an expression of functional channels (Fig. 4A-B). Current densities were significantly decreased for M243R and R590Q compared to the WT channel. M153I had major effects on channel gating (Fig. 4D), as the halfactivation voltage was shifted to the depolarizing direction by ~36 mV compared to WT channel. The M153I variant also resulted in significantly faster activation and slower deactivation kinetics than WT HCN1 (Fig. 4E). In contrast, the half-activation voltage of R590Q was shifted to the hyperpolarizing direction by ~9 mV, without significant effect on the activation and deactivation kinetics. To mimic the heterozygous state of the mutation, we performed coexpression of WT HCN1 and the more interesting variant, M153I. The shift of the half-activation voltage was intermediate between WT and homomeric channels, shifted to the depolarizing direction ~12 mV compared to WT channel. These results largely confirmed that both de novo and inherited HCN1 variants associated with epilepsy may indifferently lead to LoF or GoF of homotetrameric HCN1 channel properties in heterologous cells, without any immediately obvious correlation between phenotypes and the effects on homomeric channels.

To gain further insight into the mechanisms by which HCN1 variants cause divergent phenotypes, M305L, G391S, G391C G391D and I397L mutant channels were expressed alone or in combination with the WT channel to study the behaviour of homo and heterotetrameric channels in human HEK293 cells, as we found that these mutants express more robustly in this cell line compared to CHO cells, allowing a more detailed characterization. (Fig. 5).

When the mutant HCN1 subunits were expressed alone, a current was recorded for M305L, G391S and G391C, and I397L but not for G391D (Fig. 5A, D, G, J and M). When the WT and mutant forms were cotransfected, all the variants gave rise to measurable currents (Fig. 5A, D, G, J andM). The amount of current recorded from G391S, G391C, I397L either alone or cotransfected with the WT, were comparable to the WT condition (Fig. 5E, H andN). Interestingly, the analysis of the voltage dependence of G391S and G391C channels (Fig. 5F andI) indicates a strong but opposite effect of the two variants on V1/2. G391S induced a right shift of +21 mV (Fig. 5F), while mutation G391C led to a left shift of -19 mV (Fig. 5I). The behaviour of the heteromeric channels was intermediate in both cases, with respective shifts of +11.5 mV (G391S) and -4 mV (G391C). I397L showed the strongest shift of the V1/2 (+40 mV) and, similarly to G391S and G391C, the coexpression with the WT subunit conferred an intermediate phenotype with a shift of the V1/2 of +20mV (Fig. 5O).

Differently, the M305L substitution caused a decrease in the number of cells that were expressing current, with 45% of measured cells showing a strongly reduced current density (Fig. 5B), precluding the analysis of tail currents. Interestingly, the coexpression of mutant and WT subunits rescued this current loss, returning the current density values and the number of cells expressing current to the range of the WT condition (Fig. 5B, Supplementary Fig. 5). However, the analysis of the voltage dependence of this heteromeric channel showed a right shift of the V1/2 of +12mV and an increase in slope factor (Supplementary Table 4), indicating different gating properties than the WT channel (Fig. 5C).

A more severe picture emerged for the G391D mutant. On one hand, both the lack of current in the mutant and the halved current of the coexpression (roughly comparable to half dose of the WT, Fig. 5K), suggested a possible lack of expression for this subunit. On the other hand, the G391D/WT currents showed features which were clearly specific to the coexpression of WT/G391D subunits, such as the presence of an instantaneous component (Fig. 5J andK) and a strong reduction (80%) in the number of transfected cell expressing a measurable current (Fig. 5L), suggesting that the heteromeric channel can form, and, although poorly, conduct current.

Impact of G391D on channel structure

To better understand the impact of the G391D mutation, associated with the most severe neonatal epileptic encephalopathy phenotype, on HCN1 protein structure/function, we performed MD simulations on the transmembrane domains of WT and mutant channels.

The G391D variant generated an opening of the inner channel gate by ca. 1.8 Å during the first 25 ns of simulation. This favoured an influx of water into the channel cavity, which was absent in the WT channel (Fig. 6A, Supplementary Fig. 6A-B). The presence of carboxyl groups in mutant channels caused a strong binding of potassium ions to one or multiple aspartate 391 residues (Fig. 6B). While this position was not occupied by a cation in the WT channel (Fig. 6E), the mutant remained in this open-but non-conducting conformation for the whole 100 ns of simulation (Fig. 6F). The results of these simulations are consistent with the electrophysiological data, which showed that the homomeric channels are non-conductive, presumably because the ionic path is blocked by cations firmly bound to Aspartate 391. In addition, they correspond to previous findings on HCN global dynamics [START_REF] Weissgraeber | A reduced mechanical model for cAMP-modulated gating in HCN channels[END_REF]. A similar inhibition of channel conductance by an ion, which is complexed by negative charges at the entry into the cavity, was also reported previously [START_REF] Tayefeh | Molecular dynamics simulation of the cytosolic mouth in Kcv-type potassium channels[END_REF].

We then simulated the behaviour of the heteromeric HCN1 channels in which two of the four subunits carried the G391D variant. The simulation showed that channels in which the mutation was introduced in opposite monomers behave like the homomeric mutants; water enters the cavity and K + ions associate to Aspartate 391, blocking conductance of the channel (Fig. 6D,H). In contrast, when the mutation was introduced in adjacent subunits, the channel remained closed. There was no entry of water and no blockage by K + ions during 100 ns of simulation (Fig. 6C,H). These results are also in agreement with the electrophysiological recordings, which showed that some functional HCN1 type currents can be measured in a few cells expressing a mixture of WT and mutant channels. It is interesting to note that the helices, which carried the mutation in adjacent monomers showed small deformations (Fig. 6C). It is therefore tempting to speculate that this small widening of the inner gate, which is caused by the greater space requirement of the aspartate side chain, is responsible for the large instantaneous current observed for the heteromeric channels.

Discussion

HCN1 spectrum

We previously described five de novo HCN1 missense variants in patients with a Dravetlike phenotype (Nava et al., 2014a), recognized as early infantile epileptic encephalopathy-24 (EIEE24; OMIM #615871). Since then, a single independent study has reported a de novo HCN1 variant (p.Ala387Ser) in a patient with Rett-like syndrome [START_REF] Lucariello | Whole exome sequencing of Rett syndrome-like patients reveals the mutational diversity of the clinical phenotype[END_REF]. The clinical spectrum associated with HCN1 variants has thus remained largely unknown. The analysis of the electroclinical features of 33 patients harbouring de novo and inherited heterozygous HCN1 variants uncovered a wide phenotypic spectrum ranging from mild GGE and GEFS+ phenotypes, to infantile onset focal or unclassified epilepsies to catastrophic epilepsies assembled under the term of 'neonatal/infantile epileptic encephalopathies'. One of the two patients with neonatal onset epileptic encephalopathy carrying the G391D variant, exhibited video-EEG recorded prolonged focal seizures with an ictal discharge shifting from one hemisphere to the other within the same event, suggesting a diagnosis of MMPSI. This study also provides further evidence that there is a biological and clinical continuum between mild, benign generalized epilepsies and severe epileptic encephalopathies, as the result from genetic variants in the same gene, as previously observed for other genes encoding ion channels (e.g. SCN1A, SCN2A and KCNQ2). In our cohort, 36.8% of the sporadic and about 20% of the whole cohort exhibited severe epilepsy corresponding to EIEE whilst the great majority of both sporadic (42%) and familial cases manifested a milder phenotype comprehensive of a less severe epilepsy, associated with mild ID or normal cognition. Indeed, more than 65% of our patients manifested FS, FS+ or GGE including CAE with normal or borderline cognitive and motor functions.

The electroclinical features of cortical tremor with photosensitivity and of non-progressive action myoclonus in two individuals with HCN1 variants corroborates the hypothesis of neuronal hyperexcitability, possibly causing a depolarized resting membrane potential in neurons that are more prompt to firing. We speculate that this effect in the thalamocortical network similarly results in abnormal generalized spike-wave activity, a hallmark of GGE, observed in patients with HCN1 variants. HCN1 is also moderately expressed in the heart (source: GTEX). Yet, contrary to patients with HCN4 pathogenic variants [START_REF] Difrancesco | Funny channel gene mutations associated with arrhythmias[END_REF], no obvious cardiac abnormalities have been yet reported in patients with HCN1 variants. This is an important aspect that should also be accounted for in further studies.

Genotype-phenotype correlations and impact of HCN1 pathogenic variants

Overall, HCN1 variants causing severe phenotypes tended to cluster within or close to TM domains and have stronger impact on channel function whereas variants segregating with milder phenotypes were located in extracellular loops or in the intracellular N-and Cterminal parts of the channel and had milder effects on Ih current. Additionally, noticeable phenotypic concordance was observed in pairs of patients harbouring identical de novo HCN1 variants, indicating that the epilepsy phenotype is largely determined by this single variant. In particular, G391D observed in two unrelated patients, one of Italian origin and the other Portuguese, caused an almost identical catastrophic neonatal phenotype. Both probands presented with severe, intractable epileptic encephalopathy with daily seizures from the first days of life, and never acquired psychomotor skills. Seizure semiology was also very similar with asymmetrical tonic posturing and predominant dysautonomic signs including apnoea and cyanosis. Two patients with a different change (G391S) altering the same amino acid both showed milder phenotypes consistent with GEFS+ spectrum. The three different changes altering Glycine 391 show that the phenotype is not only determined by the position of the altered amino acid on the channel but also by the nature and consequence of the amino acid change. The impact of G391S/C, associated with milder phenotypes, was limited to shifts in the voltage dependency of the channel, whereas G391D, causing the most severe phenotype, corrupted channel function in a more complex manner: WT/mutant heteromeric channels exhibited a strong reduction in current density with a high instantaneous activating current component. MD simulation revealed that the Aspartate at the entrance to the inner pore cavity electrostatically interacts with cations preventing, in the homozygous condition, or altering, in the heterozygous state, their permeation. These results show that different amino acid substitutions at a critical position can either reduce (LoF) or increase (GoF) HCN1 homomers conductance. However, mutation spectrum and coexpression studies suggest that seizures are specific to variants leading to shifts in heteromeric channel properties that could also be interpreted as a GoF impact. We hypothesize that variants leading to a GoF lead to neuronal hyperexcitability sustaining seizures, while variants leading to haploinsufficiency of HCN1 result, on the contrary, in neuronal hypoexcitability and predispose to ID/ASD, as previously demonstrated for SCN2A [START_REF] Ben-Shalom | Opposing Effects on NaV1.2 Function Underlie Differences Between SCN2A Variants Observed in Individuals With Autism Spectrum Disorder or Infantile Seizures[END_REF][START_REF] Wolff | Genetic and phenotypic heterogeneity suggest therapeutic implications in SCN2A-related disorders[END_REF]. More suitable neuronal and animal models are needed to fully understand the complexity of the effects resulting from HCN1 dysfunction related to epilepsy and ID.

Variants of unknown significance

The observation of an adopted child with severe EIEE harbouring both missense (p.Lys261Glu) and splice site variants suggested that this severe phenotype could be associated with recessive inheritance. Functional analysis of p.Lys261Glu further confirmed that it leads to a probable LoF of homomeric channels. Yet, the phase of the variants (i.e. location in cis or in trans) could not be determined due to the unavailability of parental and patient's material. Further evidence is therefore needed to conclude on the existence of recessive HCN1 disorders. The contribution of variants introducing premature termination codon (including the de novo nonsense variant identified in this study) and of intragenic deletions (e.g. deletion of exon 4 described here in two patients), which are likely to lead to heterozygous LoF of the mutated allele remains unclear. The same applies to de novo variants associated with ID/ASD phenotypes without seizures. For this reason, we classified these variants as VUS, although they probably contribute to ID/ASD in the patients described in this study. ASD in patients with HCN1 variants could be related to the interaction of HCN1 channels with SHANK3, a scaffolding protein highly enriched in the post-synaptic density of glutamatergic synapses, whose genetic alterations have been linked to ASD [START_REF] Yi | Autism-associated SHANK3 haploinsufficiency causes Ih channelopathy in human neurons[END_REF][START_REF] Zhu | Shank3-deficient thalamocortical neurons show HCN channelopathy and alterations in intrinsic electrical properties[END_REF]. Finally, HCN1 missense variants located in parts of the channel more tolerant to variations (e.g. N-/C-terminal domains) seem associated with a lower penetrance of epilepsy/ID phenotypes. Inherited HCN1 VUS described in this study could even act as susceptibility factors and interact with variants in other genes to determine to occurrence of polygenic epilepsy, as described in the WAG/Rij rat [START_REF] Wemhoner | An N-terminal deletion variant of HCN1 in the epileptic WAG/Rij strain modulates HCN current densities[END_REF].

In conclusion, this study provides a comprehensive delineation of the phenotypic spectrum associated with HCN1 variants ranging from GEFS+ or GGE to neonatal or infantile EE.

Recurrent variants showed striking genotype-phenotype correlations. HCN1 pathogenic variants might be either de novo or dominantly inherited and lead to GoF or dominant negative effects underlying neuronal hyperexcitability in various neuron types including the thalamocortical network, thus generating aberrant generalized spike-waves as observed in our patients. Animal models reproducing HCN1 variants should help understanding more accurately the associated pathophysiological mechanisms in the hope to develop more adapted treatments for this group of disorders. electrophysiology core facility of the institute of brain and spine (ICM, Paris). This study also makes use of data generated by the DECIPHER community. A full list of centres who contributed to the generation of the data is available from http://decipher.sanger.ac.uk and via email from decipher@sanger.ac.uk. Funding for the project was provided by the Wellcome Trust. in the selectivity filter is located at 0 nm while residue 391 is at ~ -1.5 nm. For clarity, only a subset of all ions is shown.

  photoparoxysmal response. Her mother, carrying the same variant had a history of absence

FIGURE LEGENDS Figure 1

 LEGENDS1 FIGURE LEGENDS

Figure 2

 2 Figure 2 Clinical spectrum associated with HCN1 variants and examples of EEG

Figure 3

 3 Figure 3 Pedigrees of families with dominantly inherited HCN1 variants and

  4

  .

Figure 4

 4 Figure 4 Functional impact of selected de novo HCN1 variants using whole-cell patch-

  4

  .

Figure 5

 5 Figure 5 Functional impact of variants altering Glycine 391, Isoleucine 397 and

Figure 6 .

 6 Figure 6. MD simulation of the effect of G391D on HCN1 channel structure.

Table 1 Clinical and genetic summary of the 19 sporadic patients with de novo HCN1 variants.

 1 Detailed clinical information, including Brain MRI, EEG findings and antiepileptic treatment is displayed for patients 1-19 in Supplementary Table 2.

	Patient number	Gender	age at the study	Sz onset	Sz type at onset	Sz type at follow-up	Sensitivity to fever	Sz frequency	Resistance to AEDs	Development	Epilepsy type/syndromes	mutation
	1	F	12 y 6 m	12 m	TCS	TCS, At	N	D	Y	Severe ID	EIEE	p.Phe143Tyr
	2	F	7 y 3 m	5 m	FS	Fc, TCS	Y	W to D	Y	Mild ID	EIEE	p.Met153Ile
	3	M	2 y 8 m	9 m	TCS	TCS, Fc	N	W	Y	Mild language delay	Uncl Epi infantile onset	p.Met153Ile
	4	F	42 y	7 m	FS	FS, afebrile TC,Tn & Ab	Y	last sz @ 20y	N	Mild ID + autistic traits	GGE-TCS	p.Thr172Pro
	5	F	17 y	13 m	FS	FS, afebrile TCS, Ab	Y	R	N	Moderate ID	FS+	p.Met243Arg
	6	F	2 y 6 m	10 m	FS (Tn)	FS	Y	w fever	N	Normal	FS	p.Met243Arg
	7	F	2 y	8 m	FS (Cl)	Cl Gen	Y	Mt	N	Normal	FS+	p.Thr260Ile
	8	M	5 y 10 m	9 m	Fc (Cl)	TCS	N	R	N	Normal, mild language delay	Uncl Epi infantile onset	p. Ser264Cys
	9	F	9 y	42 m	Fc	Fc > TCS; My	N	D	Y	Moderate ID	Childhood Focal Epi	p.Ile275Thr
	10	F	12 m	3 m	TCS	TCS	N	4 m sz-free	N	Mild DD	Uncl Epi infantile onset	p.Met305Leu
	11	F	14 y	2 m	TCS	TCS, Tn, Fc, Cl	Y	Mt	Y	Severe ID, microcephaly	EIEE	p.Met305Leu
						Tn asymmetric
	12	M	died at 14 m	30 h	Tn asymmetric, prolonged	+/-Cl, prolonged apnea &	N	D	Y	Severe ID, microcephaly	NOEE (MMPSI) p.Gly391Asp
						cyanosis
	13	M	died at 15 m	48 h	Tn asymmetric, prolonged	Similar but w cyanosis	N	D	Y	Severe ID	NOEE	p.Gly391Asp
						FS; afebrile
	14	F	6 y 3 m	5 m	Prolonged FS (20')	TCS: Fc (LOC, cyanosis, hypotonia,	Y	Yr	N	Normal	FS+	p.Gly391Ser
						vomit)
	15	M	2 y 5 m	7 m	HemiCl	Fc, TCS	Y	Yr	N	Mild ID	GEFS+	p.Gly391Ser

F: female; M: male; h: hours; m: months; y: years; Ab: Absence; At: atonic; Cl: clonic; Fc: focal; Gen: generalized; My: myoclonic; Epi: Epilepsy; FS: febrile seizures; MA: myoclonic-atonic; TCS: tonic-clonic seizure(s); Tn: tonic; Uncl: unclassified; Sz: seizure(s); Y: Yes; N: No; @: at; w: with; D: daily; W: weekly; Mt: Monthly; Yr: Yearly; DD: developmental delay; ID: intellectual disability; LOC: Loss of consciousness; CAE: childhood absence epilepsy; EIEE: early infantile epileptic encephalopathy; FS+ febrile seizure plus; GGE: genetic generalized epilepsy; GEFS+: generalized epilepsy with febrile seizure plus; NOEE: neonatal-onset epileptic encephalopathy; NA: unavailable.

Table 2 Clinical and genetic summary of affected members of families with HCN1 variants

 2 . F: female; M: male; m: months; y: years; Ab: Absence; FS: febrile seizure plus; TCS: tonic-clonic seizure(s); Sz: seizure(s); Antiepileptic drugs (AEDs): CBZ: carbamazepine, ESM: ethosuximide, GVG: Vigabatrin, PB: phenobarbital, VPA: sodium valproate; GSW: generalized spike and wave;

IPS: intermittent photic stimulation; GGE: genetic generalized epilepsy; GEFS+: generalized epilepsy with febrile seizure plus; ID: intellectual disability; DQ: developmental quotient; IQ: intellectual quotient; PIQ: performance intellectual quotient; TIQ: full-scale intellectual quotient; VIQ: verbal intellectual quotient; NA: unavailable.

Acknowledgments

We thank the patients and their family for their participation in this study, Dr. Juliane Stieber (Universität Erlangen-Nürnberg, Germany) for providing plasmids containing the human HCN1 cDNA and Prof. Dirk Isbrandt (German Center for Neurodegenerative Diseases (DZNE) and University of Cologne) for critical reading of the manuscript and interesting discussions. Calculations required for MD simulations were conducted on the Lichtenberg high performance computer of the TU Darmstadt. The Mariani Foundation, which promoted and organised the International Workshop on the Genetic Epileptic Encephalopathies, Florence 2016, is also acknowledged. This Workshop was the starting point of an international collaboration leading to the creation of the HCN1consortium. Data collection and generation within this fruitful international collaboration has led to this manuscript. The research leading to these results was partly generated on the

Funding

The research generating these results was funded by the Agence National de la Recherche (ANR EUHFAUTISM), the "Investissements d'avenir" program ANR-10-IAIHU-06 (IHU-A-ICM), the Bio-Psy labex, INSERM, the Assistance Publique des hôpitaux de Paris (AP-HP), the Pierre and Marie Curie University, the Italian Ministry of Health (Ricerca Finalizzata Giovani Ricercatori), projects GR-2010-2304834 to JCD and AB and GR-2016-2363337 to JCD, the Ministry of Research and the Arts (HMWK) of the Hessen state (LOEWE project iNAPO), and the Telethon Exploratory Project GEP14137 to A.M. and beyond Carla Marini 1,43 * # , Alessandro Porro 2 *, Agnès Rastetter 3 *, Carine Dalle 3 *, Ilaria Rivolta 4 , Daniel Bauer 5 , Renske Oegema 6 , Caroline Nava 3,7,43 , Elena Parrini 1 , Davide Mei 1 , Catherine Mercer 8 , Radhika Dhamija 9 , Chelsea Chambers 10 , Christine Coubes 11 , Julien Thévenon 12 , Paul Kuentz 12,13 , Sophie Julia 14 , Laurent Pasquier, 15 Christèle Dubourg, 16 Wilfrid Carré, 16 Anna Rosati 1 , Federico Melani 1 , Tiziana Pisano 1 , Maria Giardino 1 , A. Michel Innes 17 , Yves Alembik 18 , Sophie Scheidecker 18 , Manuela Santos 19 , Sonia Figueiroa 19 , Cristina Garrido 19 , Carlo Fusco 20 , Daniele Frattini 20 , Carlotta Spagnoli 20 , Anna Binda 4 , Tiziana Granata 21 , Francesca Ragona 21 , Elena Freri 21 , Silvana Franceschetti 21 , Laura Canafoglia 21 , Barbara Castellotti 21 , Cinzia Gellera 21 , Raffaella Milanesi 22 , Maria Margherita Mancardi 23 , Damien R. Clark 24 , Fernando Kok 25 , Katherine L. Helbig 26 , Shoji Ichikawa 27 , Laurie Sadler 28 , Jana Neupauerová 29 , Petra Laššuthova 29 , Katalin Štěrbová 29,43 , Annick Laridon 30 , Eva Brilstra 6,43 , Bobby Koeleman 6,43 , Johannes R. Lemke 31,43 , Federico Zara 32 , Pasquale Striano 33,43 , Soblet Julie 34,35,36 , Smits Guillaume 34,35,36 , Deconinck Nicolas 37 , Andrea Barbuti 22 , Dario DiFrancesco 22 , Eric LeGuern 3,7,43 , Renzo Guerrini 1,43 Bina Santoro 38 , Kay Hamacher 5 , Gerhard Thiel 39 , Anna Moroni 2 , Jacopo C. DiFrancesco 21,40 , Christel Depienne 3,41,42,43# AFFILIATIONS 1 Pediatric Neurology, Neurogenetics and Neurobiology Unit and Laboratories, Neuroscience Department, A. Meyer Children's Hospital, University of Florence, Viale Pieraccini 24, 50139, Florence, Italy. 2 Department of Biosciences, University of Milan, 20133 Milan, Italy. 3 Inserm U 1127, CNRS UMR 7225, Sorbonne Universités, UPMC Univ Paris 06 UMR S 1127, Institut du Cerveau et de la Moelle épinière, ICM, F-75013, Paris, France. 4 School of Medicine and Surgery, University Milano-Bicocca, Monza, Italy. 5 Computational Biology & Simulation Group, Department of Biology, Technische Universität Darmstadt, 64287 Darmstadt, Germany. 6 Department of Genetics, University Medical Center Utrecht, Utrecht, The Netherlands. 7 AP-HP, Groupe Hospitalier Pitié-Salpêtrière, Département de Génétique, 75013, Paris, France. 8 Wessex Clinical Genetics Service, Princess Anne Hospital, Southampton, UK. 9 Department of Clinical Genomics and Neurology, Mayo Clinic, Phoenix, AZ, USA. 10 Department of Neurosciences, University of Virginia, Charlottesville, VA, 22908, USA. 11 Département de Génétique Médicale, Maladies Rares et Médecine Personnalisée, Hôpital Arnaud de Villeneuve, Montpellier, France. 12 FHU-TRANSLAD, Université de Bourgogne/CHU Dijon and INSERM UMR 1231 GAD team, Genetics of Developmental Anomalies, Université de Bourgogne-Franche Comté, Dijon, France. 13 Génétique Biologique Histologie, CHRU de Besançon, Besançon, France. 14 Service de génétique médicale, Pôle de biologie, CHU de Toulouse -Hôpital Purpan, Toulouse, France. 15 Service de Génétique Clinique, Centre Référence « Déficiences Intellectuelles de causes rares » (CRDI), CHU Rennes, 35203 Rennes, France. 16 Laboratoire de Génétique Moléculaire & Génomique, CHU de Rennes, 35033 Rennes, France. 17 Department of Medical Genetics and Alberta Children's Hospital Research Institute, Cumming School of Medicine, University of Calgary, Calgary, Alberta, Canada. 18 Laboratoires de génétique, Institut de génétique médicale d'Alsace, Hôpitaux Universitaires de Strasbourg, 67 000 Strasbourg, France. 19 Neuropediatric Department, Centro Hospitalar do Porto, Porto Portugal. 20 Azienda Unità Sanitaria Locale -IRCCS di Reggio Emilia, Reggio Emilia, Italy. 21 Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan, Italy. 22 Department of Biosciences, The PaceLab, Università degli Studi di Milano, Milan, Italy. 23 Child Neuropsychiatry Unit, Department of Medical and Surgical Neurosciences and Rehabilitation, IRCCS Istituto Giannina Gaslini, Genova, Italy. 24 Women's and Children's Hospital, Adelaide, Australia. 25 Mendelics Genomic Analysis, Sao Paulo, SP, Brazil. 26 Division of Neurology, Children's Hospital of Philadelphia, Philadelphia, PA, USA. 27 Department of Clinical Diagnostics, Ambry Genetics, Aliso Viejo, CA, USA. 28 Division of Genetics, Department of Pediatrics, Oishei Children's Hospital, Jacobs School of Medicine and Biomedical Sciences, University of Buffalo, State University of New York, Buffalo, NY, 14203, USA. 29 Department of Child Neurology, Charles University 2nd Faculty of Medicine and University Hospital Motol, Prague, Czech Republic. 30 Department of Neurology, Academic Center for Epileptology, Kempenhaeghe/Maastricht University Medical Center, Heeze, The Netherlands. 31 Institute of Human Genetics, University of Leipzig Hospitals and Clinics, Leipzig, Germany. 32 Laboratory of Neurogenetics and Neuroscience, Institute G. Gaslini, Genova, Italy. 33 Pediatric Neurology and Muscular Diseases Unit, Department of Neurosciences, Rehabilitation, Ophthalmology, Genetics, Maternal and Child Health, University of Genoa, "G. Gaslini" Institute, Genova, Italy. 34 Department of Genetics, Hôpital Universitaire des Enfants Reine Fabiola, ULB Center of Human Genetics, Université Libre de Bruxelles, Brussels, Belgium. 35 Department of Genetics, Hôpital Erasme. ULB Center of Human Genetics, Université Libre de Bruxelles, Brussels, Belgium. 36 Interuniversity Institute of Bioinformatics in Brussels, Université Libre de Bruxelles, Brussels, Belgium. 37 Department of Pediatric Neurology, Hôpital Universitaire des Enfants Reine Fabiola, Université Libre de Bruxelles, ULB, Brussels, Belgium. 38 Department of Neuroscience, Columbia University, New York, NY 10032, USA. 39 Membrane Biophysics, Deparment of Biology, Technische Universität Darmstadt, 64287 Darmstadt, Germany. 40 Department of Neurology, San Gerardo Hospital, University Milano-Bicocca, Monza, Italy. 41 IGBMC, CNRS UMR 7104/INSERM U964/Université de Strasbourg, 67400 Illkirch, France. 42 Institute of Human Genetics, University Hospital Essen, University Duisburg-Essen, Essen, Germany. 43 EuroEPINOMICS RES consortium.* Co-first authors; # to whom correspondence should be addressed: christel.depienne@uni-due.de or carla.marini@meyer.it

Competing interests

S.I is employed by Ambry Genetics and FK is medical director of Mendelics Genomic Analysis, companies that provide gene panel and medical exome sequencing as commercially available tests. All other authors report no competing interests.

Appendix Collaborators (ULB)

Vilain Catheline 34,35,36 , Bouysran Youssef 35,36 , Aeby Alec 37 34 Department of Genetics, Hôpital Universitaire des Enfants Reine Fabiola, ULB Center of Human Genetics, Université Libre de Bruxelles, Brussels, Belgium. 35 Department of Genetics, Hôpital Erasme. ULB Center of Human Genetics, Université Libre de Bruxelles, Brussels, Belgium. 36 Interuniversity Institute of Bioinformatics in Brussels, Université Libre de Bruxelles, Brussels, Belgium. -52.3 ± 0.9 16.4 ± 0.5 Figure 5 HCN1 WT -72.6 ± 0.7 6.4 ± 0.5 HCN1 p.WT/M305L -60.9 ± 1.9 11.4 ± 0.6 HCN1 WT (panel B) -72.9 ± 0.7 6.9 ± 0.6 HCN1 p.G391S -51.5 ± 0.9 8.1 ± 0.4 HCN1 p.WT/G391S -61.


• ppm -1 U with 10% accuracy is in good agreement with the one measured in Bessines (and for which no uncertainty was provided), 5.2 s -1 • ppm -1 U . The calculations indicate that the concrete blocks used for measuring the calibration coeff cients measured in Bessines are underestimated by about 10%. Based on the validated MCNP model, several parametric studies have been performed. For instance, the rock density and chemical composition proved to have a limited impact on the calibration coeffi ient. However, gamma self-absorption in uranium leads to a nonlinear relationship between count rate and uranium concentration beyond approximately 1% of uranium weight fraction, the underestimation of the uranium content reaching more than a factor 2.5 for a 50% uranium weight fraction. Parametric studies have also been performed with different tubing materials, diameters, and thicknesses, as well as different borehole f lling fluid representative of real measurement conditions, in view to validate gamma attenuation corrections based on the semiempirical formula. In addition, a multilinear analysis approach has been tested to further improve accuracy on uranium concentration determination, leading to only a few percent uncertainties on a large range of conf gurations.

Index Terms-

I. INTRODUCTION

T HE detection of gamma rays emitted by 238 U and its daughter nuclei is one of the reference methods for detecting uranium in borehole. One approach consists in inferring the uranium concentration in boreholes from the total count rate provided by scintillation counters such as NaI(Tl) detectors. This approach, known as gross count gammaray logging [START_REF] Killeen | Practical borehole logging procedures for mineral exploration, with emphasis on uranium[END_REF], [START_REF] Killeen | Borehole logging for uranium by measurement of natural Y -radiation[END_REF], requires a calibration coeff cient which is usually measured in the concrete blocks of well-def ned composition with known uranium concentration. However, the measurement conditions of the calibration coeff cient are not always representative of f eld conditions and corrections of the measured calibration coeff cient are needed [START_REF] Killeen | Practical borehole logging procedures for mineral exploration, with emphasis on uranium[END_REF]. This paper reports numerical simulations performed with the Monte Carlo N-Particles (MCNP) code in view to improve the accuracy of uranium concentration determination in gross count gammaray logging.

II. VALIDATION OF THE MCNP NUMERICAL MODEL

To assess uranium concentration in boreholes, a GEOVISTA Natural Gamma Ray Sonde (NGRS) [START_REF] Well | Borehole Logging Equipment[END_REF] equipped with a 2.4c m(diameter) × 3.9 cm (height) cylindrical NaI(Tl) scintillation crystal is used. The uranium concentration is linearly related to the NGRS count rate via a calibration coeff cient K [START_REF] Killeen | Borehole logging for uranium by measurement of natural Y -radiation[END_REF]. Following standard procedures [START_REF] Løvborg | Pad facility for the calibration of gamma-ray measurements on rocks[END_REF], [START_REF] Mathews | Gross gamma-ray calibration blocks[END_REF], K is measured using concrete blocks of known uranium concentration. In the AREVA Mines calibration facility in Bessines, France, the calibration block's size is 70 cm × 70 cm × 70 cm.

The calibration measurement geometry presented in Fig. 1 has been modeled with the MCNP Monte Carlo code. Being a reliable and renown photon-neutron transport code, MCNP is already used in the f eld of uranium logging to model measurement methods involving neutron sources [START_REF] Gardner | On the future of Monte Carlo simulation for nuclear logs[END_REF] or measurements based on gamma-ray detection [START_REF] Mckeon | Input preprocessor for creating MCNP models for use in developing large calculational databases[END_REF], this last approach being also manageable with free available codes like GEANT 4 [START_REF] Velker | Evaluating Geant4 platform for nuclear well-logging problems[END_REF]. The modeled concrete blocks have a1 .9g• cm -3 density and an isotropic, homogeneously distributed gamma-ray source corresponding to 2906 ppm of uranium, 15.6 ppm of thorium, and 3.7% of potassium. With a 65-keV energy threshold, the calculated reference calibration coefficien is

K MCNP air = 5.3s -1 • ppm -1
U ± 10% for a tubeless NGRS probe in the calibration block, with only air filli g the borehole (no fl id), which is compatible with the measured reference calibration coeff cient (for which the uncertainty has not been provided to the authors):

K meas air = 5.2s -1 • ppm -1
U . The 10% uncertainty on the simulation is caused not only by uncertainties associated with the numerical model precision (crystal dimensions and cement composition) but also by the precision on the detection energy threshold and the accuracy of the chemical analyzes performed to determine the uranium concentration in the cement blocks. Measurements with the NGRS probe inside tubes of different thicknesses and nature have also been modeled with MCNP. Table I shows that the calculated tube attenuation corrections match the measurements.

III. SENSITIVITY PARAMETRIC STUDIES

A. Influenc of Rock Composition

The impact of the rock mineralogy on the calibration factor has been studied, replacing SiO 2 with CaCO 3 ,C a S O 4 -2H 2 O, or Na 2 CO 3 . As shown in Table II, rock composition has a small impact on the calibration factor. This lack of sensitivity is caused by the lesser atoms sensitivity of the mass attenuation coeff cients when photons have energy larger than 100 keV.

B. Gamma Self-Absorption in Uranium

Fig. 2 shows the calculation results on a wide range of uranium mass fractions, for an NGRS probe inside an iron tube fille with water, located in a 70-cm edge concrete cube similar to Bessines calibration block. As already observed in [START_REF] Damley | Radiometric reporting methods and calibration in uranium exploration[END_REF], the deviation from the linear fi due to self-attenuation, obtained for uranium mass fractions lower than 1%, begins above uranium 1%, and the self-attenuation effect reaches a factor of 2.6 for 50% of uranium.

C. Gamma Range Seen by the NGRS Probe

Monte Carlo calculations have been performed to study the range of the gamma rays detected by the NGRS probe using the model shown in Fig. 3. The saturation of the signal is reached for a sphere with a radius of about 100 cm. Therefore, we have calculated the calibration coeff cient in a concrete block with an edge of 200 cm, instead of 70 cm for Bessines blocks. The result is

K MCNP ∞ = 5.8s -1 • ppm -1 U instead of 5.3 s -1 • ppm -1
U , indicating that calibration coeff cients measured in Bessines are underestimated by about 10%. Our calculations are in agreement with the 60-cm minimum radius recommended in [START_REF] Damley | Radiometric reporting methods and calibration in uranium exploration[END_REF] for calibration boreholes with 2 g • cm -3 material.

D. Influenc of Rock Density

Calculations with 2906 ppm U have been performed with a 200-cm edge SiO 2 block, the reference gamma-ray source, and a tubeless borehole f lled with mud. Given the lesser sensitivity of the mass attenuation coeff cients to mineralogy, mud has been simulated by water with a density of 1.2 g • cm -3 . Table II indicates that the maximum effect of this approximation would be of the order of 6%. The calculations show that the calibration coeff cient slightly decreases from 5.44 to 5.36 s -1 • ppm -1 U when the density varies from 1 . 2t o2 .6g• cm -3 . Since calculations keep the uranium concentration to 2906 ppm U , increasing rock density increases the amount of uranium. Being modif ed only by about 1.5% when increasing the density by 1.4g• cm -3 , the calibration coeff cient is therefore poorly sensitive to rock density. With the mineralogies shown in Table II, the increase of gamma attenuation is indeed compensated by a larger amount of uranium when density rises.

E. Influenc of Borehole Diameter and Filling Fluids

The correction of the calibration factor to take into account the attenuation by the filli g f uids, the borehole dimension and tube casing can be obtained by measurement at the cost of a dedicated facility that can cover a suff cient set of conf gurations [START_REF] Killeen | Borehole logging for uranium by measurement of natural Y -radiation[END_REF], [START_REF]Field Calibration Facilities for Environmental Measurement of Radium, Thorium, and Potassium[END_REF]. Up to now, to take into account the attenuation by the borehole and tube filli g f uids, the borehole dimension, and tube thickness, AREVA corrected the reference calibration coeff cient K meas air by a semiempirical factor A define as

A -1 = 1 + C 1 (Ø b -Ø s -2d) 2 [1 + C 2 d] (1)
where Ø b is the borehole diameter, Ø s is the NGRS probe diameter, d is the tube thickness, C 1 = 0.0047ρ f (mm -1 ) is an empiric gamma-ray linear attenuation coeff cient in the f uid of density ρ f (dimensionless parameter), and C 2 = 0.043 (mm -1 ) is an empiric gamma-ray attenuation coeff cient of steel. Note that this correction considers the same f uid in the tube and in the borehole, with a common C 1 attenuation factor and ρ f density, which is not always the case in the field To check the accuracy of this empirical correction, MCNP calculations have been performed with water, mud, or cement f llings. The detector response is modeled using a type-8 tally which allows obtaining the gamma-ray energy deposit spectrum in the NGRS probe. The mud is simulated by water with a density of 1.2g• cm -3 , and bentonite cement is simulated with a density of 1.8g• cm -3 . From the MCNP calculations with material m filli g the borehole and the tube, a correction B is define as

B -1 = K MCNP air K MCNP m . (2)
Table III shows a signif cant inf uence of borehole diameter and f lling f uid. On the other hand, the maximum discrepancy between the semiempiric correction A and the correction B calculated with MCNP is about 26%. Correction C -1 calculated using (4) versus the correction B -1 calculated using MCNP for PVC and aluminum tubes.

F. Influenc of the Tube Thickness

The effect of the tube thickness on the calibration factor has been studied performing simulations for thicknesses of 2, 4, 6, and 8 mm, for a 100-mm-diameter steel tube in a 300-mm-diameter hole when f lling the tube with water, mud, or cement. These simulated conf gurations have also been used to propose new values of the C 1 and C 2 parameters: C 1 = 0.0030ρ f • mm -1 and C 2 = 0.063, 0.012, and 0.007 mm -1 for steel, aluminum, and PVC, respectively.

The results shown in

IV. MULTIPARAMETRIC STUDY

In an attempt to take into account the possibility that different f uids might be present in the borehole and in the tube and to improve the accuracy of the correction to be applied on K meas air and MCNP calculations have been performed for different f uids (air, water, mud, and cement) inside different tubes made of iron, PVC, or aluminum, with a 100-mm diameter and thicknesses of 2, 4, 6 or 8 mm, and inside different boreholes of diameters of 132, 160, 216, or 300 mm.

A multiparametric study has been performed to study correlations between the calibration factor correction and different parameters, including a reduced parameter t define as

t = ρ ft Ø int t -Ø s + ρ t Ø ext t -Ø int t + ρ fb Ø b -Ø ext t ( 3
)
where Ø int t and Ø ext t are the inner and outer diameters of the tube, respectively, ρ ft is the density of the f uid inside the tube, ρ t is the density of the tube, and ρ fb is the density of the f uid between the borehole and the tube. Parameter t, in units of g • cm -2 , represents the mass per unit area that photons have to cross from the borehole border before reaching the NGRS probe. For PVC or aluminum tubes, the correction C to be applied on K meas air is expressed as

C -1 = a 0 + a t t. (4)
Fig. 4 shows that this linear correlation gives a good estimation of the "true correction" calculated with MCNP. The residual standard deviation is 0.04 for a range of correction factors extending from 1.2 to 2.8.

In the case of a 100-mm tube, borehole diameters do not exceed 132 mm in the f eld and the coeff cients of (4) are a 0 = 8.9326E-01 and a t = 2.8889E-02 (g -1 • cm 2 ), with a residual standard deviation of 0.01 on a range of correction factors between 1.20 and 1.35, which represents an accuracy of about 1%.

For steel tubes, photon attenuation is larger and the tube thickness d must also be taken into account to obtain a good linear regression, although it already appears in t.T h e correction for a steel tube is therefore

C -1 = a 0 + a t t + a d d.
(

Fig. 5 shows that this correlation also gives a good estimation of the correction calculated with MCNP. The residual standard deviation is 0.11 for a large range of correction factors extending from 1.2 to 4.2.

Limiting again the correlation (up) to borehole diameters of 132 mm in the case of 100-mm tubes, the coeff cients of (5) are a 0 = 8.8122E-01, a t = 2.6087E-02 (g -1 • cm 2 ), a d = 4.9486E-01 (cm -1 ), with a residual standard deviation of 0.03 on a range of correction factors extending from 1.35 to 2.10, which represents an accuracy of less than 2.2%.

V. C ORRECTION FORMULAS APPLIED

TO GEIGER COUNTERS Since Geiger counters are widely used for gross gammaray counting due to their robustness and simplicity to use, it is of interest to apply the above-presented corrections on gross gamma-ray counting performed with Geiger counter. To this aim, MCNP calculations have been performed replacing the NGRS probe by a 28-mm diameter Geiger Muller probe. Because of prohibitively long calculation time needed to calculate the Geiger detector response, the type-5 point detector tally has been used to get the gamma-ray f ux inside the Geiger Muller tube, instead of using the type-8 energy deposition tally as in the case of the NGRS probe based on a solid-state NaI scintillator. Three bore hole diameters that are commonly used with this kind of probes have been considered, tubing the probe with steel or PVC or using no tubing. The steel tube is 5.5 mm thick and 89-mm diameter, with a density of 7.35 g • cm -3 , whereas the PVC tube is 1.5 mm thick and 32.9-mm diameter, with a density of 1.38 g • cm -3 .C o mparisons between the corrections calculated with MCNP and obtained using (1), (4), or (5) are presented in Table V, showing that the corrections calculated with the same formula parameters as for the NGRS probe are also valid for the Geiger Muller probe. As for NGRS, the multiparametric approach leads to more precise corrections than those of the empirical formula.

VI. CONCLUSION

The MCNP Monte Carlo simulation code has been extensively used to model uranium gamma logging with an NGRS probe. MCNP reproduces with a good accuracy the gross gamma counting measurements performed with the NaI(Tl) gamma scintillator of the probe, such as the calibration coefficie t K (s -1 • ppm -1 U ) measured in the calibration facility of Bessines, France, which is used to convert the signal (s -1 ) in terms of uranium weight fraction (ppm U ): the calibration coefficie t determined by simulation 5.3s -1 • ppm -1 U with 10% accuracy is in good agreement with the one measured in Bessines (and for which no uncertainty was provided), 5.2s -1 • ppm -1 U . The calculations also indicate that the concrete blocks used for measuring the calibration coeff cients measured in Bessines are underestimated by about 10%.

Sensitivity studies have been performed with MCNP, showing that the rock density and mineralogy have a limited influenc on K coeff cient. The uranium concentration induces a signif cant self-absorption effect above a uranium mass fraction of 1%, which leads to an underestimation of the real uranium content up to a factor of 2.6 for 50% of uranium.

The simulation tool has also been used to check the validity of a semiempirical formula used to correct the reference calibration coeff cient measured in Bessines in a tubeless borehole fille with air, for in situ gamma-ray attenuation with different fl ids f lling the borehole and the tube, and with different tubes housing the NGRS probe. The discrepancy between the correction calculated with the semiempirical formula and the one calculated with MCNP can reach up to 26%. In order to improve the accuracy of this correction, a multiparametric analysis has been performed with a large series of simulated data, evidencing linear correlations between the correction and different parameters including information on the borehole diameter, density of filli g f uids, tube material, and thickness. This alternative approach leads to an estimation of the calibration coeff cient correction with a precision better than 3%. This approach has also been tested in the case of a Geiger Muller probe, showing that the same formulas can be used for both NGRS and Geiger probes in view to correct for gamma attenuation.

These simulations are the f rst step of a larger study on uranium gamma logging techniques by CEA and AREVA Mines. Gross count gamma-ray measurement indeed may underestimate the quantity of uranium in the case of disequilibrium in the uranium chain due to in situ leaching techniques (roll front deposits). For a better assessment of the uranium content, next studies will focus on the use of high energy resolution gamma-ray spectroscopy [START_REF] Marchais | Optimization of gamma-ray spectroscopy for uranium mining[END_REF].

Improving

  Gross Count Gamma-Ray Logging in Uranium Mining With the NGRS Probe C. Carasco , B. Pérot, J.-L. Ma, H. Toubon, and A. Dubille-Auchère Abstract-AREVA Mines and the Nuclear Measurement Laboratory of CEA Cadarache are collaborating to improve the sensitivity and precision of uranium concentration measurement by means of gamma-ray logging. The determination of uranium concentration in boreholes is performed with the Natural Gamma Ray Sonde (NGRS) based on a NaI(Tl) scintillation detector. The total gamma count rate is converted into uranium concentration using a calibration coeffi ient measured in concrete blocks with known uranium concentration in the AREVA Mines calibration facility located in Bessines, France. Until now, to take into account gamma attenuation in a variety of boreholes diameters, tubing materials, diameters and thicknesses, fillin flui densities, and compositions, a semiempirical formula was used to correct the calibration coeffi ient measured in Bessines facility. In this paper, we propose to use Monte Carlo simulations to improve gamma attenuation corrections. To this purpose, the NGRS probe and the calibration measurements in the standard concrete blocks have been modeled with Monte Carlo N-Particles (MCNP) computer code. The calibration coeff cient determined by simulation 5.3 s -1

  Monte Carlo N-Particles (MCNP), NaI(Tl) scintillators, uranium mining. C. Carasco, B. Pérot, and J.-L. Ma are with CEA, DEN, Cadarache, Nuclear Measurement Laboratory, F-13108 Saint-Paul-lez-Durance, France (e-mail: cedric.carasco@cea.fr). H. Toubon and A. Dubille-Auchère are with AREVA Mines, 92053 Courbevoie, France.

Fig. 1 .

 1 Fig. 1. MCNP model of a count rate measurement performed with an NGRS probe positioned inside an air-f lled borehole drilled in a 70 cm × 70 cm × 70 cm calibration concrete block.

Fig. 2 .

 2 Fig. 2. Gamma count rate as a function of uranium mass fraction in a 70 cm × 70 cm × 70 cm calibration concrete rock.

Fig. 3 .

 3 Fig. 3. MCNP model and cumulated signal due to uranium present in spheres with an increasing radius for different rocks' density and borehole f llings.

Fig. 4 .

 4 Fig. 4.Correction C -1 calculated using (4) versus the correction B -1 calculated using MCNP for PVC and aluminum tubes.

Fig. 5 .

 5 Fig. 5. Correction C -1 calculated using (4) versus correction B -1 calculated using MCNP for an iron tube.

TABLE I CALCULATED

 I AND MEASURED CALIBRATION COEFFICIENTS K MCNP FOR DIFFERENT TUBES (NATURE AND THICKNESS) AND ATTENUA-

TION CORRECTIONS RELATIVE TO THE TUBELESS CONFIGURATION

TABLE II CALCULATED

 II

CALIBRATION COEFFICIENTS FOR DIFFERENT ROCK MINERALOGIES AND A DENSITY OF 1.6g• cm -3 RELATIVE TO THE CALCULATED CALIBRATION COEFFICIENTS ASSOCIATED WITH CONCRETE

TABLE III CALIBRATION

 III COEFFICIENT K MCNP (s -1 • ppm -1 U ) CALCULATED WITH MCNP FOR DIFFERENT BOREHOLES DIAMETERS FILLED WITH AIR AND CORRECTION FACTORS A -1 AND B -1 FOR DIFFERENT FILLING FLUIDS (WATER,MUD, AND CEMENT)

TABLE IV CALIBRATION COEFFICIENT K

 IVCOEFFICIENT MCNP (s -1. ppm -1 U ) CALCULATED WITH MCNP FOR A 300-mm BOREHOLE DIAMETER AND VARIOUS FILLING FLUIDS AND STEEL TUBE THICKNESS. THE VALUES INDICATED IN BOLD USE (1) WITH THE NEW PROPOSED C 1 AND C 2 PARAMETER VALUES

TABLE V CALIBRATION

 V COEFFICIENT K MCNP (s -1 • ppm -1 U ) FOR GROSS GAMMA-RAY COUNTING EMPLOYING A GEIGER MULLERCOUNTER CALCULATED WITH MCNP FOR DIFFERENT BOREHOLES DIAMETERS,FILLING FLUIDS, AND TUBING