Catherine Lubetzki
email: catherine.lubetzki@aphp.fr

Bernard Zalc
email: bernard.zalc@upmc.fr

Anna Williams
email: anna.williams@ed.ac.uk

Christine Stadelmann
email: cstadelmann@med.uni-goettingen.de

M B Chb- Phd

Christine Stadelmann

MD Bruno Stankoff
email: bruno.stankoff@aphp.fr

Christina Stadelmann

Remyelination in multiple sclerosis: from basic science to clinical translation

come

which improves both nerve conduction velocity and metabolic support to the underlying axon. This confers an advantage to be used as a therapeutic test-bed for other neurodegenerative conditions where white matter abnormalities and demyelination have been identified [START_REF] Nasrabady | White matter changes in Alzheimer's disease: a focus on myelin and oligodendrocytes[END_REF][START_REF] Caso | Insights into White Matter Damage in Alzheimer's Disease: From Postmortem to in vivo Diffusion Tensor MRI Studies[END_REF][START_REF] Rajani | Reversal of endothelial dysfunction reduces white matter vulnerability in cerebral small vessel disease in rats[END_REF] . Here, we will review how far we have come on this therapeutic journey to help progressive MS patients. We will describe evidence that myelin regeneration is useful as neuroprotection, how it occurs and is controlled and how we can translate this knowledge into strategies and clinical trials to enhance remyelination and neuroprotection in people with MS.

We have focused on relevant topics that are novel, but with good quality of evidence, emphasizing therapeutic compounds that have emerged from different screens and been confirmed in different models. For the therapeutic trials update, we selected ongoing or completed registered phase 2 studies targeting remyelination as described below. We searched PubMed for articles published in English, with the search terms "multiple sclerosis", "demyelination", "remyelination", "oligodendrocytes", "neurodegeneration", "neuroprotection", "clinical trial". We favored papers published after 2015, but not excluding previous seminal papers.

1) What is myelin and how is it involved in MS?

Myelin, a specific acquisition of vertebrates, consists of membrane spirally wrapped around large diameter axons, synthesized by oligodendrocytes (OL) in the CNS and Schwann cells in the PNS. Compared to other biological membranes, the biochemical constitution of myelin is unique with 70% lipids and 30% proteins, i.e., the opposite to other membranes. The myelin sheath is interrupted at intervals by nodes of Ranvier.

While in non-myelinated fibres voltage dependent sodium channels (Nav) are evenly distributed along the axons causing the nerve influx to move continuously, in myelinated axons, Nav are clustered at the node of Ranvier and the action potential 'jumps' from one node to the next. This mode of propagation known as saltatory conduction allows rapid transmission of the action potential along the axon (50-to 100fold acceleration compared to unmyelinated axons of similar diameter). Apart from its impact on conduction, OL also provide nutrition to the underlying axons, in particular in the form of lactate, fueling axonal mitochondria, which crucially supports the highly energy demanding axonal transport [START_REF] Fünfschilling | Glycolytic oligodendrocytes maintain myelin and long-term axonal integrity[END_REF][START_REF] Saab | Myelin dynamics: protecting and shaping neuronal functions[END_REF][START_REF] Lee | Oligodendroglia metabolically support axons and contribute to neurodegeneration[END_REF] . K+ clearance through OL-specific K+ channels, was also shown to be critical for axonal function and integrity [START_REF] Schirmer | Oligodendrocyte-encoded Kir4.1 function is required for axonal integrity[END_REF][START_REF] Larson | Oligodendrocytes control potassium accumulation in white matter and seizure susceptibility[END_REF] .

In MS, an adaptive immune response directed against CNS antigens, consisting of both T and B cells likely drives disease pathogenesis. The innate immune system is also involved in initiation and progression of MS (review in [START_REF] Dendrou | Immunopathology of multiple sclerosis[END_REF] ), all leading to demyelination, axon and neuronal loss. In addition to an acute, inflammationdependent axonal pathology, several mechanisms contribute to neurodegeneration of long term demyelinated axons, in particular the redistribution of Nav channels along the denuded axon [START_REF] Waxman | Na+ channel expression along axons in multiple sclerosis and its models[END_REF] , the altered K+ clearance due to oligodendroglial K+ channels loss [START_REF] Schirmer | Differential loss of KIR4.1 immunoreactivity in multiple sclerosis lesions[END_REF] , and the loss of oligodendroglial nutritional support, which increases the energy demand of the denuded axon (review in 2 .) (figure 1).

2) Does remyelination promote neuroprotection?

Remyelination can occur in the CNS, restoring myelin sheaths to axons, aiding nerve conduction but also metabolic support. Several complementary lines of evidence demonstrate that remyelination can therefore confer neuroprotection.

2-1) Evidence from human neuropathology and experimental studies

In MS tissue, neuropathological studies have demonstrated that the density of axons is higher [START_REF] Schultz | Acutely damaged axons are remyelinated in multiple sclerosis and experimental models of demyelination[END_REF] and markers of acute axonal damage (beta-amyloid-precursor protein-APP-positive axons) are lower [START_REF] Kornek | Multiple sclerosis and chronic autoimmune encephalomyelitis: a comparative quantitative study of axonal injury in active, inactive, and remyelinated lesions[END_REF] in remyelinated compared to demyelinated areas, suggesting that remyelination offers neuroprotection. However, in post mortem tissue, it is impossible to unpick whether remyelination has occurred because axons have remained healthy, or whether remyelination has actually resulted in axonal preservation. Experimentally (see Panel 1 on models and review in [START_REF] Lassmann | Multiple sclerosis: experimental models and reality[END_REF] ), in mice where demyelination was induced by cuprizone, Irvine and Blakemore [START_REF] Irvine | Remyelination protects axons from demyelination-associated axon degeneration[END_REF] were among the first to demonstrate that remyelination can protect from axonal degeneration, where spontaneous repair was prevented by X-ray irradiation. Recently, using a genetic approach to accelerate remyelination by ablation of M1 muscarinic receptor, Mei et al.

demonstrated that remyelination helps preserve axonal density and therefore presumably integrity in a mouse experimental auto-immune encephalomyelitis (EAE) model [START_REF] Mei | Accelerated remyelination during inflammatory demyelination prevents axonal loss and improves functional recovery[END_REF] . Furthermore, some experimental studies have demonstrated remyelinationinduced recovery of neurological deficits, such as in a cat model of demyelination [START_REF] Duncan | Extensive remyelination of the CNS leads to functional recovery[END_REF] .

Demyelination of grey matter is particularly abundant in progressive MS, and remyelination might therefore offer additional benefits to conductivity and network function [START_REF] Chang | Cortical remyelination: a new target for repair therapies in multiple sclerosis[END_REF][START_REF] Battefeld | Myelinating satellite oligodendrocytes are integrated in a glial syncytium constraining neuronal high-frequency activity[END_REF] . It is unclear however whether remyelination provides the equivalent amount of neuroprotection to developmental myelin, bearing in mind that the myelin is thinner and shorter. After long term follow up in mice remyelinated after cuprizone treatment, there was axonal loss, suggesting that the neuroprotection may not be full, but with the caveat that cuprizone is also known to be toxic to axons [START_REF] Manrique-Hoyos | Late motor decline after accomplished remyelination: impact for progressive multiple sclerosis[END_REF] .

2-2) Evidence from human imaging studies

Whereas remyelination has been extensively described in experimental models, its natural history and extent remain only partly described in humans with MS due to difficulties in visualizing this in vivo. MRI is useful for MS diagnosis and follow up, but the sequences generally used in the clinical setting lack specificity towards myelin. The introduction of advanced quantitative sequences allows for more direct measures of remyelination in vivo. Magnetization transfer imaging (MTI) indicate the dynamics of demyelination and remyelination in MS lesions [START_REF] Chen | Magnetization transfer ratio evolution with demyelination and remyelination in multiple sclerosis lesions[END_REF] . Interestingly, recovery of the MTI signal was not restricted to recent lesions, but was also observed in older pre-existing ones, supporting the notion that repeated bouts of demyelination and remyelination could take place in the same lesions along the disease course [START_REF] Brown | Imaging of repeated episodes of demyelination and remyelination in multiple sclerosis[END_REF] . Furthermore, complementary MRI sequences based on diffusion weighted sequences or T2 relaxometry may also report myelin changes [START_REF] Petiet | Ultrahigh field imaging of myelin disease models: Toward specific markers of myelin integrity?[END_REF][START_REF] Fujiyoshi | Application of q-Space Diffusion MRI for the Visualization of White Matter[END_REF] . Although these MRI-based techniques hold great promise, they only reflect the physical properties of the brain, without direct molecular specificity.

Positron emission tomography (PET) offers the opportunity to develop a specific and sensitive technique to quantify myelin dynamics by using radiotracers that bind to myelin. Several stilbene and benzothiazole compounds, including the most recently developed fluorinated tracers [START_REF] Irvine | Remyelination protects axons from demyelination-associated axon degeneration[END_REF] F-florbetapir and 18 F-florbetaben, have been shown to bind to CNS myelin [START_REF] Stankoff | Imaging central nervous system myelin by positron emission tomography in multiple sclerosis using [methyl-11 C]-2-(4'-methylaminophenyl)-6hydroxybenzothiazole[END_REF][START_REF] Wu | Longitudinal positron emission tomography imaging for monitoring myelin repair in the spinal cord[END_REF] and could be repurposed to quantify myelin loss and repair in vivo. A pilot study in subjects with relapsing-remitting MS using the benzothiazole derivative [ 11 C]-PIB, confirmed the potential of PET to quantify myelin content in MS lesions and to capture demyelination and remyelination over time. Remyelination was detected within a 2 to 4-month period and was found to be extremely heterogeneous between subjects and lesions. The level of remyelination strongly inversely correlated with disability scores, with subjects with better remyelination profiles having a preserved normalized thalamic volume compared to those with less remyelination [START_REF] Bodini | Dynamic Imaging of Individual Remyelination Profiles in Multiple Sclerosis[END_REF] (Fig. 2), demonstrating its neuroprotective function in vivo. Whether the amount of remyelination is intrinsically different between individuals, or reflective of disease activity or stage is not yet known.

3) Which cells carry out remyelination in the human CNS?

There is currently debate as to which cells of the human adult CNS can and do carry out remyelinationoligodendrocyte precursor cells (OPCs), mature oligodendrocytes (OL) or both. This is of importance as therapeutic strategies to enhance each route to achieve remyelination are likely to be different.

3-1) Insight from experimental models

In the CNS, developmental myelination is accomplished by OL derived from OPCs.

During embryonic and early postnatal development, oligodendrocyte progenitors are generated from neural stem cells (NSC), then transit to the stage of OPCs, before differentiating into OL, which finally mature into myelin-forming OL. Each of these developmental stages is characterized by expression of specific markers [START_REF] Franklin | Regenerating CNS myelin -from mechanisms to experimental medicines[END_REF] . In the adult, OPCs persist, accounting for 5 to 8% of all CNS cells. Experimental models have established using lineage tracing that after demyelination new myelin is synthesized by newly formed OL generated from OPCs [START_REF] Zawadzka | CNS-resident glial progenitor/stem cells produce Schwann cells as well as oligodendrocytes during repair of CNS demyelination[END_REF] which can be attracted to the lesion site by guidance cues, without the need for cell division [START_REF] Piaton | Class 3 semaphorins influence oligodendrocyte precursor recruitment and remyelination in adult central nervous system[END_REF][START_REF] Boyd | Insufficient OPC migration into demyelinated lesions is a cause of poor remyelination in MS and mouse models[END_REF] . In addition to OPCs, subventricular zone NSC present in the adult CNS can differentiate into OL. Recent studies have suggested that remyelination by progenitors from NSC produce myelin sheaths which are thicker and more functional than those derived from OPCs [START_REF] Xing | Adult neural precursor cells from the subventricular zone contribute significantly to oligodendrocyte regeneration and remyelination[END_REF][START_REF] Remaud | Transient hypothyroidism favors oligodendrocyte generation providing functional remyelination in the adult mouse brain[END_REF] . In addition, we now know that mature OL may participate in myelin regeneration, as suggested by studies from demyelinating models in cats and rhesus monkeys, where during clinical recovery mature OLs were seen by electron microscopy to have produced both thick and thin myelin sheaths on similar sized axons, suggestive of normal and remyelinated sheaths respectively [START_REF] Duncan | The adult oligodendrocyte can participate in remyelination[END_REF] . These recent data are in line with the pioneering work of Gumpel showing that OL isolated from adult rat brain can remyelinate axons when grafted into newborn hypo-myelinated Shiverer mouse brain [START_REF] Lubetzki | Myelination by oligodendrocytes isolated from 4-6-week-old rat central nervous system and transplanted into newborn shiverer brain[END_REF] .

3-2) Insight from MS tissue

Although the evidence that remyelination exists in animal models of demyelination is incontrovertible, identification in humans is more complex. Presumed remyelinated lesions in human post mortem brain are identified according to the presence of thinner myelin sheaths, which are distinguishable from normal appearing white matter on Luxol Fast Blue histological stains as paler "shadow" plaques (fig. 3A).

Remyelinated areas may be complete ("shadow plaque") or positioned on the edge of a demyelinated lesion. These areas have been shown by electron microscopy to have thinner myelin sheaths [START_REF] Périer | Electron microscopic features of multiple sclerosis lesions[END_REF] and shorter internodal lengths [START_REF] Prineas | Remyelination in multiple sclerosis[END_REF][START_REF] Chang | Premyelinating oligodendrocytes in chronic lesions of multiple sclerosis[END_REF] (both characteristic of remyelinated lesions in animal models [START_REF] Bunge | Ultrastructural study of remyelination in an experimental lesion in adult cat spinal cord[END_REF][START_REF] Blakemore | Pattern of remyelination in the CNS[END_REF] ). However, on a single post mortem human sample, it is difficult to prove definitively that shadow plaques result from a dynamic remyelination process, and areas of pale myelin staining may also represent areas where myelin is instead breaking down -so called "initial lesions"-. This appears unlikely, since, if there is active breakdown of myelin, an innate immune system response is expected, while in contrast few microglia/macrophages are generally found in remyelinated areas. One needs to be very meticulous at defining areas of remyelination, so not to confuse them with areas of edema, or even areas of grey matter, where there are fewer myelin sheaths. If we assume that we can extrapolate the characteristics of animal model remyelination to human, areas of established remyelination exist on pathological examination and reflecting the evidence from in vivo imaging, as described above [START_REF] Schmierer | Magnetization transfer ratio and myelin in postmortem multiple sclerosis brain[END_REF][START_REF] Bodini | Dynamic Imaging of Individual Remyelination Profiles in Multiple Sclerosis[END_REF] . In this context, cells expressing breast carcinoma amplified sequence 1 (BCAS1), a marker for a subpopulation of myelinating oligodendrocytes, were detected in post-mortem MS tissue [START_REF] Fard | BCAS1 expression defines a population of early myelinating oligodendrocytes in multiple sclerosis lesions[END_REF] . Although rarely found in completely demyelinated lesions, clusters of BCAS1 + oligodendrocytes were detected at the lesion borders and in lesion areas characterized by pale myelin staining, providing further evidence that these areas indeed represent areas of remyelination (figure 3 B-D).

In chronic demyelinated white matter MS lesions, OPCs and newly formed myelinating OL have been identified using specific markers [START_REF] Chang | Premyelinating oligodendrocytes in chronic lesions of multiple sclerosis[END_REF][START_REF] Fard | BCAS1 expression defines a population of early myelinating oligodendrocytes in multiple sclerosis lesions[END_REF] and an increased density of sub-ventricular zone progenitors (expressing the polysialylated form of neural cell adhesion molecule (PSA-NCAM)) has been reported in MS compared to control samples [START_REF] Nait-Oumesmar | Activation of the subventricular zone in multiple sclerosis: evidence for early glial progenitors[END_REF] , suggesting a precursor-led process, similar to that in development and in animal models of remyelination. However, new data using carbon dating of oligodendrocytes have suggested that myelin repair in the adult CNS might depend mostly on pre-existing oligodendrocytes. Testing of nuclear bombs released [START_REF] Schirmer | Differential loss of KIR4.1 immunoreactivity in multiple sclerosis lesions[END_REF] C which is integrated into genomic DNA by dividing cells in concentrations matching those in the atmosphere, allowing inference of the age of cells and cell turnover by their [START_REF] Schirmer | Differential loss of KIR4.1 immunoreactivity in multiple sclerosis lesions[END_REF] C content [START_REF] Yeung | Dynamics of oligodendrocyte generation and myelination in the human brain[END_REF] . Using this technique on sorted nuclei from post mortem MS human brains (with CC1 and SOX10 antibodies to identify nuclei from mature OL and OPCs, respectively), there were some patients with aggressive MS where there was evidence of many newly formed oligodendrocytes. However, in most patients apparent 'shadow plaques' showed [START_REF] Schirmer | Differential loss of KIR4.1 immunoreactivity in multiple sclerosis lesions[END_REF] C levels consistent with older cells (rather than newly generated ones), and no increase in the number of mature oligodendroglia or OPC proliferation, suggesting that pre-existing (older) OL (or OPCs that did not divide before maturing) may have formed the new myelin sheaths [START_REF] Yeung | Dynamics of oligodendrocyte generation in multiple sclerosis[END_REF] . The novel implication here is that pre-existing OL may be able to extend processes and form new myelin sheaths to remyelinate axons in MS. Some tentative further support for this comes from studies of heterogeneity of human oligodendroglia from single nuclei RNAsequencing from human post mortem brain. Here, fewer OPCs were found in MS brain compared to controls, and there were heterogeneous functional states of mature myelinating OL, including those producing many RNAs involved in the process of (re)myelination and others with more RNAs involved in signaling and presumed metabolic support [START_REF] Jäkel | Altered human oligodendrocyte heterogeneity in multiple sclerosis[END_REF] [START_REF] Chang | Premyelinating oligodendrocytes in chronic lesions of multiple sclerosis[END_REF][START_REF] Stangel | Achievements and obstacles of remyelinating therapies in multiple sclerosis[END_REF] . The steps needed for achieving successful remyelination may therefore differ depending on the lesion type. For each step, key molecular pathways have been identified: PDGF and FGF induce cell division [START_REF] Woodruff | Platelet-derived growth factor regulates oligodendrocyte progenitor numbers in adult CNS and their response following CNS demyelination[END_REF][START_REF] Wang | Contrasting effects of mitogenic growth factors on myelination in neuron-oligodendrocyte co-cultures[END_REF] , several guidance cues shown to be re-expressed after demyelination influence OPC recruitment towards the lesion, Semaphorin 3F being attractant [START_REF] Piaton | Class 3 semaphorins influence oligodendrocyte precursor recruitment and remyelination in adult central nervous system[END_REF] , in contrast to the repellent effect of Semaphorin 3A

and Netrin 1 [START_REF] Piaton | Class 3 semaphorins influence oligodendrocyte precursor recruitment and remyelination in adult central nervous system[END_REF][START_REF] Tepavčević | Early netrin-1 expression impairs central nervous system remyelination[END_REF] . Major progress has also been made in the identification of cues and pathways favoring or inhibiting the OPC maturation process. Among the inhibitors of OPC maturation are the Notch signaling pathway [START_REF] Mathieu | Demyelination-Remyelination in the Central Nervous System: Ligand-Dependent Participation of the Notch Signaling Pathway[END_REF] , Lingo-1 [START_REF] Mi | LINGO-1 negatively regulates myelination by oligodendrocytes[END_REF] , the Wnt pathway [START_REF] Fancy | Dysregulation of the Wnt pathway inhibits timely myelination and remyelination in the mammalian CNS[END_REF][START_REF] Dai | Stage-specific regulation of oligodendrocyte development by Wnt/β-catenin signaling[END_REF] , muscarinic receptor signaling [START_REF] Mei | Micropillar arrays as a high-throughput screening platform for therapeutics in multiple sclerosis[END_REF] , hyaluronan [START_REF] Back | Hyaluronan accumulates in demyelinated lesions and inhibits oligodendrocyte progenitor maturation[END_REF] , chondroitin sulfate proteoglycan [START_REF] Pu | The extracellular matrix: Focus on oligodendrocyte biology and targeting CSPGs for remyelination therapies[END_REF] , and fibrinogen [START_REF] Petersen | Fibrinogen Activates BMP Signaling in Oligodendrocyte Progenitor Cells and Inhibits Remyelination after Vascular Damage[END_REF] . The mechano-responsive ion channel PIEZO1 has been identified as an

inhibitor of maturation, with potential role in age-related loss of function of OPC [START_REF] Segel | Niche stiffness underlies the ageing of central nervous system progenitor cells[END_REF] . In contrast, activation of the retinoid X receptor on OPCs favors oligodendroglial maturation [START_REF] Huang | Retinoid X receptor gamma signaling accelerates CNS remyelination[END_REF] , as well as thyroid hormone [START_REF] Hartley | Myelin repair stimulated by CNS-selective thyroid hormone action[END_REF] and Vitamin D [START_REF] De La Fuente | Vitamin D receptor-retinoid X receptor heterodimer signaling regulates oligodendrocyte progenitor cell differentiation[END_REF] . Optimal expression of different miRNAs regulate the oligodendroglial maturation process [START_REF] Emery | Transcriptional and Epigenetic Regulation of Oligodendrocyte Development and Myelination in the Central Nervous System[END_REF] . Recent results have highlighted the role of the cytoskeleton in OL maturation, through RhoGTPase Vav3 [START_REF] Ulc | The guanine nucleotide exchange factor Vav3 modulates oligodendrocyte precursor differentiation and supports remyelination in white matter lesions[END_REF] . From this very active research field, and with the caveat that these different steps of remyelination might differ between experimental models and MS, several therapeutic targets have emerged, paving the way to translation.

4-2) Role of neuronal activity in myelination and remyelination

The role of neuronal activity in myelination was shown by adding neurotoxins either blocking or stimulating electrical activity in myelinating CNS neuron-glial co-cultures, confirmed in vivo in the optic nerve after silencing electrical activity by intra-vitreal injection of tetrodotoxin [START_REF] Demerens | Induction of myelination in the central nervous system by electrical activity[END_REF] , then later corroborated for peripheral nervous system myelination [START_REF] Stevens | Control of myelination by specific patterns of neural impulses[END_REF] . More than 10 years later, optogenetics has allowed this question to be revisited showing that stimulation of neuronal activity promotes myelination in the mammalian brain [START_REF] Gibson | Neuronal activity promotes oligodendrogenesis and adaptive myelination in the mammalian brain[END_REF] and demonstrating that electrically active axons are preferentially myelinated [START_REF] Koudelka | Individual Neuronal Subtypes Exhibit Diversity in CNS Myelination Mediated by Synaptic Vesicle Release[END_REF][START_REF] Mitew | Pharmacogenetic stimulation of neuronal activity increases myelination in an axon-specific manner[END_REF] . Although it has been shown in different neuronal populations and in different species [START_REF] Koudelka | Individual Neuronal Subtypes Exhibit Diversity in CNS Myelination Mediated by Synaptic Vesicle Release[END_REF][START_REF] Stedehouder | Activity-Dependent Myelination of Parvalbumin Interneurons Mediated by Axonal Morphological Plasticity[END_REF] , the mechanisms supporting the influence of neuronal activity on myelination remain only partially understood. There is no evidence that this effect is mediated through axo-glial synapses between axons and OPC [START_REF] Bergles | Glutamatergic synapses on oligodendrocyte precursor cells in the hippocampus[END_REF] , although these may have an indirect role by favoring maturation of cells along the oligodendroglial lineage.

Alternatively, the electrical activity-related effect on myelination may be mediated through vesicular glutamate release [START_REF] Wake | Nonsynaptic junctions on myelinating glia promote preferential myelination of electrically active axons[END_REF] along axons, activating signaling pathways involved in local translation of the myelin gene MBP [START_REF] Wake | Control of Local Protein Synthesis and Initial Events in Myelination by Action Potentials[END_REF] . Such adaptive myelination has been hypothesized to be involved in experience-associated CNS plasticity (see review in [START_REF] Fields | A new mechanism of nervous system plasticity: activity-dependent myelination[END_REF] ). In addition, the role of electrical activity has also been demonstrated in different experimental models of remyelination [START_REF] Gautier | Neuronal activity regulates remyelination via glutamate signalling to oligodendrocyte progenitors[END_REF][START_REF] Ortiz | Neuronal activity in vivo enhances functional myelin repair[END_REF] , and this has paved the way for designing translational studies in humans aimed at stimulating electrical activity to foster remyelination (see below). In line with these results is the demonstration that exercise increases remyelination rate following toxin-induced demyelination in mice [START_REF] Jensen | Multimodal Enhancement of Remyelination by Exercise with a Pivotal Role for Oligodendroglial PGC1α[END_REF] , a result which might possibly bring new insight into the known influence of physical activity on wellbeing in MS.

It is not trivial to reconcile that electrically active axons are preferentially myelinated, but only axons are myelinated (and not dendrites or other cell processes) [START_REF] Lubetzki | Even in culture, oligodendrocytes myelinate solely axons[END_REF] and that proper myelin sheaths can also be formed around non-electrically active synthetic fibers of the size of axons [START_REF] Bechler | CNS Myelin Sheath Lengths Are an Intrinsic Property of Oligodendrocytes[END_REF] . One explanation, suggested by ffrench-Constant [START_REF] Bechler | Intrinsic and adaptive myelination-A sequential mechanism for smart wiring in the brain[END_REF] is that there may be two programs of myelination: an intrinsic myelination program, where myelination is dictated by physical cues and an adaptive program, in which myelin sheaths are modified by electrical activity.

4-3) Immune cells, the newcomers in remyelination

Several studies have suggested that both the adaptive and innate immune systems influence myelination and remyelination. For adaptive immunity, mice lacking CD4+ or CD8+ T cells remyelinate to a much lesser extent than in normal mice [START_REF] Bieber | Efficient central nervous system remyelination requires T cells[END_REF] , regulatory T cells enhance CNS remyelination [START_REF] Dombrowski | Regulatory T cells promote myelin regeneration in the central nervous system[END_REF] and Th17 lymphocytes inhibit remyelination [START_REF] Baxi | Transfer of myelin-reactive th17 cells impairs endogenous remyelination in the central nervous system of cuprizone-fed mice[END_REF] .

Grafting lymphocytes from different MS patients into murine CNS demyelinated lesions influence remyelination, with inter-individual heterogeneity [START_REF] Behi | Adaptive human immunity drives remyelination in a mouse model of demyelination[END_REF] . For innate immunity, microglia and blood-derived macrophages are present in the inflamed CNS, which can be distinguished in rodent models, but with more difficulty in the human damaged CNS [START_REF] Zrzavy | Loss of 'homeostatic' microglia and patterns of their activation in active multiple sclerosis[END_REF][START_REF] Peferoen | Activation status of human microglia is dependent on lesion formation stage and remyelination in multiple sclerosis[END_REF] . Microglia are highly heterogeneous with a continuous spectrum of activation states [START_REF] Ransohoff | A polarizing question: do M1 and M2 microglia exist?[END_REF][START_REF] Stratoulias | Microglial subtypes: diversity within the microglial community[END_REF] . They are often implicated in neural cell damage [START_REF] Masuda | Spatial and temporal heterogeneity of mouse and human microglia at single-cell resolution[END_REF] , and in this context it was recently suggested that the envelope protein Env of a human endogenous retrovirus HERV might drive microglial-mediated axonal damage [START_REF] Kremer | pHERV-W envelope protein fuels microglial cell-dependent damage of myelinated axons in multiple sclerosis[END_REF] . In contrast, studies have suggested that microglia/macrophages can have a regenerative function, and in particular can promote remyelination [START_REF] Kotter | Macrophage depletion impairs oligodendrocyte remyelination following lysolecithin-induced demyelination[END_REF][START_REF] Lloyd | The pro-remyelination properties of microglia in the central nervous system[END_REF] . This regenerative impact is partly related to their capacity to clear myelin debris, crucial for myelin wrapping. Aging slows remyelination, which may be in part due to decreased phagocytic ability, which can be rejuvenated by innate immune cells from young animals delivered by parabiosis [START_REF] Ruckh | Rejuvenation of regeneration in the aging central nervous system[END_REF] .

Efficient remyelination requires death of pro-inflammatory microglia followed by repopulation to a pro-regenerative state [START_REF] Lloyd | Central nervous system regeneration is driven by microglia necroptosis and repopulation[END_REF] , where they can secrete regenerative factors (including galectin 3, activin A, LIF, TNF) promoting OPC recruitment and differentiation 88,99,100,101,102 . In MS, activated microglia can be detected even in the normal-appearing white matter, whereas in active and slowly expanding lesions a drastic reduction of the homeostatic microglial marker P2RY12 has been reported [START_REF] Zrzavy | Loss of 'homeostatic' microglia and patterns of their activation in active multiple sclerosis[END_REF] .

Pre-clinical and clinical studies have suggested that the pro-remyelinating potency of some compounds might actually be acting by targeting (directly or indirectly) microglia 103,104 .

Our better understanding of the machinery of myelin regeneration has led to discovery of target pathways to manipulate to improve it.

5) Progress to remyelinating strategies in MS

5-1) Identification of potential pro-remyelinating candidates

Initial screening strategies have been used to discover potential pro-remyelination candidate therapies via in vitro assays amenable to high-throughput of compounds and combinatorial chemistry. During the last 10 years, there have been several screens of bioactive small molecules on expression of myelin markers by primary rat optic nerve derived OPCs 105 or mouse pluripotent epiblast stem-cell-derived OPCs 106 . These methods do not discriminate between drugs enhancing OPC proliferation and differentiation of OPC into OL or whether these differentiated OL can form myelin sheaths. To test the latter is more complex, needing use of myelinating OL/neuron cocultures, for example using transgenic lines in which reporter expression is driven by a regulatory sequence turned on only in myelinating OL 107 , or perhaps using the binary indicant for myelination using micropillar arrays 108 . To validate these hits in remyelination, the most commonly used animal model is rodent EAE or the use of toxin-induced demyelination (see panel 1 on the experimental models). Despite their advantages these rodent models are not suitable to screen large numbers of compounds, but are rather a semi-final in vivo test of a handful of candidate molecules pre-selected by in vitro screening. Intermediate animal models have been developed: a novel screening platform for identifying potential remyelination-promoting compounds has been developed using zebrafish larvae 109 . A Xenopus laevis transgenic line has also been developed allowing conditional ablation of myelinating oligodendrocytes. After completion of demyelination, spontaneous remyelination occurs, and can be accelerated by adding drugs to the swimming water. This model constitutes a robust medium-throughput screening platform for myelin regeneration therapeutics 110 .

These experimental strategies have led to the identification of promising lead compounds to enhance remyelination, both repurposed and new compounds, targeting diverse pathways. This includes modulators of sphingosine-1-phosphate, muscarinic M1, histamine H3, retinoid X receptor or opioid kappa receptors; inhibitors of gammasecretase/Notch or leukotriene pathways; modulators of hormone signaling (androgens, estrogens, T3-T4); antipsychotics (quetiapine); antifungal (miconazole); steroids (clobetasol). Some of these compounds were shown to enhance OL maturation independently of their canonical targets, by enhancing the production of 8,9 unsaturated sterols, suggesting a unifying signaling mechanism for OL maturation enhancers 111 . This was shown for instance for muscarinic antagonists (clemastine, benztropine), selective estrogen modulators (tamoxifen, bazedoxifene) or antifungal drugs (miconazole) 112 , but not for thyroid hormones or retinoid X receptor  modulators that target transcription factors. Finally, it was recently demonstrated that fasting mimetic metformin can restore age-related impaired differentiation capacity of OPC 113 .

Overall, despite the very large number of identified promyelinating drugs only a few have been applied to date in phase 2 clinical trials.

5-2) Update on clinical trials targeting myelin regeneration in MS

We interrogated two clinical trials registers: "clinical trial.gov" and "EU clinical trial register" excluding phase 1 studies and studies for which the last posted information dated more than 4 years ago, with no publication since. Text search terms were "remyelination" "repair" "multiple sclerosis", "optic neuritis". We selected trials in which remyelination/repair evaluation was either a primary or secondary outcome and excluded studies in which outcomes related to remyelination were part of exploratory or post-hoc analysis. Trials targeting neuroprotection directly (phenytoin, amiloride, ACTH, Sprint MS (ibudilast), MS SMART (multi-arm evaluating fluoxetine, amiloride, riluzole), biotin) were not included.

As shown in table 1, most trials enrolled patients with optic neuritis, with a few including patients with relapsing MS. Focusing on the optic nerve to assess repair is attractive as it allows i) an evaluation of remyelination through the quantification of latency of visual evoked potentials (VEP) (a reduced latency being indicative of remyelination)

and ii) a quantitative assessment of retinal neuronal loss using optical coherence tomography (OCT). In addition, optic neuritis is a frequent symptom of MS often occurring during the early phase of the disease. It is not known, however, whether findings in the optic nerve extrapolate to other CNS areas or patients with MS. The few completed trials on patients with RMS (MS with relapses, with either a relapsingremitting or a progressive phenotype) have not demonstrated clinical impact (clinical outcome was the primary outcome in one single study evaluating opicinumab, NCT01864148) 114 . As for imaging outcomes, a small but significant MTR increase (which might correspond to remyelination) has been reported in two studies (GNbAC1, NCT02782858 and GSK239512, NCT01772199) 115,116 . In addition, GNbAC1-treated RRMS patients showed a reduced number of black holes and reduced brain atrophy 115 .

Among the trials including patients with optic neuritis, only two have been completed so far, and have included patients with acute (opicinumab, NCT01721161) and chronic (clemastine, NCT02040298) optic neuritis (this latter trial with a cross-over design). These two trials 117,118 showed some positive results, with reduced latency of the VEP, although only significant in the per-protocol population (and not in the intention to treat population) in the opicinumab study. Even if a solid conclusion from these trials is premature, these very recent results are exciting for MS therapeutic development, aimed at reducing disability progression, the major unmet need in MS treatments.

Conclusions and Future Directions

Recently, great progress has been made in understanding the biological mechanisms regulating remyelination success or failure and for the identification of candidate molecules promoting such repair. This is leading to novel strategies to promote remyelination in MS, in addition to targeting the auto-immune component of the disease. Already, in addition to electrophysiological devices, over 50 compounds have been identified as potent candidates for pro-remyelination trials, including repurposing of approved drugs. However, we are facing novel challenges to best design and optimally evaluate clinical trials for remyelination. Beyond classical short-term parallel arms studies, cross-over trials may indicate the sustainability of repair following drug withdrawal. However, this may result in very complex trials when several drugs, or dose-efficacy responses are analyzed. As heterogeneous endogenous remyelination profiles have been described among patients with MS and outcomes reflecting repair might be influenced by individual-related fluctuations, pre-therapeutical run-in periods preceding placebo-controlled phases could also help to capture the real pharmacological effect of tested drugs. Finally, for the optimal strategy for pivotal phase III trials, adaptive designs might be employed to offer flexible methods allowing preplanned changes after interim analysis 119 . However, such studies need sensitive outcomes than can be assessed in a short time frame for interim analysis. Further challenges include: i) which tools should be applied for remyelination assessment (neurovisual outcomes? Imaging tools covering the whole brain? Blood biomarkers?);

ii) which MS patients should be included in trials (relapsing remitting or progressive?

With still ongoing inflammatory demyelination or stable under highly efficient diseasemodifying therapy? With already efficient endogenous remyelination capacities or a global repair failure? With minor disability in order to prevent disability worsening or with high disability in order to promote recovery?); iii) which clinical metrics should be assessed to reflect remyelination and predict subsequent disability worsening? This latter point will be of crucial importance once a compound reaches the pivotal phase III stage and may be a candidate for regulatory approval. Global disability scales such as EDSS represent consensual outcomes, but more focused reproducible metrics such as walking, processing speed and hand function, reflecting highly myelinated networks, might also be considered as primary outcomes. Whether a remyelinating strategy should improve preexisting disability (a strategy that implies viable demyelinated axons still permissive to repair) or prevent subsequent disability worsening (which would attest of the neuroprotective role of myelin regeneration) also remain key unanswered questions. Overall, there is a need for strong methodological research that will combine and test these complementary options as secondary or exploratory objectives to allow us to choose the most powerful study designs that will best detect repair success.

Otherwise, we risk dismissing drugs that actually work by simply measuring the wrong outcomes in the wrong patients. However, that the field has reached this stage is success itself and should provide hope for people with MS and their physicians. Lysophosphatidylcholine (LPC) damages the myelin sheaths at the site of injection, followed by efficient remyelination (for details see the very comprehensive review in [START_REF] Lassmann | Multiple sclerosis: experimental models and reality[END_REF]

Figure 1 :

 1 Figure 1 : Schematic representation of the different steps leading to disability progression in MS, as well as proposed strategies to prevent neurodegeneration.

Figure 2 :

 2 Figure 2 : Individual remyelination profiles measured in vivo with a combination of MRI and [ 11 C] PIB-PET associated with thalamic atrophy (courtesy of Matteo Tonietto and Benedetta Bodini). An illustrative MS patient shown in A and B has been evaluated with a combination of MRI and [ 11 C] PIB-PET at study entry (A) and after 4 months (B). White matter lesions detected by MRI are displayed in white. Regions of demyelination detected by PET within lesions at study entry (A) are coloured in red. From the longitudinal follow up, individual indices of dynamic demyelination (not shown) and individual indices of dynamic remyelination were calculated; (B) areas in blue indicate voxels that were demyelinated at study entry and recovered normal myelin content at month 4. As described 26 from a pilot cohort of 19 patientswith a relapsing form of MS, patients with a high remyelination index were classified as "good remyelinators" (n=9), whereas patients with a low remyelination index were classified as "bad remyelinators" (n=10). (C) Thalami were segmented and their normalized volumes calculated.(D) Good remyelinators showed less thalamic atrophy compared to bad remyelinators.

Figure 3 :

 3 Figure 3 : BCAS1+ oligodendrocytes map areas of active remyelination in chronic multiple sclerosis. (A) Luxol fast blue/periodic-acid Schiff (LFB/PAS) histochemistry and (B, C, D) BCAS1 immunohistochemistry of subcortical white matter containing a chronic demyelinated lesion with an area of active remyelination (aRM). (C) Area of active remyelination depicted at higher magnification. (D) BCAS1+ oligodendrocyte in the demyelinated lesion, close to the edge of the area of active remyelination. Arrowheads indicate BCAS1 + cells.

Figure 4 :

 4 Figure 4 : schematic representation of the mechanisms/pathways involved in recruitment and maturation of oligodendrocyte precursor cells

PANEL 1 :

 1 Experimental modelsroles and limitations for the study of remyelination Current EAE (experimental auto-immune encephalomyelitis) models rely on encephalitogenic T cells either induced in the animal (active) or transfused into the animal (passive). Although reflecting some important features of MS (inflammation and axonal loss), their usefulness for understanding demyelination and remyelination is limited because demyelination and/or neurodegeneration is not always seen, predicting the size and localization of lesions is difficult and demyelination and remyelination can occur at the same time. Some chronic EAE models have been developed but most still insufficiently mimic progressive MS pathology. Viral models are complex and not well adapted to study de-and remyelination. Toxin models, although lacking the inflammatory component of MS, are extremely useful to unravel the mechanisms of demyelination and remyelination. Cuprizone, a copper chelator, induces OL apoptosis and demyelination, mostly in corpus callosum and cortex, leading to robust remyelination initially, which is impaired by longer exposure. Ethidium bromide induces OL and astrocyte death, with focal demyelination at the site of injection, followed by extensive remyelination.

Table 1 :

 1 Trials (phase 2) targeting remyelination RR-MS : relapsing-remitting MS; RMS : MS with relapses (either relapsing-remitting or progressive disease); ON : optic neuritis: VEP : visual evoked potentials; RNFL : retinal nerve fiber layer; MTR : magnetization transfer ratio; PP : per-protocol population; ITT : intention to treat population; MOA : mechanism of action;

	Mab : monoclonal antibody

Acknowledgements :

France: We thank ARSEP foundation, FRM (Fondation pour la Recherche Médicale), Bouvet-Labruyere Family, INSERM-DHOS, APHP (Assistance Publique des Hôpitaux de Paris), the program "Investissements d'Avenir" ANR-10-IAIHU-06, NeurATRIS, ANR grant BRECOMY to B.Z. and NRJ foundation for their precious support related to basic and clinical research on remyelination in Paris. UK: We thank the MS Society UK, MRC Regenerative Medicine Platform and the UK Dementia Research Initiative. Germany : CS was supported by the Deutsche Forschungsgemeinschaft (DFG) transregional collaborative research centers (CRC) 43 "The brain as a target of inflammatory processes" and 274 "Checkpoints of CNS recovery", STA 1389/5-1, the DFG under Germany's Excellence Strategy (EXC 2067/1-390729940), the Gemeinnützige Hertie Foundation, the Deutsche Multiple Sklerose Gesellschaft (DMSG), and the National MS Society (USA).

NOVARTIS, personal fees from ROCHE, grants from MedDay, outside the submitted work. Bruno Stankoff reports grants and personal fees from ROCHE, SANOFI-GENZYME, and MERCK-SERONO , personal fees from NOVARTIS, BIOGEN and TEVA, outside the submitted work


Henri Boutin
email: boutin@ircam.fr

John Smith

Joe Wolfe

'Warming up' a wind instrument: the time-dependent effects of exhaled air on the resonances of a trombone Running title: 'Warming up' a wind instrument

Keywords: brass instrument, warming up, wind instrument, temperature, pitch

To study the effect of 'warming up' a wind instrument, the acoustic impedance spectrum at the mouthpiece of a trombone was measured after different durations of playing. When an instrument filled with ambient air is played in a room at 26-27 °C, the resonance frequencies initially fall. This is attributed to ! in the breath initially increasing the density of air in the bore and more than compensating for increased temperature and humidity. Soon after, the resonance frequencies rise to near or slightly above the ambient value as the effects of temperature and humidity compensate for that of increased ! . The magnitudes and quality factors of impedance maxima decrease with increasing playing time whereas the minima increase. Using the measured change in resonance frequency, it proved possible to separate the changes in impedance due to changes in density and changes in acoustic losses due to water condensing in the bore. When the room and instrument temperature exceed 37 °C, condensation is not expected and, experimentally, smaller decreases in magnitudes and quality factors of impedance maxima are observed. The substantial compensation of the pitch fall due to ! by the rise due to temperature and humidity is advantageous to wind players.

I. INTRODUCTION

Players of wind instruments 'warm up' their instruments by playing or breathing into them before tuning: they know that, all else equal, a cold, dry instrument usually plays at lower pitch than it does when filled with warm, humid, exhaled air. During extended sections of rests in ensemble music, they often breathe quietly into the instrument to warm it to ensure that, on reentry, they will be playing an instrument already filled, at least partly, with warm, humid, exhaled air.

The speed of sound in air increases with increasing temperature and humidity and decreases with the increasing concentration of . (The expansion of the instrument itself CO

over the small temperature change produced by playing is negligible.) Consequently, and all else equal, increased temperature and humidity raise the frequencies of resonances and thus the pitch of notes played. Increases in playing pitch of 1.2 to 2.6 cents per °C increase in temperature are reported for brass instruments [START_REF] Young | Dependence of tuning of wind instruments on temperature[END_REF]. The increase in during playing of a phrase would be expected, all else equal, to lower the pitch, while humidity is expected to increase it (see calculations by [START_REF] Fuks | Prediction of pitch effects from measured CO2 content variations in wind instrument playing[END_REF]Balasubramanian and Kausel, 2015).

Measurements on (already warm) oboe and bassoon show decreases in pitch of order 10 cents (0.6% in frequency) in the 10 s of playing following inhalation; these are attributed to increased concentration [START_REF] Fuks | Measurements of exhaled air effects in the pitch of wind instruments[END_REF].

To a non-musician, effects of less than one percent (the size of the effects reported here) may seem small, but to a musician, one percent is a sixth of a semitone and, for a sustained note, an important error in intonation.

By adjustment of blowing pressure and other control parameters that players would include in the term 'embouchure', players of modern brass instruments can 'lip up or down', i.e. raise or lower the pitch over a total range of roughly two semitones [START_REF] Boutin | Trombone lip mechanics with inertive and compliant loads ("lipping up and down[END_REF] and thus can usually correct quickly for expected or heard errors in intonation. (Trombonists also have the slide available.) Consequently, simple measurements of the played pitch, especially for experienced musicians, are not expected to reveal the effects of breath composition or temperature in the absence of compensation. Nevertheless, it is interesting for both scientists and musicians to know the magnitude of these effects.

There have been several previous measurements of the input impedance of a trombone filled with cool, dry air (e.g. Backus, 1976;[START_REF] Caussé | Input impedance of brass musical instruments-Comparison between experiment and numerical models[END_REF][START_REF] Braden | Trombone bore optimization based on input impedance targets[END_REF]. One of the motivations for the present study is that knowledge of the impedance in playing conditions can allow determination of the acoustic flow into the instrument [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF]2020).

CO 2 CO 2 ! 3
This paper reports measurements of the impedance spectrum of the bore of a trombone, initially filled with dry, ambient air, but then played for differing durations. A preliminary set of measurements was briefly reported previously [START_REF] Boutin | Lip motion, the playing frequency of the trombone and upstream and downstream impedances[END_REF] as part of a different study. Those results are reanalyzed here, as are a more detailed set of results over a larger range of conditions. All but one set of measurements were made at room temperature (between 26 °C and 27 °C). The other set was made in a laboratory heated to 39 °C so as to avoid the effect of condensation of water in the bore of the instrument.

II. MATERIALS AND METHODS

A. The instrument

The trombone (Yamaha YBL 321) and a modified mouthpiece were used and described in a previous study [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF]. The mouthpiece had the same volume and rim diameter as a normal mouthpiece but was modified for other experiments conducted at the same time. The B♭-F 'trigger' mechanism was used in its shorter configuration and the main slide had its minimum length throughout. Players call this 'first position': it is used to play notes in an incomplete harmonic series, including B ♭2 (nominally 117 Hz at A440), F3, B ♭3, D4 etc. The tuning slide was maintained at 18 mm from its shortest position (a typical position for playing at A440). The player for the detailed study was the first author, who has very limited experience playing the trombone, but has no unusual respiratory issues and plays with an air flow rate typical of experienced players [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF]. For the larger preliminary study, measurements were made on three more additional players two of whom had orchestral or band experience on brass and one of whom was a beginner. For the data reported here, no measurements were made of the players-only of the instrument, after different periods of being played.

! 4

B. The trombone input impedance

The input impedance of the trombone bore, called , was measured using an impedance head mounted in a plane plate that was sealed to the rim of the mouthpiece with petroleum jelly [START_REF] Boutin | Relationships between pressure, flow, lip motion and upstream and downstream impedances for the trombone[END_REF]. An acoustic current source was located next to a microphone (4944A, Brüel & Kjaer, Denmark) connected to a pre-amplifier and a FireWire audio interface (MOTU 828, Cambridge, MA), see Fig. 1. This impedance head [START_REF] Smith | The acoustic impedance of the Boehm flute: Standard and some non-standard fingerings[END_REF] was calibrated by measuring the impedance of an acoustically infinite duct, 142 m long and 7.8 mm diameter. The broadband signals used for calibration and measurement were sums of sine waves between 50 Hz and 1.8 kHz, with a spacing of 0.67 Hz (= 44.1 kHz/ ) corresponding to a time window lasting 1.5 s. This was a compromise between resolution in frequency and time; the 0.67 Hz frequency resolution allowed accurate determination of the maxima and minima, whilst the 1.5 s time resolution was needed for the extrapolation of measurements back to the cessation of playing. Measurements were conducted in a lab at temperature of 26.3 ± 0.3 °C and 55 ± 6% relative humidity, except for one series. That series was conducted with the temperature of the laboratory and the trombone raised to 39 ± 2 °C with relative humidity 45 ± 6%. This temperature was chosen to avoid water condensation in the bore of the instrument when played. The instrument was initially at ambient temperature and flushed with ambient air and equilibrated in the lab at ambient temperature and humidity. The impedance head was connected to the mouthpiece and the input impedance was measured before each note was played. The trombone was then played for a predetermined duration. For the 3 s and 10 s measurements, a single sustained note was played. For the 30, 60, 120 and 240 s measurements, the player played long notes but briefly inhaled as needed. The slide was left in first position and the player mainly played the first two notes of the harmonic series (B ♭2 and F3). The impedance head was then connected and an impedance measurement started within 3 s of the cessation of playing; each impedance measurement comprised 32 cycles of samples at 44.1 kHz, consequently each cycle lasted 1.49 s and the total measurement lasted 48 s. The instrument was then flushed with ambient air. This protocol of a measurement before and after each playing was repeated three times for each note duration. Thus 36 impedance measurements were obtained at 26.3 °C and another 28 at 39 °C.

The measurement of each cycle took 1.49 s and this limits the frequency resolution.

Because the proportional change is of interest here, the resulting uncertainty has a greater effect on the low-frequency impedance peaks. On the other hand, the eighth and higher peaks are weaker and so less sharp, see Fig. 3a, which introduces uncertainty at high frequencies.

Analysis showed that peaks three to seven gave least variance among measurements. (These also fall towards the middle of the instrument's range: the first peak is not used, and those above the eighth are rarely used.) In the following analysis, averages over the third to seventh peaks are used.

Around each maximum and minimum of each impedance measurement, a cubic spline interpolation was used to achieve a frequency resolution of 0.1 Hz. The associated Q factor is estimated as the ratio between the peak frequency and its 3-dB bandwidth. A finer cubic spline interpolation with a frequency resolution of 0.001 Hz was used to achieve a precision lower than 0.01. The frequency and magnitude of each impedance maximum and minimum and the Q factor of each impedance maximum were then calculated for each cycle of the measurement. The values at the moment when playing ceased (i.e. 3 s before the first cycle of measurement) were determined by linear regression over the following 32 contiguous cycles during the measurement period, as shown by the extrapolations to t = 0 in Fig. 2. Note that the magnitudes of the minima (especially those after 240 s of playing) are more scattered from cycle to cycle than the other data. This may be due to the difficulty of quickly measuring the magnitudes of the impedance minima with a variation less than 1% in a duct with water condensing on the walls. (The magnitudes of the minima and maxima are taken from the same measurement of and the minima are typically about 30-40 times smaller than the maxima-see Fig. 3-with a corresponding decrease in measured precision).

III. RESULTS AND DISCUSSION

When the player commences playing an instrument that had previously been flushed

with dry air and equilibrated in the lab at ambient temperature and humidity, the input impedance of the instrument can be affected via the following three mechanisms.

The first is that the temperature rises in the bore and the gas composition changes; this will change the density ρ of the air in the bore. (The gas composition and temperature will vary with time and also with distance along the bore.) The speed of sound is given by , where denotes atmospheric pressure and γ denotes the heat capacity ratio, whose variation with composition is shown later to be several times less than that due to changes in density. For a simple open cylindrical duct of effective length L, the frequencies of impedance extrema are given by and where n = 0,1,2,3, ... Thus, all else equal, an increase in ρ will decrease the resonance frequencies.

The characteristic impedance of a simple cylindrical duct is given by = ,

where A denotes the cross-sectional area of the duct. An increase in ρ or will increase the magnitude of the characteristic impedance, and consequently increase the magnitudes of

Z bore ( f ) Z bore T c = γP 0 /ρ P 0 f max = (2n + 1)c /4L f min = nc /2L Z 0 Z 0 ρ γP 0 /A γ Z 0 ! 8
the maxima and minima.

The second occurs when water vapour in the bore has begun to condense on the walls:

this can increase the acoustic losses [START_REF] Hickey | Effects of thermal diffusion on sound attenuation in evaporating and condensing gas-vapor mixtures in tubes[END_REF][START_REF] Coltman | Acoustical losses in wet instrument bores[END_REF]. All else equal, increased acoustic losses will decrease the magnitude of maxima, increase the magnitude of minima and broaden the resonances, i.e. reduce their Q factors.

The third is a much smaller effect due to loss by sound radiation in air as a function of composition; this should be negligible in comparison with the wall losses [START_REF] Morse | Theoretical Acoustics[END_REF].

A. Measurements at ambient temperature: 26 to 27 °C At constant atmospheric pressure, the effects of increasing T and water concentration in the bore would both on their own lower the density of air and so increase the speed of sound;

this would tend to increase the frequency of each bore resonance. However, concentration in the bore also rises, which tends to lower the speed of sound. (Oxygen concentration also falls, but because has a molar mass close to the average for air, the effect of falling concentration is expected to be modest. Molar masses for water, air, oxygen, and are 18, 29, 32 and 44 respectively. Figure 3 shows measurements on a section of the impedance spectrum of the trombone when played for 10, 30, 60 and 240 s. The lowest resonance, which is not played, does not occur in the frequency range of these measurements.

The resonance frequencies initially decrease for short playing durations, until they begin to increase; this is consistent with an initial increase in density produced by increasing concentration until it is counteracted by increasing T and humidity. However, from consideration of gas density alone, a decrease in frequency produced by an increase in density would be accompanied by a corresponding increase in the magnitudes of and hence .

CO 2 O 2 O 2 CO 2 kg . kmol -1 CO 2 Z 0 Z max ! 9
The measurements show that the actually decrease for longer playing duration, presumably as a consequence of increased losses. The increase in after 30 s is also consistent with increased losses. These losses are discussed below. Figure 4 shows the average of the data at ambient room temperature obtained by the extrapolation procedure explained in the Methods section for the 36 measurements at 26.3 °C and the 40 measurements in a preliminary study at 27 °C, reported in a conference paper [START_REF] Boutin | Lip motion, the playing frequency of the trombone and upstream and downstream impedances[END_REF]. It shows the mean percentage changes in the frequencies and magnitudes of the peaks in ! after playing for 3, 10, 30, 60, 120 and 240 s.

Both and initially decrease when playing starts, the lowest frequency being produced after playing for 10 s -see Fig. 4a. Over this short time, the effect of on the speed of sound dominates over those of temperature and humidity. For the longer durations, the players inhaled at least once. Consequently, the concentration and effect of did not increase monotonically over time, while the effects of temperature and humidity presumably did increase and eventually more than compensated for the effect of . This is consistent with the observed slow increase in and after 10 s. (The fact that increased concentration significantly cancels the effect of increased temperature and humidity is a fortunate one for wind players.) Changes in density should affect and equally; over all measurements the ratio of the changes in to the preceding was 0.99967 ± 0.00126.

There is a nearly monotonic decrease in the magnitude of the impedance maxima with increasing playing time and the magnitude of the minima increases in an almost monotonic fashion -see Fig. 4b. After 240 s duration of playing, the magnitudes of the extrema have changed by around 4%, in opposite directions. Assuming that the observed initial decrease in frequency is caused by an increase in density, a corresponding increase in , and hence and , would be expected. The change due to density can be calculated from Fig. 4a, neglecting that due to specific heat ratio. The effect of density on can then be removed from the measured magnitude of the impedance extrema, leaving only the changes produced et al. (2000) and [START_REF] Coltman | Acoustical losses in wet instrument bores[END_REF] (see also [START_REF] Slaton | Comment on "Acoustical losses in web instrument bores[END_REF]) identify a significant energy loss mechanism in instrument bores when water is present and the humidity is at or close to saturation: water can condense and evaporate in each cycle of a standing wave. To eliminate condensation, a set of measurements were conducted in a lab that had been heated to 39 °C, with the instrument equilibrated at that temperature.

Z bore f max f min CO 2 CO 2 CO 2 f max f min CO 2 f max f min f min f max Z 0 Z max Z min

Hickey

Z max Z min Z max Z max m 3 s -1 MPa -1 Z max ! 13
B. Measurements at elevated temperature: 39 °C

The 39 °C measurements show that the mean frequencies of the maxima and minima are initially reduced only slightly, if at all, for most playing durations (see Fig. 6a). However, the changes are generally not statistically significant at the 95% confidence level. In this experiment, a negligible change in temperature with playing time is expected. However, the fact that the initial decrease in frequency at 39 °C is smaller than that at ambient temperature can be explained by humidity: the water concentration at saturation is 1.83 times higher at body temperature (37 °C) than at 26.3 °C (Engineering Toolbox, 2020), so the humidity offsets the ! -induced fall in frequency to a greater extent at the higher temperature.

The rise in frequency towards 240 s might be explained if the player at this stage had reached his steady-state respiration, breathing more often at high temperature than he would for shorter phrases or lower temperature, and were thus keeping the ! concentration lower than for shorter intervals.

The smaller changes in resonant frequencies also mean that changes in impedance magnitude due to density changes will be smaller than at ambient temperature: see Fig. 7.

However, for playing durations greater than 10 s, rather than decreasing as for ambient temperature, the mean of now slightly increases with increasing duration of playing, although this increase is not statistically significant at the 95% level. The air in the lungs at 37 °C is close to saturated at this temperature. The relative humidity of this air falls further below saturation when it enters the warmer instrument at 39 °C. So, no condensation is expected inside a trombone at 39 °C and hence, unlike at ambient temperature, there is no expected loss due to condensation-evaporation cycles, even though the humidity rises.

The Q values for 39 °C fall by about 2% in the first 3 s (as soon as the bore is largely 289, 1.330 and 1.400 (Bhattacharjee, 2020;Engineering Toolbox, 2020). The speed of sound is given by or, for constant pressure,

Z bore Z max Z min CO 2 kg . kmol -1 H 2 O O 2 kg . kmol -1 kg . kmol -1 γ CO 2 H 2 O c = γP 0 /ρ 1 + Δc c = ( 1 + Δγ γ ) 1 2 ( 1 + Δρ ρ )
At constant temperature and pressure, consider only small increases and in fractional molar concentrations of and in the air respectively, where these gases replace air in the usual mixture of nitrogen and oxygen. The adiabatic ratio is changed by and the density by an analogous expression. From substitution and retaining only zeroth and first order terms, the speed of sound is increased by a factor! . (If instead ! and ! replace pure nitrogen or oxygen, the numerical results are only a little different.)

For inhaled and expired air under normal breathing, is typically about 4% by volume or mole [START_REF] Buszewski | Human exhaled air analytics: biomarkers of diseases[END_REF], which on its own would give a fall in the speed of sound of a little more than 1%. However, the difference is likely to be smaller on average in this experiment, because the players began exhaling into the instrument as soon as they finished inhaling, which would give exhaled gas whose initial concentration would be lower than normal.

If the temperature change were ! and uniform, the speed of sound would increase by a factor about ! . Taking ! , and using ! for an effective, overall change in T, the speed of sound and so the frequency are proportional to ! So the proportional change in frequency would be ! . Thus a 1% increase in frequency would require either ! +6°C, ! -3%, or ! +6% or some linear combination of these. For example, Fig. 4 could be explained by a ! concentration of 2-4% that is gradually offset by a combination of a few degrees increase in effective temperature and a few percent increase in water concentration. Once there is condensation, a rise ! 17

in ! usually means a rise in absolute humidity, because the water content at saturation rises strongly with ! .

IV. CONCLUSIONS

Playing the dry instrument at room temperature, the frequency of the impedance peaks of the bore fall by about 0.6% in the first 10 seconds, as the density of the air in the bore increases. This is a result of in the breath more than compensating for increased temperature and humidity. Over the next few minutes, the frequencies rise to close to or a little above their original values, as the effects of humidity and temperature overcome that of the . The magnitude and quality factors of impedance maxima decrease with increasing playing time, consistent with enhanced wall losses due to water condensing in the bore. This effect is attributed to losses associated with latent heat exchange between humid air and wet walls. Playing in a room at 39 °C, and therefore without condensation, the effect on the magnitudes of impedance extrema and the Q factor is substantially reduced.

60(

  FIG. 1. Schematic (not to scale) of the impedance spectrometer used to measure ! for

!

  FIG. 2. (Color online) Examples of the extrapolation procedure used to estimate the

FIG. 3

 3 FIG. 3.measured between 50 Hz and 1 kHz showing the second and higher

  FIG. 5. Separation of the percentage changes in the mean values of and into those

  FIG. 6. (Color online) The mean percentage changes in the frequencies (a), magnitudes (b) of

  Δγ = ΔC ( γ CO 2γ air ) + ΔH ( γ H 2 Oγ air )

					ΔC	ΔH
			CO 2	H 2 O
					1-0.30ΔC + 0.16ΔH
	CO 2	H 2 O
					ΔC
					CO 2
				ΔT
		1 +	ΔT 2T	T~300 K	ΔT
					1 +	ΔT 600 K	.
				Δf/f = ΔT /600 K -0.30ΔC + 0.16ΔH
				ΔT ≅	ΔC ≅	ΔH ≅
					CO 2

  2),470-480. Balasubramanian, S., and Kausel, W. (2015). "Pitch shifts in wind instruments due to changes in air composition," Proceedings of the Third Vienna Talk on Music Acoustics, Vienna, Austria, pp. 16-19.Bhattacharjee. S. "Properties of various ideal gases (at 300 K)" (San Diego State Univ.) https://www.ohio.edu/mechanical/thermo/property_tables/gas/idealgas.html downloaded 19 July 2020.

	T
	T
	CO 2
	CO 2
	! 18

! 16

ACKNOWLEDGMENTS

We thank the Australian Research Council for support and our volunteer subjects. Backus, J. (1976). "Input impedance curves for the brass instruments," J. Acoust. Soc. Am.


B Cenki-Tok

P F Rey

D Arcay

Strain and retrogression partitioning explain long-term stability of crustal roots in stable continents

Away from tectonically active regions, the continental crust has an average thickness of 40 ± 1 km. Yet, it shows a remarkable variability from 25 to 65 km, comparable to that of the most tectonically active regions. Here, we consider the problem of the formation and preservation of anomalous deep crustal roots in stable intracontinental regions. Using two-dimensional thermomechanical experiments, we show that the interplay between partial melting, the formation of garnet-pyroxene-bearing rocks, and their strain rate-dependent retrogression result in the preservation of thick and strong crustal roots. We argue that it is the partitioning into narrow regions of strain, retrogression, and weakening coupled into a positive feedback loop that explains why

INTRODUCTION

The crust-mantle transition is generally well-defined on geophysical images, enabling detailed knowledge of crustal thickness at global and regional scales [START_REF] Prodehl | 100 years of seismic research on the Moho[END_REF]. Discarding tectonically active regions, the thickness of the stable continental crust has a global average of ~40 km (±1 km error on the calculated average crustal thickness) [START_REF] Christensen | Seismic velocity structure and composition of the continental crust: A global view[END_REF]Fig. 1A). Yet, crustal root anomalies as much as 65 km deep exist in all stable continents (e.g., [START_REF] Szwillus | Global crustal thickness and velocity structure from geostatistical analysis of seismic data[END_REF] from cratonic regions such as the Baltic and Canadian Shields [START_REF] Clark | How the crust meets the mantle: Lithoprobe perspectives on the Mohorovic discontinuity and crust-mantle transition[END_REF][START_REF] Artemieva | EUNAseis: A seismic model for Moho and crustal structure in Europe, Greenland, and the North Atlantic region[END_REF]; Fig. 1B) to Proterozoic and Paleozoic terranes such as Antarctica and Australia [START_REF] Salmon | The Moho in Australia and New Zealand[END_REF][START_REF] An | S-velocity model and inferred Moho topography beneath the Antarctic Plate from Rayleigh waves[END_REF][START_REF] Ebbing | Earth tectonics as seen by GOCE-Enhanced satellite gravity gradient imaging[END_REF]Fig. 1C). Some of these crustal roots have been interpreted as inherited regions of thick orogenic crust (e.g., [START_REF] Fischer | Waning buoyancy in the crustal roots of old mountains[END_REF][START_REF] Studinger | Subice geology inland of the Transantarctic Mountains in light of new aerogeophysical data[END_REF], others as mantle-derived mafic roots accreted below a continental crust of normal thickness (e.g., [START_REF] Thybo | Moho and magmatic underplating in continental lithosphere[END_REF]. In both cases, we expect that the enhanced heat flow would thermally weaken the deep crust, enabling efficient viscous flow to relax gradients of crustal thickness and to flatten the Moho on a regional scale [START_REF] Clark | How the crust meets the mantle: Lithoprobe perspectives on the Mohorovic discontinuity and crust-mantle transition[END_REF][START_REF] Beaumont | Himalayan tectonics explained by extrusion of a low-viscosity crustal channel coupled to focused surface denudation[END_REF][START_REF] Nábělek | Underplating in the Himalaya-Tibet collision zone revealed by the Hi-CLIMB Experiment: Science[END_REF]Rey et al., 2010). Hence, the persistence over hundreds of millions of years of thick crustal roots poses an intriguing problem. Although high heat flow produces migmatites and granites that contribute to the transient weakening of the deep continental crust, it also produces drier and stronger garnet-pyroxene rocks such as granulites (e.g., [START_REF] Jackson | Metastability, mechanical strength, and the support of mountain belts[END_REF]. Upon cooling, hydration, and deformation, these stronger rocks may be Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 3 of 16 retromorphosed into weaker amphibolitic gneisses. Here, we explore through twodimensional (2-D) thermomechanical experiments how the interplay between mechanical weakening due to partial melting, strengthening and density increase due to the crystallization of garnet-pyroxene assemblages, and post-orogenic weakening due to retrogression may impact the long-term crustal thickness. Our results suggest that thick crustal root anomalies could be the remnants of dry garnet-pyroxene-bearing rocks that survived post-orogenic extension and retrogression. These garnet-pyroxene-bearing crustal-scale boudins strengthen the lower crust and reduce its capacity to flow. Our experiments are a first step toward explaining why relaxed orogenic crust may maintain heterogeneities in crustal thickness hundreds of millions of years after orogeny has ceased.

NUMERICAL EXPERIMENTS, CODE, AND MODEL SETUP

Our 2-D thermomechanical experiments consider a 360-km-wide orogenic plateau with a 70-km-thick crust (i.e., the thickness of the Tibetan Plateau; [START_REF] Nábělek | Underplating in the Himalaya-Tibet collision zone revealed by the Hi-CLIMB Experiment: Science[END_REF] above 40 km of mantle (Fig. 2). A layer of air-like material with low viscosity and low density is imposed on top of the crust to accommodate the development of surface topography. The plateau experiences extensional deformation as the crust returns to a normal thermomechanical state. Extensional-velocity boundary conditions are imposed on both vertical walls of the model. We have tested slow (0.18 cm yr -1 ) and fast (1.8 cm yr -1 ) velocities, delivering a strain rate averaged over the length of the model of 3 × 10 -16 s -1 and 3 × 10 -15 s -1 respectively. Horizontal boundaries of the model are free slips. The thermal properties of the material combined with constant basal heat flow and constant top temperature deliver an initial steady-state geotherm leading to a Moho temperature of Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 4 of 16 ~900 °C (Fig. 2). We select from the literature plausible visco-plastic parameters (see the GSA Data Repository 1 ) so the mechanical behavior of the modeled lithosphere depends on temperature, strain rate, deviatoric stress, and accumulated strain. Details of modeling procedures, rheological and thermal parameters, as well as the input Python script are available in the Data Repository.

In order to explore the interplay between partial melting, the formation of stronger garnet-pyroxene-bearing rocks, and their retrogression into weaker amphibolite facies rocks, we parameterize three first-order metamorphic phase transitions. The first phase change simulates partial melting and its feedback on density, viscosity, and temperature [START_REF] Rey | Extension rates, crustal melting, and core complex dynamics[END_REF]; see the Data Repository). A second phase change with feedback on density and viscosity occurs at temperature T = 777 °C to simulate prograde amphibolite to garnet-pyroxene rock reaction [START_REF] Philpotts | Principles of Igneous and Metamorphic Petrology[END_REF]. Finally, a third phase change with feedback on density and viscosity accounts for the retrogression of garnetpyroxene-bearing rocks back into amphibolite facies rocks. This third phase change occurs at T = 777 °C as well and for a strain rate ≥10 -14 s -1 . Our model implicitly assumes that water is available. Therefore, retrogression is contingent upon strain rate, which simulates the metastability of dry high-grade rocks during exhumation. This strainrate threshold is in the range of expected strain rates measured in orogenic shear zones [START_REF] Sassier | Direct measurement of strain rates in ductile shear zones: A new method based on syntectonic dikes[END_REF][START_REF] Boutonnet | Ductile strain rate measurements document long-term strain localization in the continental crust[END_REF][START_REF] Fagereng | New perspectives on 'geological strain rates' calculated from both naturally deformed and actively deforming rocks[END_REF]. Rock solidus depends on rock fertility and availability of fluid. Hence, we have tested different solidii for the continental crust and the garnet-pyroxene-bearing rocks (Data Repository) in the range commonly accepted for these rock types. For the continental crust, we have tested a solidus representative of fertile metapelites with a melting temperature at room pressure Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 5 of 16 of 650 °C (Figs. 3A and 3B;[START_REF] White | Calculation of partial melting equilibria in the system Na 2 O-CaO-K 2 O-FeO-MgO-Al 2 O 3 -SiO 2 -H 2 O (NCKFMASH)[END_REF], and a solidus representative of lessfertile rocks with a melting temperature at room pressure of 720 °C (Fig. 3C; [START_REF] Rey | Fragmentation of active continental plate margins owing to the buoyancy of the mantle wedge[END_REF]. For the dry garnet-pyroxene-bearing crust, we use a melting temperature at room pressure of 790 °C representative of refractory granulites [START_REF] Cenki-Tok | Formation and preservation of biotiterich microdomains in high-temperature rocks from the Antananarivo Block, Madagascar[END_REF]. We use Underworld, a well-tested open-source finite-element code (https://underworld2.readthedocs.io/), to solve the equations of conservation of momentum, mass, and energy for an incompressible fluid on a Cartesian Eulerian mesh [START_REF] Moresi | Computational approaches to studying non-linear dynamics of the crust and mantle[END_REF][START_REF] Beucher | UWGeodynamics: A teaching and research tool for numerical geodynamic modelling[END_REF].

RESULTS

When a slow divergent velocity is imposed (0.18 cm yr -1 ), the crust thins homogeneously, the Moho remains flat, and deformation is dominated by pure shear strain whether melt and/or garnet-pyroxene rocks are present or not (Fig. DR1 in the Data Repository). In contrast, under faster extensional velocities (1.8 cm yr -1 ), the experimental outcome depends on phase changes. When the formation of strong garnetpyroxene rocks is not allowed, partial melting makes the deep crust hot and mobile, which allows the formation of a migmatitic dome (Fig. 3A). In the partially molten dome, finite strain ellipses are strongly flattened, with a vertical long axis indicating the presence of a vertical high-strain zone separating two sub-domes. This double-dome geometry has been well documented [START_REF] Rey | Viscous collision in channel explains double domes in metamorphic core complexes[END_REF][START_REF] Rey | The origin of contractional structures in extensional gneiss domes[END_REF][START_REF] Korchinski | Numerical investigation of deep-crust behavior under lithospheric extension[END_REF].

Figures 3B and3C show a different result when prograde garnet-pyroxene rock formation and retrogression into amphibolite are allowed. In the case where retrogression does not occur (Fig. DR2A), the crust thins homogeneously. As the formation of garnet-pyroxene rocks strengthens the deep crust, its capacity to flow is much reduced and the upper crust Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 6 of 16 remains mechanically coupled to the mantle. Extensional deformation is more distributed and heterogeneous as documented by the crustal-scale pinch-and-swell strain pattern, as well as the finite strain field imaged by the finite strain ellipses (Fig. 3B). As strain rate controls the retrogression of garnet-pyroxene rocks (Figs. DR2B andDR2C), we observe that retrogression is partitioned into the pinch regions where strain rate is higher, whereas garnet-pyroxene pods are preferentially preserved in the swell regions where strain rate is lower and below the threshold required to activate retrogression. Because retrogression leads to weakening, favoring strain localization and therefore higher strain rates, there is a positive feedback loop between strain rate, retrogression, and weakening. When the crustal solidus is that of a fertile metapelite, portions of the lower crust are partially molten and able to flow under gravitational stresses, whereas flow is inhibited in the strong garnet-pyroxene rock pods (Fig. 3D). Raising the solidus temperature of the continental crust by 70 °C results in a similar outcome except that there are no more partially molten domains within the continental crust (Fig. 3C). Because of the formation of garnet-pyroxene rock pods, the Moho presents a winding geometry with crustal thickness variations of as much as 50%, from 35 to 53 km. After 25% of extension and thinning, we have left these experiments to thermally and mechanically relax over 180 m.y. under fixed boundary conditions (i.e., setting the kinematic boundary condition to 0 cm yr -1 ). We observe that the heterogeneity of crustal thickness persists throughout this long cooling history.

DISCUSSION

Our numerical experiments suggest that strain rate-dependent retrogression that typically localizes along ductile shear zones cutting through high-grade rocks may Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 7 of 16 explain how remnants of thick and strong orogenic crust can survive orogenic collapse.

These regions can be ~50% thicker than the adjacent crust and as narrow as a few tens of kilometers across, and survive for hundreds of millions of years. Anomalous deep crustal roots have been imaged in stable intracontinental regions all around the globe. In the eastern Canadian Shield, for example, the Lithoprobe project (https://lithoprobe.eos.ubc.ca/) has documented several crustal roots [START_REF] Clark | How the crust meets the mantle: Lithoprobe perspectives on the Mohorovic discontinuity and crust-mantle transition[END_REF].

Below the Torngat orogen along the eastern Canadian Shield, a Paleoproterozoic crustal root as much as 50 km deep, 15 km deeper that the average adjacent crust, and ~80 km wide and >200 km long has been imaged on seismic profiles (Fig. 1B; [START_REF] Funck | Wide-angle seismic transect across the Torngat Orogen, northern Labrador: Evidence for a Proterozoic crustal root[END_REF]. It is interesting to note that this Paleoproterozoic crustal root is bounded to the north and east by major shear zones [START_REF] Clark | How the crust meets the mantle: Lithoprobe perspectives on the Mohorovic discontinuity and crust-mantle transition[END_REF]. In the Baltic Shield, along an Archean-Paleoproterozoic suture, the Moho reaches a depth of ~60 km over a region centered on southern Finland [START_REF] Artemieva | EUNAseis: A seismic model for Moho and crustal structure in Europe, Greenland, and the North Atlantic region[END_REF]. In central Australia, even though this continent has been tectonically relatively stable for the past 300 m.y., crustal roots reaching 65 km depth have been imaged as deep regions of diffuse reflectivity over circular domains a few hundred kilometers in diameter (Fig. 1C; [START_REF] Kennett | AusMoho: The variation of Moho depth in Australia[END_REF][START_REF] Salmon | The Moho in Australia and New Zealand[END_REF]. In Antarctica, a series of crustal roots as much as 60 km deep have been documented between Dronning Maud Land and Gamburtsev Subglacial Mountains [START_REF] An | S-velocity model and inferred Moho topography beneath the Antarctic Plate from Rayleigh waves[END_REF][START_REF] Ebbing | Earth tectonics as seen by GOCE-Enhanced satellite gravity gradient imaging[END_REF]. In peninsular India, made up of Archean to Paleozoic terranes, the Moho depth varies from ~38 km below the southernmost tip of India's Proterozoic Southern Granulite terrane, to 50 km below the Archean Dharwar craton in semicircular regions ~250 km in diameter [START_REF] Reddy | Seismic images of the continental Moho of the Indian shield[END_REF][START_REF] Das | Crust and shallow mantle structure of south India by inverting interpolated receiver function with surface wave dispersion[END_REF]. The structure and nature of the lower crust below the Southern Granulite Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 8 of 16 terrane is heterogeneous, but because the middle and upper crust shows a constant thickness of 20-25 km, this variability must be accommodated by variation in thickness of the lower crust (18-32 km; [START_REF] Das | Crust and shallow mantle structure of south India by inverting interpolated receiver function with surface wave dispersion[END_REF].

The gravimetric and seismic characteristics of these crustal roots suggest the presence of garnet-pyroxene-bearing rocks. For example, in Canada, crustal roots showing P-wave velocities >7 km s -1 led Cook et al. (2010) to propose that in the absence of later tectonic reworking, the variations in Moho depth originate solely from rheological variations. In southern India, crustal roots display compressional-wave velocities that are systematically >7 km s -1 [START_REF] Reddy | Seismic images of the continental Moho of the Indian shield[END_REF], and shearwave velocities between 4 and 4.2 km s -1 [START_REF] Das | Crust and shallow mantle structure of south India by inverting interpolated receiver function with surface wave dispersion[END_REF]. The contrasting density and seismic characteristics between granitic rocks and/or amphibolite facies gneisses (<2700 kg m -3 and <6.4 km s -1 ) and higher-grade garnet-pyroxene-bearing rocks (>2800 kg m -3 and >6.6 km s -1 ; [START_REF] Christensen | Seismic velocity structure and composition of the continental crust: A global view[END_REF][START_REF] Artemieva | EUNAseis: A seismic model for Moho and crustal structure in Europe, Greenland, and the North Atlantic region[END_REF] suggest that deep crustal roots are made of the latter [START_REF] Williams | Garnetforming reactions in felsic orthogneiss: Implications for densification and strengthening of the lower continental crust[END_REF]. This proposition is compatible with the seismically diffuse boundary that is commonly observed between the lower crust and the mantle [START_REF] O'reilly | Moho vs crust-mantle boundary: Evolution of an idea[END_REF]. Because the petrophysical properties of garnet-pyroxene-bearing rocks are intermediate between the ones of the crust and the mantle, a garnet-pyroxene-rich lower crust would explain the seismic properties of the transition between the crust and the mantle observed in Peninsular India for example [START_REF] Reddy | Seismic images of the continental Moho of the Indian shield[END_REF].

Importantly, in all of these examples, crustal roots are interpreted as inherited remnants of ancient orogenic crust that have survived gravitational collapse and the flattening of the Moho. We propose that these strong orogenic crustal roots owe their Publisher: GSA Journal: GEOL: Geology DOI:10.1130/G47301.1 Page 9 of 16 survival to the presence of retrogressed and therefore weaker adjacent crusts in which deformation is strongly partitioned. The positive feedback loop between strain, retrogression, and weakening insures that deformation remains localized into retrogressed domains, isolating and protecting garnet-pyroxene-bearing pods that remain largely immune to deformation.

CONCLUSIONS

In this study, we have explored through 2-D thermomechanical modeling how the interplay between partial melting, the formation of garnet-pyroxene high-grade rocks, and strain rate-dependent retrogression could explain the long-term preservation of deep crustal roots in stable continents. Though 2-D experiments are sufficient to illustrate how strain rate, retrogression, and weakening can explain the preservation of thick roots, future work involving 3-D experiments will allow investigation of triclinic boundary conditions. Our experiments show that following the formation of high-grade rocks in deep orogenic crusts, extension is partitioned into regions where strain, retrogression, and weakening are coupled into a positive feedback loop. This results in the preservation of thick, dense, and strong garnet-pyroxene-rich pods, separated by retrogressed and attenuated pinched regions. The strong high-grade pods form crustal-scale boudins that are able to survive through the orogenic relaxation phase and over a duration of >100 m.y. As a result, the equilibrated orogenic crust preserves deep crustal roots similar to those documented in all stable continents. These results are first steps toward understanding of the feedback between metamorphic reactions and deformation. In the future, 3-D models involving porous flow and surface processes will allow a more detailed understanding of these systems.

Strain and retrogression partitioning explain long-term stability of crustal roots in stable continents

Bénédicte Cenki-Tok

Figure 1 .

 1 FIGURE CAPTIONS

Figure 2 .

 2 Figure 2. Model geometry and initial conditions, as well as geotherm, viscosity, and

Figure 3 .

 3 Figure 3. Fast-velocity modeling results (1.8 cm yr -1 extension speed) at average strain rate of 3 × 10 -15 s -1 and 25% extension. Colors are the same as in Figure 2. (Model A)

  Figure 1

  1,2 , P.F. Rey 2 and D. Arcay 1

TABLE DR1 .

 DR1 THERMAL AND MECHANICAL PARAMETERS

	Parameter	Continental Crust	Retrogressed Amphibolites	Garnet-Pyroxene CC	Upper Mantle	Fault
	Reference temperature (K)	293	293
	Dislocation creep viscous rheology	Wet quartzite a	Wet quartzite a	Dry Maryland Diabase b	Wet dunite c	0.1 *Wet quartzite a
	Reference density (kg•m -3 )	2600	2600	2950	3370	2600
	Thermal expansivity (K-1)	-1.00E-04	-1.00E-04	-1.00E-04	2.80E-05	-1.00E-04
	Compressibility (Pa -1 )	8.00E-11	8.00E-11	-	-	8.00E-11
	Heat capacity (J K -1 kg -1 )	1000	1000	1000	1000	1000
	Thermal diffusivity (m 2 s -1 )	9E-07	9E-07	9E-07	9E-07	9E-07
	Latent heat of fusion (kJ kg -1 K -1 )	250	250	250	-	250
	Radiogenic heat production (W m -3 ) d	5.00E-07	5.00E-07	5.00E-07	-	5.00E-07
	Melt fraction density change e	0.13	0.13	-	-	0.13
	Solidus term 1 (K)	923	923	1063	-	923
	Solidus term 2 (K Pa -1 )	-1.20E-07	-1.20E-07	-1.20E-07	-	-1.20E-07
	Solidus term 3 (K Pa -2 )	1.20E-16	1.20E-16	1.20E-16	-	1.20E-16
	Liquidus term 1 (K)	1423	1423	1563	-	1423
	Liquidus term 2 (K Pa -1 )	-1.20E-07	-1.20E-07	-1.20E-07	-	-1.20E-07
	Liquidus term 3 (K Pa -2 )	1.60E-16	1.60E-16	1.60E-16	-	1.60E-16
	Friction coefficient	0.44	0.44	0.44	0.44	0.44
	Softened friction coefficient	0.088	0.088	0.088	0.088	0.088
	Cohesion (MPa)	15	15	15	15	1.5
	Softened cohesion (MPa)	3	3	3	3	0.3
	Pre-exponential factor (MPa -n s -1 )	5.00E-06	5.00E-06	5.05E-22	70000	5.00E-06
	Stress exponent (n)

ACKNOWLEDGMENTS

We acknowledge funding from the European Union's Horizon 2020 research and innovation program under grant agreement 793978. This research was undertaken with the assistance of resources from the National Computational Infrastructure (NCI), through the National Computational Merit Allocation Scheme supported by the Australian Government; the Pawsey Supercomputing Centre (Perth, Australia) with funding from the Australian Government and the Government of Western Australia, and support from the Australian Research Council through the Industrial Transformation Research Hub grant ARC-IH130200012. We thank Julian Giordani and Romain Beucher for their expert support with Underworld (https://underworld2.readthedocs.io/). We thank Chris Clark for editorial handling, as well as Gregory Dumond and two anonymous reviewers for their constructive reviews.

Additional parameters:

Model Size: 360 km length (241 nodes, constant spacing) -120 km thick (81 nodes, constant spacing) i.e. 15 km air-like material, 70 km crust, 35 km upper mantle. The marker density is uniform (60 per grid cell). A weak prismatic region dipping 45 °C simulates a detachment in the upper crust Basal heat flow is set at 0.015 W.m -2 Velocities tested: 1.8 cm.y -1 (fast) or 0.18 cm.y -1 (slow) and Isostasy is activated Prograde amphibolite to garnet-pyroxene rock phase change set at 1050 K Retrograde garnet-pyroxene rock to amphibolite phase change set at 1050 K and 10-14 s -1 strain rate Moho temperature at the start of the model is 883 °C Solidus and liquidus are defined by a polynomial function of pressure (P):

The density of the continental crust changes according to T and P: