Novelty of Sphingolipids in the Central Nervous System Physiology and Disease: Focusing on the Sphingolipid Hypothesis of Neuroinflammation and Neurodegeneration

Sphingolipid changes in mouse brain and plasma after mild traumatic brain injury at the acute phases

BACKGROUND

Traumatic brain injury (TBI) causes neuroinflammation and can lead to long-term neurological dysfunction, even in cases of mild TBI (mTBI). Despite the substantial burden of this disease, the management of TBI is precluded by an incomplete understanding of its cellular mechanisms. Sphingolipids (SPL) and their metabolites have emerged as key orchestrators of biological processes related to tissue injury, neuroinflammation, and inflammation resolution. No study so far has investigated comprehensive sphingolipid profile changes immediately following TBI in animal models or human cases. In this study, sphingolipid metabolite composition was examined during the acute phases in brain tissue and plasma of mice following mTBI.

METHODS

Wildtype mice were exposed to air-blast-mediated mTBI, with blast exposure set at 50-psi on the left cranium and 0-psi designated as Sham. Sphingolipid profile was analyzed in brain tissue and plasma during the acute phases of 1, 3, and 7 days post-TBI via liquid-chromatography-mass spectrometry. Simultaneously, gene expression of sphingolipid metabolic markers within brain tissue was analyzed using quantitative reverse transcription-polymerase chain reaction. Significance (P-values) was determined by non-parametric t-test (Mann-Whitney test) and by Tukey's correction for multiple comparisons.

RESULTS

In post-TBI brain tissue, there was a significant elevation of 1) acid sphingomyelinase (aSMase) at 1- and 3-days, 2) neutral sphingomyelinase (nSMase) at 7-days, 3) ceramide-1-phosphate levels at 1 day, and 4) monohexosylceramide (MHC) and sphingosine at 7-days. Among individual species, the study found an increase in C18:0 and a decrease in C24:1 ceramides (Cer) at 1 day; an increase in C20:0 MHC at 3 days; decrease in MHC C18:0 and increase in MHC C24:1, sphingomyelins (SM) C18:0, and C24:0 at 7 days. Moreover, many sphingolipid metabolic genes were elevated at 1 day, followed by a reduction at 3 days and an absence at 7-days post-TBI. In post-TBI plasma, there was 1) a significant reduction in Cer and MHC C22:0, and an increase in MHC C16:0 at 1 day; 2) a very significant increase in long-chain Cer C24:1 accompanied by significant decreases in Cer C24:0 and C22:0 in MHC and SM at 3 days; and 3) a significant increase of C22:0 in all classes of SPL (Cer, MHC and SM) as well as a decrease in Cer C24:1, MHC C24:1 and MHC C24:0 at 7 days.

CONCLUSIONS

Alterations in sphingolipid metabolite composition, particularly sphingomyelinases and short-chain ceramides, may contribute to the induction and regulation of neuroinflammatory events in the early stages of TBI, suggesting potential targets for novel diagnostic, prognostic, and therapeutic strategies in the future.

Two Omics Methods Expose Anti-Depression Mechanism of Raw and Vinegar-Baked Bupleurum Scorzonerifolium Willd

Bupleurum scorzonerifolium willd. (BS) and its vinegar-baked product (VBS) has been frequently utilized for depression management in clinical Chinese medicine. This paper aims to elucidate the antidepressant mechanism of BS and VBS from the perspectives of metabonomics and gut microbiota. A rat model of depression was established by CUMS combined with feeding alone to evaluate the antidepressant effects of BS and VBS. UPLC-Q-TOF-MS/MS-based metabolomics and 16S rRNA sequencing of rat feces were applied and the correlation of differential metabolic markers and intestinal floras was analyzed. The result revealed that BS and VBS significantly improved depression-like behaviors and the levels of monoamine neurotransmitters in CUMS rats. There were 27 differential endogenous metabolites between CUMS and normal rats, which were involved in 8 metabolic pathways. Whereas, BS and VBS could regulate 18 and 20 metabolites respectively, wherein fifteen of them were shared metabolites. On the genus level, BS and VBS could regulate twenty-five kinds of intestinal floras in CUMS rats, that is, they increased the abundance of beneficial bacteria and decreased the abundance of harmful bacteria. In conclusion, both BS and VBS exert excellent antidepressant effects by regulating various metabolic pathways and ameliorating intestinal microflora dysfunction.

Gut microbiota in overweight and obesity: crosstalk with adipose tissue

Overweight and obesity are characterized by excessive fat mass accumulation produced when energy intake exceeds energy expenditure. One plausible way to control energy expenditure is to modulate thermogenic pathways in white adipose tissue (WAT) and/or brown adipose tissue (BAT). Among the different environmental factors capable of influencing host metabolism and energy balance, the gut microbiota is now considered a key player. Following pioneering studies showing that mice lacking gut microbes (that is, germ-free mice) or depleted of their gut microbiota (that is, using antibiotics) developed less adipose tissue, numerous studies have investigated the complex interactions existing between gut bacteria, some of their membrane components (that is, lipopolysaccharides), and their metabolites (that is, short-chain fatty acids, endocannabinoids, bile acids, aryl hydrocarbon receptor ligands and tryptophan derivatives) as well as their contribution to the browning and/or beiging of WAT and changes in BAT activity. In this Review, we discuss the general physiology of both WAT and BAT. Subsequently, we introduce how gut bacteria and different microbiota-derived metabolites, their receptors and signalling pathways can regulate the development of adipose tissue and its metabolic capacities. Finally, we describe the key challenges in moving from bench to bedside by presenting specific key examples.

Neuroinflammation underlies the development of social stress induced cognitive deficit in sickle cell disease

Cognitive deficit is a debilitating complication of SCD with multifactorial pathobiology. Here we show that neuroinflammation and dysregulation in lipidomics and transcriptomics profiles are major underlying mechanisms of social stress-induced cognitive deficit in SCD. Townes sickle cell (SS) mice and controls (AA) were exposed to social stress using the repeat social defeat (RSD) paradigm concurrently with or without treatment with minocycline. Mice were tested for cognitive deficit using novel object recognition (NOR) and fear conditioning (FC) tests. SS mice exposed to RSD without treatment had worse performance on cognitive tests compared to SS mice exposed to RSD with treatment or to AA controls, irrespective of their RSD or treatment disposition. Additionally, compared to SS mice exposed to RSD with treatment, SS mice exposed to RSD without treatment had significantly more cellular evidence of neuroinflammation coupled with a significant shift in the differentiation of neural progenitor cells towards astrogliogenesis. Additionally, brain tissue from SS mice exposed to RSD was significantly enriched for genes associated with blood-brain barrier dysfunction, neuron excitotoxicity, inflammation, and significant dysregulation in sphingolipids important to neuronal cell processes. We demonstrate in this study that neuroinflammation and lipid dysregulation are potential underlying mechanisms of social stress-related cognitive deficit in SS mice.

First-in-human single-dose study of nizubaglustat, a dual inhibitor of ceramide glucosyltransferase and non-lysosomal glucosylceramidase: Safety, tolerability, pharmacokinetics, and pharmacodynamics of single ascending and multiple doses in healthy adults

Nizubaglustat is a novel, orally available, brain penetrant, potent, and selective dual inhibitor of ceramide glucosyltranferase and non-lysosomal neutral glucosylceramidase (NLGase), which is currently under development for the treatment of subjects with neurological manifestations in primary and secondary gangliosidoses. The objectives of this first-in-human study were to evaluate the safety and tolerability, pharmacokinetics, and pharmacodynamics (PD) of single oral doses of nizubaglustat after single (1, 3, and 9 mg) and multiple oral doses (9 mg once per day (QD) over 14 days) in healthy adults. Nizubaglustat was rapidly absorbed and systemic exposure was dose-proportional. Steady-state was achieved after three days of QD multiple dosing with minimal accumulation. Renal clearance accounted for around 15% of nizubaglustat elimination. Following multiple dosing, plasma concentrations of glucosylceramide (GlcCer), lactosylceramide (LacCer), and monosialodihexosylganglioside (GM3) decreased to a nadir at Day 10. PD target engagement of GCS inhibition was shown by a median decrease from baseline of plasma concentrations of GlcCer, LacCer, and GM3 ganglioside by 70%, 50%, and 48%, respectively. NLGase inhibition was also manifested by increased concentrations of GlcCer in cerebrospinal fluid from Day 1 to Day 14. Nizubaglustat was safe and well-tolerated at all doses tested. Consistent with the high selectivity, and the absence of intestinal disaccharidases inhibition, no cases of diarrhea were reported. No decreased appetite or weight loss was noted. Only treatment-emergent adverse events with preferred terms belonging to the system organ class skin and subcutaneous disorders of mild intensity were reported as drug-related in the nizubaglustat arm, in line with the pharmacological mechanism targeting glucosylceramide metabolism. Taken together, these data support QD dosing of nizubaglustat and its ongoing development in patients with primary and secondary forms of gangliosidoses.

The role of sphingosine-1-phosphate in the development and progression of Parkinson's disease

Parkinson's disease (PD) could be viewed as a proteinopathy caused by changes in lipids, whereby modifications in lipid metabolism may lead to protein alterations, such as the accumulation of alpha-synuclein (α-syn), ultimately resulting in neurodegeneration. Although the loss of dopaminergic neurons in the substantia nigra is the major clinical manifestation of PD, the etiology of it is largely unknown. Increasing evidence has highlighted the important role of lipids in the pathophysiology of PD. Sphingosine-1-phosphate (S1P), a signaling lipid, has been suggested to have a potential association with the advancement and worsening of PD. Therefore, better understanding the mechanisms and regulatory proteins is of high interest. Most interestingly, S1P appears to be an important target to offers a new strategy for the diagnosis and treatment of PD. In this review, we first introduce the basic situation of S1P structure, function and regulation, with a special focus on the several pathways. We then briefly describe the regulation of S1P signaling pathway on cells and make a special focused on the cell growth, proliferation and apoptosis, etc. Finally, we discuss the function of S1P as potential therapeutic target to improve the clinical symptoms of PD, and even prevent the progression of the PD. In the context of PD, the functions of S1P modulators have been extensively elucidated. In conclusion, S1P modulators represent a novel and promising therapeutic principle and therapeutic method for PD. However, more research is required before these drugs can be considered as a standard treatment option for PD.

Sphingosine 1 phosphate lyase inhibition rescues cognition in diabetic mice by promoting anti-inflammatory microglia

Sphingosine-1-phosphate (S1P) is emerging as a crucial sphingolipid modulating neuroinflammation and cognition. S1P levels in the brain have been found to be decreased in cognitive impairment. S1P lyase (S1PL) is the key enzyme in metabolizing S1P and has been implicated in neuroinflammation. This study evaluated the effect of S1PL inhibition on cognition in type 2 diabetic mice. Fingolimod (0.5mg/kg and 1mg/kg) rescued cognition in high-fat diet and streptozotocin-induced diabetic mice, as evident in the Y maze and passive avoidance test. We further evaluated the effect of fingolimod on the activation of microglia in the pre-frontal cortex (PFC) and hippocampus of diabetic mice. Our study revealed that fingolimod inhibited S1PL and promoted anti-inflammatory microglia in both PFC and hippocampus of diabetic mice as it increased Ym-1 and arginase-1. The levels of p53 and apoptotic proteins (Bax and caspase-3) were elevated in the PFC and hippocampus of type 2 diabetic mice which fingolimod reversed. The underlying mechanism promoting anti-inflammatory microglial phenotype was also explored in this study. TIGAR, TP53-associated glycolysis and apoptosis regulator, is known to foster anti-inflammatory microglia and was found to be downregulated in the brain of type 2 diabetic mice. S1PL inhibition decreased the levels of p53 and promoted TIGAR, thereby increasing anti-inflammatory microglial phenotype and inhibiting apoptosis in the brain of diabetic mice. Our study reveals that S1PL inhibition could be beneficial in mitigating cognitive deficits in diabetic mice.

Lipid Mediated Brain Disorders: A Perspective

The brain, one of the most resilient organs of the body is highly enriched in lipid content, suggesting the essential role of lipids in brain physiological activities. Lipids constitute an important structural part of the brain and act as a rich source of metabolic energy. Besides, lipids in their bioactive form (known as bioactive lipids) play an essential signaling and regulatory role, facilitating neurogenesis, synaptogenesis, and cell-cell communication. Brain lipid metabolism is thus a tightly regulated process. Any alteration/dysregulation of lipid metabolism greatly impact brain health and activity. Moreover, since central nervous system (CNS) is the most metabolically active system and lacks an efficient antioxidative defence system, it acts as a hub for the production of reactive oxygen species (ROS) and subsequent lipid peroxidation. These peroxidation events are reported during pathological changes such as neuronal tissue injury and inflammation. Present review is a modest attempt to gain insights into the role of dysregulated bioactive lipid levels and lipid oxidation status in the pathogenesis and progression of neurodegenerative disorders. This may open up new avenues exploiting lipids as the therapeutic targets for improving brain health, and treatment of nervous system disorders.

Treatment with THI, an inhibitor of sphingosine-1-phosphate lyase, modulates glycosphingolipid metabolism and results therapeutically effective in experimental models of Huntington's disease

Huntington's disease (HD) is a fatal neurodegenerative disorder with no effective cure currently available. Over the past few years our research has shown that alterations in sphingolipid metabolism represent a critical determinant in HD pathogenesis. In particular, aberrant metabolism of sphingosine-1-phosphate (S1P) has been reported in multiple disease settings, including human postmortem brains from HD patients. In this study, we investigate the potential therapeutic effect of the inhibition of S1P degradative enzyme SGPL1, by the chronic administration of the 2-acetyl-5-tetrahydroxybutyl imidazole (THI) inhibitor. We show that THI mitigated motor dysfunctions in both mouse and fly models of HD. The compound evoked the activation of pro-survival pathways, normalized levels of brain-derived neurotrophic factor, preserved white matter integrity, and stimulated synaptic functions in HD mice. Metabolically, THI restored normal levels of hexosylceramides and stimulated the autophagic and lysosomal machinery, facilitating the reduction of nuclear inclusions of both wild-type and mutant huntingtin proteins.

Characterization and Comparison of Lipid Profiles of Selected Chicken Eggs Based on Lipidomics Approach

The present study aimed to analyze the lipid profiles of three selected chicken eggs (Nixi, silky fowl, and ordinary eggs) from the market of China by an UPLC-Q-Exactive-MS based untargeted lipidomics approach. In total, 11 classes and 285 lipid molecular species were identified from the egg yolks. Glycerophospholipids (GPLs, 6 classes, 168 lipid species) are the most abundant lipids groups, followed by sphingolipids (3 classes, 50 lipid species), and two neutral lipid classes (TG and DG). Notably, two ethersubclass of GPLs (PC-e and PE-p) and 12 species of cerebrosides were firstly detected from the chicken eggs. Furthermore, multivariate statistical analysis was performed and the lipids profiles of the three types of eggs were well discriminated from each other by 30 predominant lipids species. The characteristic lipid molecules of the different kind of eggs were also screened out. This study provides a novel insight for better understanding the lipid profiles and nutritional values of different chicken eggs.

Ceramide induces macrophage migration inhibitory factor -mediated parthanatos in mouse neurons by increasing ROS levels

Ceramides, the key component of sphingolipid metabolism and second messengers, have been associated with neurodegenerative diseases progression and pathology, and can induce neuronal apoptosis and necrosis, but the effect of ceramide on parthanatos has not been fully elucidated. In this study, we investigated the ceramide-mediated parthanatos pathway and the role of macrophage inhibitory factor (MIF) in parthanatos. We found that ceramide significantly diminished the viability and induced the death of primary cortical neurons. These effects were not prevented by treatment with the pan-caspase inhibitor Z-VAD-FMK treatment; in contrast, treatment with the poly (ADP ribosyl) polymerase-1 (PARP-1) inhibitor ABT-888 prevented these ceramide-mediated effects. Specifically, ceramide induced PARP-1 overactivation, increased PAR polymer levels, facilitated apoptosis-inducing factor (AIF) and MIF nuclear translocation and induced DNA damage. Knockdown of MIF with an adenovirus carrying a MIF short hairpin RNA (shRNA) inhibited ceramide-induced DNA damage and neuronal death, but nuclear translocation of AIF was unaffected. Furthermore, ceramide increased reactive oxygen species (ROS) levels, and N-acetyl cysteine (NAC) significantly inhibited PAR production and neuronal death. These findings suggested that ceramide induced neuronal parthanatos by increasing ROS levels and that MIF might be downstream of AIF in the ceramide-mediated parthanatos pathway. In conclusion, our results suggest that knocking down MIF expression may be a potential therapeutic strategy for nervous system diseases.

Implications of glial metabolic dysregulation in the pathophysiology of neurodegenerative diseases

Glial cells are the most abundant cells of the brain, outnumbering neurons. These multifunctional cells are crucial for maintaining brain homeostasis by providing trophic and nutritional support to neurons, sculpting synapses, and providing an immune defense. Glia are highly plastic and undergo both structural and functional alterations in response to changes in the brain microenvironment. Glial phenotypes are intimately regulated by underlying metabolic machinery, which dictates the effector functions of these cells. Altered brain energy metabolism and chronic neuroinflammation are common features of several neurodegenerative diseases. Microglia and astrocytes are the major glial cells fueling the ongoing neuroinflammatory process, exacerbating neurodegeneration. Distinct metabolic perturbations in microglia and astrocytes, including altered carbohydrate, lipid, and amino acid metabolism have been documented in neurodegenerative diseases. These disturbances aggravate the neurodegenerative process by potentiating the inflammatory activation of glial cells. This review covers the recent advances in the molecular aspects of glial metabolic changes in the pathophysiology of neurodegenerative diseases. Finally, we discuss studies exploiting glial metabolism as a potential therapeutic avenue in neurodegenerative diseases.

LC-MS/MS Insight into Vitamin C Restoration to Metabolic Disorder Evoked by Amyloid β in Caenorhabditis elegans CL2006

The transitional expression and aggregation of amyloid β (Aβ) are the most important causative factors leading to the deterioration of Alzheimer’s disease (AD), a commonly occurring metabolic disease among older people. Antioxidant agents such as vitamin C (Vc) have shown potential effects against AD and aging. We applied an liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) method and differential metabolites strategy to explore the metabolic disorders and Vc restoration in a human Aβ transgenic (Punc-54::Aβ1–42) nematode model CL2006. We combined the LC-MS/MS investigation with the KEGG and HMDB databases and the CFM-ID machine-learning model to identify and qualify the metabolites with important physiological roles. The differential metabolites responding to Aβ activation and Vc treatment were filtered out and submitted to enrichment analysis. The enrichment showed that Aβ mainly caused abnormal biosynthesis and metabolism pathways of phenylalanine, tyrosine and tryptophan biosynthesis, as well as arginine and proline metabolism. Vc reversed the abnormally changed metabolites tryptophan, anthranilate, indole and indole-3-acetaldehyde. Vc restoration affected the tryptophan metabolism and the biosynthesis of phenylalanine, tyrosine and tryptophan. Our findings provide supporting evidence for understanding the metabolic abnormalities in neurodegenerative diseases and the repairing effect of drug interventions.

The Role of Sphingomyelin and Ceramide in Motor Neuron Diseases

Amyotrophic Lateral Sclerosis (ALS), Spinal Bulbar Muscular Atrophy (SBMA), and Spinal Muscular Atrophy (SMA) are motor neuron diseases (MNDs) characterised by progressive motor neuron degeneration, weakness and muscular atrophy. Lipid dysregulation is well recognised in each of these conditions and occurs prior to neurodegeneration. Several lipid markers have been shown to predict prognosis in ALS. Sphingolipids are complex lipids enriched in the central nervous system and are integral to key cellular functions including membrane stability and signalling pathways, as well as being mediators of neuroinflammation and neurodegeneration. This review highlights the metabolism of sphingomyelin (SM), the most abundant sphingolipid, and of its metabolite ceramide, and its role in the pathophysiology of neurodegeneration, focusing on MNDs. We also review published lipidomic studies in MNDs. In the 13 studies of patients with ALS, 12 demonstrated upregulation of multiple SM species and 6 demonstrated upregulation of ceramides. SM species also correlated with markers of clinical progression in five of six studies. These data highlight the potential use of SM and ceramide as biomarkers in ALS. Finally, we review potential therapeutic strategies for targeting sphingolipid metabolism in neurodegeneration.

Ceramide and Sphingosine-1-Phosphate in Neurodegenerative Disorders and Their Potential Involvement in Therapy

Neurodegenerative disorders (ND) are progressive diseases of the nervous system, often without resolutive therapy. They are characterized by a progressive impairment and loss of specific brain regions and neuronal populations. Cellular and animal model studies have identified several molecular mechanisms that play an important role in the pathogenesis of ND. Among them are alterations of lipids, in particular sphingolipids, that play a crucial role in neurodegeneration. Overall, during ND, ceramide-dependent pro-apoptotic signalling is promoted, whereas levels of the neuroprotective spingosine-1-phosphate are reduced. Moreover, ND are characterized by alterations of the metabolism of complex sphingolipids. The finding that altered sphingolipid metabolism has a role in ND suggests that its modulation might provide a useful strategy to identify targets for possible therapies. In this review, based on the current literature, we will discuss how bioactive sphingolipids (spingosine-1-phosphate and ceramide) are involved in some ND (Alzheimer’s disease, Parkinson’s disease, amyotrophic lateral sclerosis) and their possible involvement in therapies.

Genomic, transcriptomic, and metabolomic profiles of hiPSC-derived dopamine neurons from clinically discordant brothers with identical PRKN deletions

We previously reported on two brothers who carry identical compound heterozygous PRKN mutations yet present with significantly different Parkinson's Disease (PD) clinical phenotypes. Juvenile cases demonstrate that PD is not necessarily an aging-associated disease. Indeed, evidence for a developmental component to PD pathogenesis is accumulating. Thus, we hypothesized that the presence of additional genetic modifiers, including genetic loci relevant to mesencephalic dopamine neuron development, could potentially contribute to the different clinical manifestations of the two brothers. We differentiated human-induced pluripotent stem cells (hiPSCs) derived from the two brothers into mesencephalic neural precursor cells and early postmitotic dopaminergic neurons and performed wholeexome sequencing and transcriptomic and metabolomic analyses. No significant differences in the expression of canonical dopamine neuron differentiation markers were observed. Yet our transcriptomic analysis revealed a significant downregulation of the expression of three neurodevelopmentally relevant cell adhesion molecules, CNTN6, CNTN4 and CHL1, in the cultures of the more severely affected brother. In addition, several HLA genes, known to play a role in neurodevelopment, were differentially regulated. The expression of EN2, a transcription factor crucial for mesencephalic dopamine neuron development, was also differentially regulated. We further identified differences in cellular processes relevant to dopamine metabolism. Lastly, wholeexome sequencing, transcriptomics and metabolomics data all revealed differences in glutathione (GSH) homeostasis, the dysregulation of which has been previously associated with PD. In summary, we identified genetic differences which could potentially, at least partially, contribute to the discordant clinical PD presentation of the two brothers.

Involvement of Ceramide Metabolism in Cerebral Ischemia

Ischemic stroke, caused by the interruption of blood flow to the brain and subsequent neuronal death, represents one of the main causes of disability in worldwide. Although reperfusion therapies have shown efficacy in a limited number of patients with acute ischemic stroke, neuroprotective drugs and recovery strategies have been widely assessed, but none of them have been successful in clinical practice. Therefore, the search for new therapeutic approaches is still necessary. Sphingolipids consist of a family of lipidic molecules with both structural and cell signaling functions. Regulation of sphingolipid metabolism is crucial for cell fate and homeostasis in the body. Different works have emphasized the implication of its metabolism in different pathologies, such as diabetes, cancer, neurodegeneration, or atherosclerosis. Other studies have shown its implication in the risk of suffering a stroke and its progression. This review will highlight the implications of sphingolipid metabolism enzymes in acute ischemic stroke.

Plasma Ceramides Pathophysiology, Measurements, Challenges, and Opportunities

Ceramides are a family of lipid molecules, composed of sphingosine and a fatty acid, and transported by lipoproteins (primarily by low-density lipoproteins) in the bloodstream. They are not only structural lipids, but multifunctional and bioactive molecules with key roles in many important cellular pathways, such as inflammatory processes and apoptosis, representing potential biomarkers of cardiometabolic diseases as well as pharmacological targets. Recent data reported ceramide modulation by diet and aerobic exercise, suggesting nutrients and exercise-targeting sphingolipid pathways as a countermeasure, also in combination with other therapies, for risk and progression of chronic disease prevention and health maintenance. In this review, we focus on the available data regarding remarks on ceramide structure and metabolism, their pathophysiologic roles, and the effect of dietary habit and aerobic exercise on ceramide levels. Moreover, advancements and limitations of lipidomic techniques and simplification attempts to overcome difficulties of interpretation and to facilitate practical applications, such as the proposal of scores, are also discussed.