Pillar Array Mixer for Postcolumn Derivatization Integrated into Liquid Chromatography-Based Microfluidic Device.

The chemical derivatization of target analytes can enhance the sensitivity and selectivity of separation-based methods for metabolite analysis using microfluidic devices. However, the development of chromatography-based microfluidic devices with integrated derivatization units is challenging. In this study, a novel derivatization unit with a pillar array (PA)-based mixing channel was developed for postcolumn derivatization during on-chip liquid chromatography (LC). The PA mixer enhanced mixing between the derivatization reagents and analytes in the transverse direction, while preventing analyte dispersion in the flow direction. After the concept was confirmed using computational fluid dynamics analysis, microfluidic devices with a LC column and PA mixer were fabricated on a 20 × 20 mm silicon plate. Fluid experiments were performed using a PA mixer with a pillar size of 5 or 10 µm or a hollow-channel mixer, which revealed that the PA mixer enhanced transverse mixing without increasing the width of the analyte peak. Moreover, the developed device enabled the analysis of three amino acids within 40 s by separation via hydrophilic interaction chromatography followed by postcolumn fluorogenic derivatization with naphthalene-2,3-dicarboxaldehyde and fluorescence detection. Our results demonstrate the potential of integrated derivatization units for the development of micrototal analysis systems for use in bioanalysis.

Development of a Two-Dimensional Liquid Chromatographic Method for Analysis of Urea Cycle Amino Acids.

The urea cycle has been found to be closely associated with certain types of cancers and other diseases such as cardiovascular disease and chronic kidney disease. An analytical method for the precise quantification of urea cycle amino acids (arginine, ornithine, citrulline, and argininosuccinate) by off-line two-dimensional liquid chromatography (2D-LC) combined with fluorescence-based detection was developed. Before analysis, the amino acids were derivatised with 4-fluoro-7-nitro-2,1,3-benzoxadiazole (NBD-F) to obtain NBD-amino acids. The first dimension involved the reversed-phase separation, in which NBD derivatives of urea cycle amino acids were completely separated from each other and mostly separated from the 18 NBD-proteinogenic amino acids. The samples were eluted with stepwise gradient using 0.02% trifluoroacetic acid in water-acetonitrile as the mobile phase. In the second dimension, an amino column was used for the separation of NBD-ornithine, -citrulline, and -argininosuccinate, while a sulfonic acid column was used to separate NBD-arginine. The developed 2D-LC system was used to analyse human plasma samples. The fractions of NBD-urea cycle amino acids obtained in the first dimension were collected manually and introduced into the second dimension. By choosing appropriate mobile phases for the second dimension, each NBD-urea cycle amino acid eluted in the first dimension was well separated from the other proteinogenic amino acids and interference from endogenous substance. This could not be achieved in the first dimension. The urea cycle amino acids in human plasma sample were quantified, and the method was well validated. The calibration curves for each NBD-urea cycle amino acid showed good linearity from 3 (ASA) or 15 (Orn, Cit, and Arg) to 600 nM, with correlation coefficients higher than 0.9969. The intraday and interday precisions were less than 7.9% and 15%, respectively. The 2D-LC system is expected to be useful for understanding the involvement of the urea cycle in disease progression.

Cancer progression by reprogrammed BCAA metabolism in myeloid leukaemia.

Reprogrammed cellular metabolism is a common characteristic observed in various cancers. However, whether metabolic changes directly regulate cancer development and progression remains poorly understood. Here we show that BCAT1, a cytosolic aminotransferase for branched-chain amino acids (BCAAs), is aberrantly activated and functionally required for chronic myeloid leukaemia (CML) in humans and in mouse models of CML. BCAT1 is upregulated during progression of CML and promotes BCAA production in leukaemia cells by aminating the branched-chain keto acids. Blocking BCAT1 gene expression or enzymatic activity induces cellular differentiation and impairs the propagation of blast crisis CML both in vitro and in vivo. Stable-isotope tracer experiments combined with nuclear magnetic resonance-based metabolic analysis demonstrate the intracellular production of BCAAs by BCAT1. Direct supplementation with BCAAs ameliorates the defects caused by BCAT1 knockdown, indicating that BCAT1 exerts its oncogenic function through BCAA production in blast crisis CML cells. Importantly, BCAT1 expression not only is activated in human blast crisis CML and de novo acute myeloid leukaemia, but also predicts disease outcome in patients. As an upstream regulator of BCAT1 expression, we identified Musashi2 (MSI2), an oncogenic RNA binding protein that is required for blast crisis CML. MSI2 is physically associated with the BCAT1 transcript and positively regulates its protein expression in leukaemia. Taken together, this work reveals that altered BCAA metabolism activated through the MSI2-BCAT1 axis drives cancer progression in myeloid leukaemia.

Improvement of an Automated Sample Injection System for Pillar Array Columns to Increase Analytical Reproducibility.

In our previous study, we developed an automatic sample injection system for pillar array columns for quantitative analysis. An autosampler was used to maintain a constant sample injection volume. However, the sample was diluted during injection using the autosampler, thus deteriorating the analytical reproducibility. In this study, we have substituted the autosampler with a syringe pump to overcome the abovementioned problem and improve the system. Sample dilution was avoided by filling the entire capillary with the sample at a constant rate. This improved system also increased the analytical reproducibility. In the previous system, the relative standard deviation (RSD) exceeded 17% of the peak height for coumarin dyes. In contrast, the improved system decreased the RSD to the range 1.2-1.8%. The analytical reproducibility was evaluated by using five types of amino acids. The RSD of each peak height was within 3.0%, confirming good reproducibility. These results indicate that the sample injection method developed in this study can be applied to biological sample analyses as a simple quantitative analysis method for pillar array columns.

Quantification of Intracellular Thiols by HPLC-Fluorescence Detection.

Biothiols, such as cysteine and glutathione, play important roles in various intracellular reactions represented by the redox equilibrium against oxidative stress. In this study, a method for intracellular thiol quantification using HPLC-fluorescence detection was developed. Thiols were derivatized with a thiol-specific fluorescence derivatization reagent, viz. ammonium 7-fluoro-2,1,3-benzoxadiazole-4-sulfonate (SBD-F), followed by reversed-phase separation on an InertSustain AQ-C18 column. Six different SBD-thiols (homocysteine, cysteine, cysteinylglycine, γ-glutamylcysteine, glutathione, and N-acetylcysteine as an internal standard) were separated within 30 min using a citric buffer (pH 3.0)/MeOH mobile phase. The calibration curves of all the SBD-thiols had strong linearity (R2 > 0.999). Using this developed method, the thiol concentrations of human chronic myelogenous leukemia K562 cell samples were found to be 5.5-153 pmol/1 × 106 cells. The time-dependent effect of a thiol scavenger, viz. N-ethyl maleimide, on intracellular thiol concentrations was also quantified. This method is useful for elucidating the role of intracellular sulfur metabolism.

Suppression of behavioral activity and hippocampal noradrenaline caused by surgical stress in type 2 diabetes model mice.

BACKGROUND: There has been much discussion recently about the occurrence of neuropsychological complications during the perioperative period. Diabetes is known to be one of the metabolic risk factors. Although the number of patients with diabetes mellitus (DM) has been increasing, the pathophysiology of postoperative neuropsychological dysfunction in DM patients is still unclear. Recently, a deficiency of neurotransmitters, such as monoamines, was reported to be associated with mental disorders. Therefore, we investigated the effects of surgical stress on behavioral activity and hippocampal noradrenaline (NA) level in type 2 diabetes mellitus model (T2DM) mice. METHODS: Eighty-four 6-week-old male C57BL/6J mice were divided into four groups (non-diabetes, non-diabetes with surgery, T2DM, and T2DM with surgery groups). T2DM mice were established by feeding a high-fat diet (HFD) for 8 weeks. At 14 weeks of age, fifteen mice in each group underwent a series of behavioral tests including an open field (OF) test, a novel object recognition (NOR) test and a light-dark (LD) test. In the surgery groups, open abdominal surgery with manipulation of the intestine was performed 24 h before the behavioral tests as a surgical stress. Hippocampal noradrenaline (NA) concentration was examined in six mice in each group by high-performance liquid chromatography. The data were analyzed by the Mann-Whitney U test, and p values less than 0.05 were considered significant. RESULTS: The T2DM group showed significantly increased explorative activity in the NOR test (P = 0.0016) and significantly increased frequency of transition in the LD test (P = 0.043) compared with those in the non-diabetic group before surgery. In T2DM mice, surgical stress resulted in decreased total distance in the OF test, decreased explorative activity in the NOR test, and decreased frequency of transition in the LD test (OF: P = 0.015, NOR: P = 0.009, LD: P = 0.007) and decreased hippocampal NA (P = 0.015), but such differences were not observed in the non-diabetic mice. CONCLUSIONS: Mice with T2DM induced by feeding an HFD showed increased behavioral activities, and surgical stress in T2DM mice caused postoperative hypoactivity and reduction of the hippocampal NA level.

Analysis of Total Thiols in the Urine of a Cystathionine ß-Synthase-Deficient Mouse Model of Homocystinuria Using Hydrophilic Interaction Chromatography.

Homocysteine and related thiols (cysteine, cysteinylglycine, and glutathione) in the urine of a cystathionine ß-synthase (CBS)-deficient mouse model were quantified using hydrophilic interaction chromatography with fluorescence detection. Urine samples were incubated with tris(2-carboxyethyl) phosphine to reduce disulfide bonds into thiols. After deproteinization, thiols were fluorescently derivatized with ammonium 7-fluoro-2,1,3-benzoxadiazole-4-sulfonate (SBD-F). Homocysteine, cysteine, cysteinylglycine, and glutathione in mouse urine were analyzed using an amide-type column with a mobile phase of acetonitrile/120 mM ammonium formate buffer (pH 3.0) (81:19). The developed method was well-validated. Thiol concentrations in the urine of CBS-wild type (-WT), -heterozygous (-Hetero), and -knockout (-KO) mice were quantified using the developed method. As expected, total homocysteine concentration in CBS-KO mice was significantly higher than that in CBS-WT and CBS-Hetero mice. The developed method shows promise for diagnoses in preclinical and clinical studies.

Liquid-Chromatographic Methods for Carboxylic Acids in Biological Samples.

Carboxyl-bearing low-molecular-weight compounds such as keto acids, fatty acids, and other organic acids are involved in a myriad of metabolic pathways owing to their high polarity and solubility in biological fluids. Various disease areas such as cancer, myeloid leukemia, heart disease, liver disease, and lifestyle diseases (obesity and diabetes) were found to be related to certain metabolic pathways and changes in the concentrations of the compounds involved in those pathways. Therefore, the quantification of such compounds provides useful information pertaining to diagnosis, pathological conditions, and disease mechanisms, spurring the development of numerous analytical methods for this purpose. This review article addresses analytical methods for the quantification of carboxylic acids, which were classified into fatty acids, tricarboxylic acid cycle and glycolysis-related compounds, amino acid metabolites, perfluorinated carboxylic acids, α-keto acids and their metabolites, thiazole-containing carboxylic acids, and miscellaneous, in biological samples from 2000 to date. Methods involving liquid chromatography coupled with ultraviolet, fluorescence, mass spectrometry, and electrochemical detection were summarized.

Pyruvate secreted from patient-derived cancer-associated fibroblasts supports survival of primary lymphoma cells.

Cancer-associated fibroblasts (CAF) are a key component in the tumor microenvironment and play functional roles in tumor metastasis and resistance to chemotherapies. We have previously reported that CAF isolated from lymphoma samples increase anaerobic glycolysis and decrease intracellular production of reactive oxygen species, promoting the survival of tumor cells. Herein, we analyzed the mechanisms underlying this support of tumor-cell survival by CAF. As direct contact between lymphoma cells and CAF was not indispensable to survival support, we identified that the humoral factor pyruvate was significantly secreted by CAF. Moreover, survival of lymphoma cells was promoted by the presence of pyruvate, and this promotion was canceled by inhibition of monocarboxylate transporters. Metabolome analysis of lymphoma cells in coculture with CAF demonstrated that intermediates in the citric acid cycle were significantly increased, indicating that tumor cells produced energy by aerobic metabolism. These findings indicate that energy production in lymphoma cells is regulated in coordination not only with anaerobic glycolysis, but also with aerobic metabolism termed the reverse-Warburg effect, involving the secretion of pyruvate from CAF resulting in increased use of the citric acid cycle in lymphoma cells.

Collection of biochemical samples with brain-wide electrophysiological recordings from a freely moving rodent.

Bridging accumulating insights from microscopic and macroscopic studies in neuroscience research requires monitoring of neuronal population dynamics and quantifying specific molecules or genes from the brain of identical animals. To this end, by minimizing the size and weight of an electrode array, we developed a method that records local field potential signals of multiple brain regions from one side of the hemisphere in a freely moving rodent. At the same time, extracellular cerebrospinal fluid for biochemical assays or a small part of brain tissue samples for gene expression assays are collected from the other side of the hemisphere. This method allows ongoing stable recordings and sample collections for at least two months. The methodological concept is applicable to a wide range of biological reactions at various spatiotemporal scales, allowing us to integrate an idea of physiolomics into existing omics analyses, leading to a new combination of multi-omics approaches.

Investigation of the interaction between serotonin-related compounds and phenylboronate moieties in monolithic silica disk-packed spin columns.

Solid-phase extraction technologies are widely used for sample pretreatment in bioanalysis. Monolithic silica disk-packed spin columns modified with phenylboronate moieties have been developed for the selective extraction of cis-diol compounds such as catecholamines. However, in our preliminary studies, serotonin was found to also be extracted in this treatment, along with catecholamines. In this study, the interaction between serotonin-related compounds (serotonin, tryptophan, 5-hydroxy-tryptophan and 5-hydroxyindoleacetic acid) and phenylboronate moieties was investigated. We found that only serotonin was extracted with phenylboronate-modified monolithic silica, whereas tryptophan, 5-hydroxy-tryptophan and 5-hydroxyindoleacetic acid were not. Hydrophobic interactions rather than ionic interactions were the primary factor for the adsorption of serotonin to phenylboronate. Finally, the selective pretreatment procedure for catecholamines was improved: thus, the method could be applied for the pretreatment of bio-samples.

A Modified QuEChERS Method for Determination of Pyrethroid Residues in Traditional Chinese Medicine Oral Liquids by High-Performance Liquid Chromatography.

Pyrethroid residues in traditional Chinese medicines have been a serious threat to the health and treatment of patients. However, because of the matrix complexity of traditional Chinese medicine, the detection of pyrethroid residues remains a challenge. Therefore, we developed a QuEChERS method coupled with high-performance liquid chromatography and ultraviolet detection (HPLC-UV) for the determination of pyrethroid pesticides in three kinds of traditional Chinese medicine oral liquid preparations, and we investigated and optimized the extraction conditions. The matrix effect was estimated in the organic solvent and the actual samples by comparing the slopes of calibration curves, and the results showed that the matrix effect is not significant when using the modified QuEChERS method. The pyrethroid pesticides could be completely separated in 30 min. The linear correlation coefficients were more than 0.999, and the recoveries of all the pyrethroid pesticides ranged from 87.2% to 104.8%. The intra-day precisions (n = 5) were 2.44-4.62%, and the inter-day precisions (n = 5) were 1.06-3.02%. Moreover, the limits of detection were in the range of 0.007-0.018 ng mL-1, while the limits of quantitation were in the range of 0.022-0.057 ng mL-1. This simple, low-cost, and highly sensitive analytical method can be a potential tool for the analysis of pyrethroid residues in traditional Chinese medicine oral liquid preparations.

Identification of methylated tubulin through analysis of methylated lysine.

Post-translational modifications to tubulin such as acetylation and detyrosination play important roles in microtubule functions. Methylation is an important post-translational modification; however, to date, few methylated tubulins have been identified. In the present study, we developed a method for analyzing methylated lysine with the aim of identifying methylated tubulin. This method involves four steps: (1) acid hydrolysis of tubulin into amino acids, (2) selective extraction of methylated lysine using a monolithic-silica disk-packed spin column, (3) fluorescence derivatization of methylated lysine with 4-fluoro-7-nitro-2,1,3-benzoxadiazole (NBD-F), and (4) separation of NBD-methylated lysine on a column consisting of C18, cation and anion ligand, and fluorescence detection. Using the newly developed method, the dimethylation of lysine in tubulin was identified. This new method could be applied to searches for other methylated proteins.

Liquid Chromatography Chip with Low-Dispersion and Low-Pressure-Drop Turn Structure Utilizing a Distribution-Controlled Pillar Array.

To realize efficient, fast separations on pillar array columns with turns, a novel turn with low-dispersion and low-pressure-drop properties was developed. This "pillar-distribution-controlled" (PDC) turn was designed as a constant-radius turn filled with octagonal pillars that were arranged to control the linear velocity of the mobile phase in the radial direction. After the pillar positions were adjusted by computational fluid dynamics analysis, 27 mm long pillar array columns with two turns were fabricated on a 20 × 20 mm(2) silicon glass plate. The PDC turns suppressed the sample dispersion to a similar extent as the previously developed tapered turn, and the pressure drop of the newly designed turn was reduced to ∼1/6 that of the tapered turn. Moreover, the C18-modified pillar array column with the PDC turns showed good bioanalytical applicability; five fluorescently labeled amino acids were separated in only 24 s at a linear velocity of 7.5 mm/s. The developed turn structure offers the advantages of longer pillar array columns with more turns for the fast analysis of complex samples.

Rapid quantitative method for the detection of phenylalanine and tyrosine in human plasma using pillar array columns and gradient elution.

This study reports a fast and quantitative determination method for phenylalanine (Phe) and tyrosine (Tyr) in human plasma using on-chip pressure-driven liquid chromatography. A pillar array column with low-dispersion turns and a gradient elution system was used. The separation of fluorescent derivatives of Phe, Tyr, and other hydrophobic amino acids was successfully performed within 140 s. Under the optimized conditions, Phe and Tyr in human plasma were quantified. The developed method is promising for rapid diagnosis in the clinical field.

Determination of catecholamines and related compounds in mouse urine using column-switching HPLC.

We have developed an analytical method for the determination of catecholamines and related compounds in mouse urine by column-switching HPLC. Selective extraction of the catechol compounds was performed using a precolumn modified with phenylboronic acid, which has a pH dependent affinity for the catechol structures. The pretreatment buffer, which facilitated binding of the catechols to the precolumn, was optimized to ensure high analyte recoveries and good peak shapes. We found that using the same acetonitrile content in the pretreatment buffer and hydrophilic interaction liquid chromatography mobile phase was necessary to improve peak shapes. Eight catechol compounds were selectively extracted and separated using 100 mmol L(-1) ammonium formate/acetonitrile (20/80 v/v, pH 8.0) for the extraction step, and 20 mmol L(-1) ammonium formate (pH 2.5)/acetonitrile (20/80 v/v) for elution and separation. Native fluorescence of the separated catechol compounds was monitored, and the limits of detection, corresponding to a signal to noise ratio of 3, were 9-58 nmol L(-1). Five catechol compounds (dopamine, epinephrine, norepinephrine, 3,4-dihydroxyphenylglycol, and 3,4-dihydroxymandelic acid) were successfully quantified in mouse urine. Intra- and inter-day precisions were less than 10%, and performance was superior to that afforded by manual sample pretreatment.

Effect of ascorbic acid deficiency on catecholamine synthesis in adrenal glands of SMP30/GNL knockout mice.

PURPOSE: The effect of an AA deficiency on catecholamine biosynthesis in adult mice in vivo is unknown. Therefore, we quantified catecholamine and the expression of catecholamine synthetic enzymes in the adrenal glands of senescence marker protein-30 (SMP30)/gluconolactonase (GNL) knockout (KO) mice placed in an AA-deficient state. METHODS: At 30 days of age, mice were divided into the following 4 groups: AA (-) SMP30/GNL KO, AA (+) SMP30/GNL KO, AA (-) wild type (WT), and AA (+) WT. The AA (+) groups were given water containing 1.5 g/L AA, whereas the AA (-) groups received water without AA until the experiment ended. In addition, all mice were fed an AA-depleted diet. Catecholamine levels were measured by a liquid chromatographic method. Tyrosine hydroxylase, dopa decarboxylase, dopamine ß-hydroxylase, and phenylethanolamine N-methyltransferase mRNA expression levels were measured with the quantitative real-time polymerase chain reaction (qPCR). Tyrosine hydroxylase and dopamine ß-hydroxylase protein levels were quantified by Western blot analysis. RESULTS: In the adrenals of AA (-) SMP30/GNL KO mice, noradrenaline and adrenaline levels decreased significantly compared to other three groups of mice, although there were no significant differences in dopamine ß-hydroxylase or phenylethanolamine N-methyltransferase mRNA content. Moreover, there was no significant difference in their dopamine ß-hydroxylase protein levels. On the other hand, AA depletion did not affect dopamine levels in adrenal glands of mice. CONCLUSION: An AA deficiency decreases the noradrenaline and adrenaline levels in adrenal glands of mice in vivo.

Simultaneous determination of N(G)-monomethyl-L-arginine, N(G),N(G)-dimethyl-L-arginine, N(G),N(G')-dimethyl-L-arginine, and L-arginine using monolithic silica disk-packed spin columns and a monolithic silica column.

We have developed and validated a high-performance liquid chromatography method that uses monolithic silica disk-packed spin columns and a monolithic silica column for the simultaneous determination of N(G)-monomethyl-L-arginine, N(G),N(G)-dimethyl-L-arginine, and N(G),N(G')-dimethyl-L-arginine in human plasma. For solid-phase extraction, our method employs a centrifugal spin column packed with monolithic silica bonded to propyl benzenesulfonic acid as a cation exchanger. After pretreatment, the methylated arginines are converted to fluorescent derivatives with 4-fluoro-7-nitro-2,1,3-benzoxadiazole, and then the derivatives are separated on a monolithic silica column. L-arginine concentration was also determined in diluted samples. Standard calibration curves revealed that the assay was linear in the concentration range 0.2-1.0 µM for methylated arginines and 40-200 µM for L-arginine. Linear regression of the calibration curve yielded equations with correlation coefficients of 0.999 (r(2)). The sensitivity was satisfactory, with a limit of detection ranging from 3.75 to 9.0 fmol for all four compounds. The RSDs were 4.3-4.8% (intraday) and 3.0-6.8% (interday). When this method was applied to samples from six healthy donors, the detected concentrations of N(G)-monomethyl-L-arginine, N(G),N(G)-dimethyl-L-arginine, N(G),N(G')-dimethyl-L-arginine and L-arginine were 0.05 ± 0.01, 0.41 ± 0.07, 0.59 ± 0.11, and 83.8 ± 30.43 µM (n = 6), respectively.

HPLC-fluorescence determination of thiol compounds in the serum of human male and female subjects using HILIC-mode column.

High-performance liquid chromatography-fluorescence detection using a hydrophilic interaction chromatography-mode column (ZIC®-HILIC) was used to determine four kinds of thiol compounds in human serum. Sera were obtained from 34 subjects for this study (17 male subjects aged 22-38 years and 17 female subjects aged 18-38 years). Serum cysteine, cysteinylglycine, glutathione, and γ-glutamylcysteine, derivatized with ammonium 7-fluoro-2,1,3-benzoxadiazole-4-sulfonate, were separated on the ZIC®-HILIC column and quantified. The serum concentrations of cysteine, cysteinylglycine, glutathione and γ-glutamylcysteine were 226 ± 4.7, 23.4 ± 1.3, 3.7 ± 0.2 and 3.2 ± 0.1 µm, respectively. In addition, the concentrations of serum thiol compounds from male subjects were significantly higher than those of the female subjects (p < 0.05).

Simultaneous determination of five constituents of areca nut extract in rat plasma using UPLC-MS/MS and its application in a pharmacokinetic study.

Areca nuts have been used as a traditional Chinese medicine (TCM) for thousands of years. Recent studies have shown that it exhibits good pharmacological activity and toxicity. In this study, the pharmacokinetics of five major components of areca nut extract in rats were investigated using a highly sensitive ultra-performance liquid chromatography coupled with triple quadrupole mass spectrometry (UPLC-MS/MS) method. Arecoline, arecaidine, guvacoline, guvacine, and catechin were separated and quantified accurately using gradient elution with mobile phases of (A) water containing 0.1 % formic acid-10 mM ammonium formate, and (B) methanol. The constituents were detected under a timing switch between the positive and negative ion modes using multiple reaction monitoring (MRM). Each calibration curve had a high R2 value of >0.99. The method accuracies ranged -7.09-11.05 % and precision values were less than 14.36 %. The recovery, matrix effect, selectivity, stability, and carry-over of the method were in accordance with the relevant requirements. It was successfully applied for the investigation of the pharmacokinetics of these five constituents after oral administration of areca nut extract. Pharmacokinetic results indirectly indicated a metabolic relationship between the four areca nut alkaloids in rats. For further clarification of its pharmacodynamic basis, this study provided a theoretical reference.