Simultaneous Analysis of Neopterin, Kynurenine and Tryptophan by Amine-HPLC Shows Minor Oxidative

Spec. Matrices 2019; 7:1–19 Research Article Open Access Kazumasa Nomura* and Paul Terwilliger Pteridines 2019; 30: 21–32 Self-dual Leonard pairs Research Article Open Access https://doi.org/10.1515/spma-2019-0001 Gregory Baxter-Parker*, Anna Chu, Peter Petocz,Received MaySamir 8, 2018; Samman, accepted Steven September P. 22,Gieseg* 2018 Simultaneous analysisAbstract: of neopterin,Let F denote a eld andkynurenine let V denote a vector space over F with nite positive dimension. Consider a pair A, A∗ of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for the other one in an and tryptophan by amine-HPLCirreducible tridiagonal shows fashion. Such minor a pair is called a Leonard pair. We consider the self-dual case in which there exists an automorphism of the endomorphism algebra of V that swaps A and A∗. Such an automorphism is unique, and called the duality A A∗. In the present paper we give a comprehensive description of this oxidative stress from short-term exhaustion↔ duality. In particular, we display an invertible F-linear map T on V such that the map X TXT− is the duality → A A∗. We express T as a polynomial in A and A∗. We describe how T acts on ags, decompositions, exercise ↔ and 24 bases for V. https://doi.org/10.1515/pteridines-2019-0003 received January 24, 2019; accepted February 18, 2019. Keywords: Conclusion:Leonard pair, Amine-HPLC tridiagonal matrix,can self-dualbe used for simultaneous determination of kynurenine, tryptophan 17B37,15A21 Abstract: Introduction: Neopterin, kynurenine Classication:and and neopterin in plasma. Short intense exercise causes tryptophan can be used to measure activation of monocytes a significant increase in plasma neopterin suggesting a and macrophages during immunological events such as prolonged activation of monocytes and macrophages. exercise inducing inflammation. Endurance exercise and high-impact sports have shown significant increases inIntroduction Keywords: Neopterin; biomarker analysis; high- these biomarkers. Measurement is typically conducted by performance liquid chromatography; Indoleamine high-performance liquid chromatography (HPLC) usingLet F denote2,3-dioxygenase; a eld and immune let V activation.denote a vector space over F with nite positive dimension. We consider a C18 or SCX columns. However, kynurenine and tryptophanpair A , A∗ of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for the other one in an are not measured simultaneously to neopterin usingirreducible tridiagonal fashion. Such a pair is called a Leonard pair (see [13, Denition 1.1]). The Leonard pair these separation systems. Here we have used an amineA, A∗ isIntroduction said to be self-dual whenever there exists an automorphism of the endomorphism algebra of V that column for separation and simultaneous determinationswaps of A and A∗. In this case such an automorphism is unique, and called the duality A A∗. ↔ neopterin, kynurenine and tryptophan. TheClinical literature and contains experimental many research examples is often of self-dual limited by Leonard the pairs. For instance (i) the Leonard pair associ- Methods: Optimization and validation for atedthe withinability an irreducible to quantify module compounds for the of interest Terwilliger in a convenient, algebra of the hypercube (see [4, Corollaries 6.8, 8.5]); (ii) a amine-HPLC method was conducted using plasma Leonardfrom simple pair ofand Krawtchouk cost-effective type manner. (see [10, Neopterin, Denition kynurenine 6.1]); (iii) the Leonard pair associated with an irreducible 43 participants subjected to a short maximal exercise and tryptophan are frequently used as plasma biomarkers module for the Terwilliger algebra of a distance-regular graph that has a spin model in the Bose-Mesner alge- bicycling regime or rest period. The order of exercise and of immune system activation in clinical research. These bra (see [1, Theorem], [3, Theorems 4.1, 5.5]); (iv) an appropriately normalized totally bipartite Leonard pair rest was randomized and separated by a 3-5 week washout compounds have been analyzed in plasma, serum and period. (see [11,urine Lemma as biomarkers 14.8]); (v) of the oxidative Leonard stress pair and consisting inflammation, of any two of a modular Leonard triple A, B, C (see [2, Results: Using an amine column developed Denitionwith with 1.4]); measurements (vi) the Leonard traditionally pair being consisting made ofusing a pair HPLC of opposite generators for the q-tetrahedron alge- ammonium acetate formic acid (33%) and acetonitrilebra, actingwith ona C-18 an evaluationor SCX column module utilizing (see reverse [5, Proposition phase or 9.2]).ion The example (i) is a special case of (ii), and the (72%) provided optimal separation and run timeexamples for exchange (iii), (iv) mechanisms, are special casesrespectively, of (v). and fluorescence analysis. Neopterin increased significantly post-exerciseLet detectionA, A∗ denote [1 - 4]. a LeonardHowever, pairthese on methodsV. We canhave determine not been whether A, A∗ is self-dual in the following way. d and subsided to baseline by 30 minutes. Total neopterinBy [13, Lemmasuitable for 1.3] simultaneous each eigenspace detection of A of, allA∗ threehas dimensionbiomarkers. one. Let θ denote an ordering of the eigen- { i}i= remained elevated until 60 minutes following exercise. Neopterin is a product of oxidative stress and d values of A. For ≤ i ≤ d let vi denote a θi-eigenvector for A. The ordering θi i= is said to be standard inflammation, which has ledd to it being studied in { } d whenever A∗ acts on the basis vi i= in an irreducible tridiagonal fashion. If the ordering θi i= is standard many fields of research,d { }including exercise [5, 6], { } then the ordering θd−i i= is also standard, and no further ordering is standard. Similar comments apply to atherosclerosisd { [7]} and surgery [8], amongst others. d A∗. Let θ denote a standard ordering of the eigenvalues of A. Then A, A∗ is self-dual if and only if θ Neopterin{ i}i= is an oxidation product of its parent { i}i= *Corresponding author: Steven P. Gieseg, Gregory Baxter-Parker,is a standard ordering of the eigenvalues of A∗ (see [7, Proposition 8.7]). School of Biological Sciences, University of Canterbury, Christchurch, compound, 7,8-dihydroneopterin, which is a monocyte 8140, New Zealand, E-mail: [email protected], and macrophage synthesized antioxidant, produced [email protected] from guanosine triphosphate metabolism (GTP) by Anna Chu, Samir Samman: Department of Human Nutrition, University GTP cylclohydrolase-I (GTPCH-I) upon stimulation by of Otago, Dunedin, 9016, New Zealand *Correspondinginterferon-γ Author: (IFN-γ) Kazumasa [9, 10]. Nomura:As 7,8-dihydroneopterinTokyo Medical and does Dental University, Ichikawa, 272-0827,Japan, Peter Petocz: Department of Statistics, Macquaire University, Sydney,E-mail: [email protected] not have strong absorbance or fluorescent characteristics, 2006 , NSW, Australia Paul Terwilliger: Department of Mathematics, University of Wisconsin, Madison, WI53706, USA, E-mail: it is typically oxidized to neopterin for detection. The Samir Samman: School of Life and Environmental Sciences, [email protected] of Sydney, Sydney, 2109, NSW, Australia neopterin measured following chemical oxidation of Journal xyz 2017; 1 (2): 122–135 Open Access. © 2019 Gregory Baxter-Parker et al., published byOpen De Gruyter. Access. ©This2019 work Kazumasa is licensed Nomura under and the Paul Creative Terwilliger, Commons published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License. Attribution alone 4.0 License. The First Decade (1964-1972) Research Article Max Musterman, Paul Placeholder What Is So Different About Neuroenhancement? Was ist so anders am Neuroenhancement? Pharmacological and Mental Self-transformation in Ethic Comparison Pharmakologische und mentale Selbstveränderung im ethischen Vergleich https://doi.org/10.1515/xyz-2017-0010 received February 9, 2013; accepted March 25, 2013; published online July 12, 2014 Abstract: In the concept of the aesthetic formation of knowledge and its as soon as possible and success-oriented application, insights and profits without the reference to the arguments developed around 1900. The main investigation also includes the period between the entry into force and the presentation in its current version. Their function as part of the literary portrayal and narrative technique. Keywords: Function, transmission, investigation, principal, period Dedicated to Paul Placeholder 1 Studies and Investigations The main investigation also includes the period between the entry into force and the presentation in its current version. Their function as part of the literary portrayal and narrative technique. *Max Musterman: Institute of Marine Biology, National Taiwan Ocean University, 2 Pei-Ning Road Keelung 20224, Taiwan (R.O.C), e-mail: [email protected] Paul Placeholder: Institute of Marine Biology, National Taiwan Ocean University, 2 Pei-Ning Road Keelung 20224, Taiwan (R.O.C), e-mail: [email protected] Open Access. © 2017 Mustermann and Placeholder, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. 22 Gregory Baxter-Parker et al. a sample is termed “total neopterin” and represents Methods neopterin plus 7,8-dihydroneopterin [11, 12]. Kynurenine is a product of tryptophan metabolism Study design and population by indoleamine 2,3-dioxygenase (IDO), which

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