Kinetic Analysis of the Hydrolysis of Pentose‐1‐phosphates through Apparent Nucleoside Phosphorolysis Equilibrium Shifts

Abstract Herein, we report an addition to the toolbox for the monitoring and quantification of the hydrolytic decay of pentose‐1‐phosphates, which are known to be elusive and difficult to quantify. This communication describes how apparent equilibrium shifts of a nucleoside phosphorolysis reaction can be employed to calculate hydrolytic loss of pentose‐1‐phosphates based on the measurement of post‐hydrolysis equilibrium concentrations of a nucleoside and a nucleobase. To demonstrate this approach, we assessed the stability of the relatively stable ribose‐1‐phosphate at 98 °C and found half‐lives of 1.8–11.7 h depending on the medium pH. This approach can be extended to other sugar phosphates and related reaction systems to quantify the stability of UV‐inactive and hard‐to‐detect reaction products and intermediates.


General remarks
All chemicals used in this study were of analytical grade or higher and purchased from Sigma Aldrich (Steinheim, Germany), Carbosynth (Berkshire, UK), Carl Roth (Karlsruhe, Germany), TCI Deutschland (Eschborn, Germany) or VWR (Darmstadt, Germany) and used without prior purification. Water deionized to 18.2 MΩ•cm with a Werner water purification system was used for the preparation of all enzymatic reactions as well as purification and storage buffers. For the preparation of NaOH solutions for quenching, deionized water was used. All experiments were carried out in duplicate.

Experimental
Geobacillus thermoglucosidasius pyrimidine nucleoside phosphorylase (GtPyNP) was obtained via heterologous expression in E. coli as described recently. [3,4] Briefly the enzyme was heterologously expressed in E. coli as His6-tagged proteins through IPTG-induced overexpression. Purification was achieved through cell disruption, heat treatment of the crude extract (60 °C for 30 min) and Ni-NTA affinity chromatography. Proteins were eluted with buffer containing 250 mM imidazole, 50 mM sodium phosphate, 300 mM NaCl (pH 8) and desalted into 2 mM potassium phosphate buffer (pH 7).
The protein was stored as a stock solution of 1.2 g L -1 (calculated with 1 AU cm -1 at 280 nm being equal to a protein concentration of 1 g L -1 ) at −20 °C in 50% (v/v) glycerol. Note: We used GtPyNP in our study because that was what we happened to have on hand and, having used this enzymes in previous studies, [5,6] knew about its robustness and performance. In principle, any nucleoside phosphorylase can be employed for the first and second phosphorolysis steps in the described approach. However, this may necessitate the application of different working spaces and consideration of the temperaturedependence of the equilibrium constant of phosphorolysis. [7] Rib1P was generated in situ via enzymatic phosphorolysis of 2 mM uridine with 8 mM potassium phosphate catalyzed by 5 µg mL -1 GtPyNP in 10 mM MOPS buffer pH 7 at 50 °C in a total volume of 1.3 mL in an Eppendorf tube. This yielded 1.02 mM Rib1P in the equilibrium, corresponding to 50.8% conversion of the nucleoside to the nucleobase. Under these conditions, the equilibrium was reached after ca. 20 min and the reaction was run for an additional 20 min (40 min total) to ensure that the equilibrium was truly established (please also note that the concentrations chosen for this experiment are arbitrary and not relevant -the experiment would have worked the same way with higher or lower concentrations of all components). The resulting reaction mixture was then aliquoted into PCR tubes and diluted with a buffer mix for pH adjustment (150 µL reaction mixture + 50 µL buffer stock) to achieve final concentrations of 0.75 mM Rib1P, 5 mM citrate, 17.5 mM MOPS and 20 mM glycine at pH 7−9. These mixtures were transferred to a PCR cycler and incubated at 98 °C (with 105 °C lid temperature to prevent evaporation). At various points in time, tubes were removed from the PCR cycler and stored at 4 °C until analysis. A second phosphorolysis step was initiated to determine the amount of hydrolyzed Rib1P. To this end, further phosphorolysis of this mixture was started by the addition of fresh GtPyNP and MOPS buffer pH 7 to reach final concentrations of 5 µg mL -1 and 50 mM, respectively (150 µL incubation mix + 50 µL enzyme and buffer mix containing 20 µg mL -1 GtPyNP and 50 mM MOPS buffer). The resulting mixture contained 0.56 mM ribosyl compound (Rib1P and ribose), 3.8 mM citrate, 63.1 mM MOPS, 15 mM glycine and 5 µg mL -1 GtPyNP. This second phosphorolysis reaction was run into its equilibrium and samples of 40 µL were withdrawn and quenched in 300 µL 100 mM aqueous NaOH after 20, 30 and 40 min. The dilution steps described above effected a decrease in concentration of all initial reaction components. Since all initial components (nucleoside, base, phosphate, Rib1P) were diluted equally with each step, this dilution factor can be neglected since our chosen analytical method [4,8] records molar ratios of the nucleoside and the nucleobase and derived conversions are relative. Using a concentration-independent method to determine the concentration allowed direct extrapolation of the relative amounts observed after dilution to the relative amounts present in the initial reaction.
Reaction monitoring was achieved via spectral unmixing. From reactions in equilibrium, samples of 40 µL were withdrawn and quenched in 300 µL 100 mM aqueous NaOH as described previously. [4,8] Of these diluted alkaline samples, 200 µL were transferred to UV/Vis-transparent 96-well plates (UV star, GreinerBioOne, Kremsmünster, Austria) for analysis. UV absorption spectra were recorded from 250−350 nm with a BioTek PowerWave HT platereader (BioTek Instruments, Winooski, USA) and subjected to spectral unmixing using analogously obtained reference spectra. Reference spectra used in this study are freely available in the externally hosted Supplementary Information and can, alternatively, be obtained from the Supplementary Information of previous publications. [9] The degree of conversion was determined directly from the spectra fit which considers the UV-active substrate and product in relation to one another. [4] All experimental spectra were fit to the information-rich shoulder region of the uridine-uracil pair (270−300 nm) and corrected for time-and conditiondepended background spectra as detailed in the metadata files in the externally hosted supplementary information.

Equations
The following describes the derivation of the equations given in the main text and further equations and assumptions used for calculation. For equations appearing in the main text, the equation numbers as listed in the main text were adopted, even if their order in this document may not be identical. All other equations were listed in order as supplementary equations (S1)−(S26).
The initial phosphorolysis reaction can be described by the law of mass action with the initial mass balances where is the equilibrium constant of phosphorolysis and Termination of the enzymatic reaction (e.g. through short boiling of the reaction mixture) prevents further phosphorolysis of the nucleoside. When this mixture is then subjected to hydrolyzing conditions, a fraction (or all) of the provided pentose-1-phosphate will by hydrolyzed into ribose and phosphate, giving the new mass balances where [ 1 ] ℎ is the amount of hydrolyzed pentose-1-phosphate. The mass balances of the nucleoside and the nucleobase remain identical. This process yields a reaction mixture containing the nucleoside and nucleobase concentration established by the initial phosphorolysis with the phosphate and pentose-1-phosphate concentrations depending on the extent of hydrolysis of the latter. At this point, continuation of phosphorolysis (through addition of fresh enzyme) will establish a new equilibrium to account for the loss of pentose-1-phosphate and the increase of phosphate compared to its phosphorolysis equilibrium concentration. Therefore, continued conversion of the nucleoside to the nucleobase and pentose-1-phosphate will be observed until a new equilibrium is reached, which again complies with the law of mass action given in equation (1). The resulting extended mass balances in this new equilibrium can be formulated as where [ ] is the concentration of newly consumed nucleobase. Since conversion of the nucleoside to the nucleobase is easily measured in relation (i.e. molar ratios), for example by spectral unmixing, [4,8] the degree of conversion in these equilibria can be employed to simplify these equations by assuming where 1 is the degree of conversion of the nucleoside to the nucleobase in the first equilibrium as given in equation (5) and 2 is the degree of conversion in the second equilibrium defined as These degrees of conversion are equivalent to the relative molar amounts of the nucleobase compared to the nucleoside (i.e. a 1 = 0.1 is equivalent to 10% conversion of the nucleoside to the nucleobase).
Substitution in the above equations gives the mass balances which can be simplified by collapsing all terms containing 1 to yield To determine the quantity of interest, [ 1 ]  [ ] 0 ( 2 − 2 − ) (S17) simplified to The expected maximum conversion in the second equilibrium 2, can be obtained through the assumption of full hydrolysis of the initially generated sugar phosphate Substitution in equation (9) Since water as a reagent for the hydrolysis of pentose-1-phosphates is present in excess, this reaction most likely proceeds via first-order kinetics where the decrease of the pentose-1-phosphate concentration can be describes by where [ 1 ] 0 is the concentration of the pentose-1-phosphate in the first equilibrium (before hydrolysis), is the incubation time and is the mean half-life. The decay constant is then available via = −1 (S24) and the half-life 1/2 can be obtained through The temperature-dependence of the rate constant likely follows the Eyring equation [10] = ℎ exp (− ‡  Information for all raw data and calculations. [2] Figure S3. Comparison of the kinetic data of Bunton and Humeres [11] with those obtained in this study. The data of Bunton were extrapolated from 82 °C to 98 °C assuming temperature-independent ∆ ‡ values as listed in Table S1. Bunton used diluted acid in their experiments and monitored the hydrolysis of pure Rib1P via liberation of phosphate as assessed by a colorimetric assay. This study employed a buffered enzymatic reaction and in situ generated Rib1P and monitored its hydrolysis through apparent equilibrium shifts of a nucleoside phosphorolysis reaction. Table S1. Extrapolation of the kinetic data of Bunton and Humeres [11] pH (82 °C) [