title: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

text: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

year: 2011

title: An investigation of the accelerated loss of diastase (α-amylase) activity in mānuka honey

authors: Kaur, Harmanpreet

abstract: New Zealand’s multi-million dollar apiculture industry exports over 10,000 tonnes of honey annually. Each country has import guidelines to ensure honey quality. The diastase activity assay is used to determine whether honey has been exposed to harsh conditions (excess storage time or high temperatures will denature diastase) and reports the activity as diastase number (DN), where DN must be >8 for exports. Unfortunately, mānuka honey (NZ’s high value honey with unique properties) fails the diastase assay more often than other NZ floral honeys. Bioactive compounds [methylglyoxal (MGO), dihydroxyacetone (DHA) and 3-phenyllactic acid (3PLA)] in mānuka honey were predicted to decrease diastase activity by forming modifications on diastase. Hence, the extent, diversity, location and functional impacts of these modifications on diastase were investigated.

Two fresh mānuka honeys, a clover control and clover spiked (MGO, DHA, 3PLA, 3PLA+MGO and 3PLA+DHA) honey samples were stored at 27 °C for ~200 days and periodically tested to observe chemical compositional changes in relation to the loss of diastase activity. The results corroborated previous data; DN decreased in honey over time with increased loss rates observed in mānuka. In the spiked clover samples both DHA and MGO increased rates of diastase activity loss and these rates were enhanced by 3PLA (a proton donor). Enzyme kinetics (enzyme-substrate binding and enzyme rate constants) suggest that denaturation is not the sole mechanism for reduced DN values in honey over time, rather, surface level modifications from bioactive compounds are affecting the affinity of diastase for the substrate.

Diastase was isolated from the honeys (days 0 and ~200) using SDS-PAGE gels and analysed with LC-MS/MS to identify surface modifications on diastase. Results showed evidence of diastase modification over the time trial for all honeys. This occurred in unique locations for both mānuka honeys and MGO and 3PLA+DHA spiked clover honeys. Some of these locations were in proximity to the active site of diastase.

The most abundant honey protein, MRJP1, was used to accurately identify trends in modification changes on proteins over time as a model for the effect occurring on diastase (since similar reactive amino acids are present on both MRJP1 and diastase). All honeys (except the clover control) had an increased number of modifications. The largest increases were observed for the MGO, DHA and 3PLA+MGO spiked honeys. Fewer modifications were detected for the 3PLA+DHA spiked honey despite this having the most pronounced changes in the enzyme kinetic parameters. This is likely because the modification library focused on MGO-induced modifications and did not account for DHA modifications.

In summary, MGO modifications on proteins in honey were observed. DHA modifications and the role of 3PLA as a proton donor were deduced from the enzyme kinetic parameters. While time and temperature denature diastase, surface modifications on diastase may be contributing to the accelerated loss of diastase activity observed for mānuka honey. This necessitates the reassessment of diastase activity as a test for honey quality, especially in the context of complex honey matrices (such as mānuka honey).

text: An investigation of the accelerated loss of diastase (α-amylase) activity in mānuka honey New Zealand’s multi-million dollar apiculture industry exports over 10,000 tonnes of honey annually. Each country has import guidelines to ensure honey quality. The diastase activity assay is used to determine whether honey has been exposed to harsh conditions (excess storage time or high temperatures will denature diastase) and reports the activity as diastase number (DN), where DN must be >8 for exports. Unfortunately, mānuka honey (NZ’s high value honey with unique properties) fails the diastase assay more often than other NZ floral honeys. Bioactive compounds [methylglyoxal (MGO), dihydroxyacetone (DHA) and 3-phenyllactic acid (3PLA)] in mānuka honey were predicted to decrease diastase activity by forming modifications on diastase. Hence, the extent, diversity, location and functional impacts of these modifications on diastase were investigated.

Two fresh mānuka honeys, a clover control and clover spiked (MGO, DHA, 3PLA, 3PLA+MGO and 3PLA+DHA) honey samples were stored at 27 °C for ~200 days and periodically tested to observe chemical compositional changes in relation to the loss of diastase activity. The results corroborated previous data; DN decreased in honey over time with increased loss rates observed in mānuka. In the spiked clover samples both DHA and MGO increased rates of diastase activity loss and these rates were enhanced by 3PLA (a proton donor). Enzyme kinetics (enzyme-substrate binding and enzyme rate constants) suggest that denaturation is not the sole mechanism for reduced DN values in honey over time, rather, surface level modifications from bioactive compounds are affecting the affinity of diastase for the substrate.

Diastase was isolated from the honeys (days 0 and ~200) using SDS-PAGE gels and analysed with LC-MS/MS to identify surface modifications on diastase. Results showed evidence of diastase modification over the time trial for all honeys. This occurred in unique locations for both mānuka honeys and MGO and 3PLA+DHA spiked clover honeys. Some of these locations were in proximity to the active site of diastase.

The most abundant honey protein, MRJP1, was used to accurately identify trends in modification changes on proteins over time as a model for the effect occurring on diastase (since similar reactive amino acids are present on both MRJP1 and diastase). All honeys (except the clover control) had an increased number of modifications. The largest increases were observed for the MGO, DHA and 3PLA+MGO spiked honeys. Fewer modifications were detected for the 3PLA+DHA spiked honey despite this having the most pronounced changes in the enzyme kinetic parameters. This is likely because the modification library focused on MGO-induced modifications and did not account for DHA modifications.

In summary, MGO modifications on proteins in honey were observed. DHA modifications and the role of 3PLA as a proton donor were deduced from the enzyme kinetic parameters. While time and temperature denature diastase, surface modifications on diastase may be contributing to the accelerated loss of diastase activity observed for mānuka honey. This necessitates the reassessment of diastase activity as a test for honey quality, especially in the context of complex honey matrices (such as mānuka honey).

year: 2025

title: Translated identities: 'Pakeha' as subjects of the Treaty of Waitangi

authors: Goldsmith, Michael

subjects: Treaty of Waitangi

abstract: The politics of translation is clearly a perennial focus of debate in New Zealand, as shown by thematic links between the New Zealand social anthropology conferences at Waikato in 1990 and Auckland in 2004. Of the many issues of translation swirling around ongoing attempts to interpret the Treaty of Waitangi, a surprisingly neglected one concerns the identities of the people on behalf of whom the Crown signed the Treaty. The term 'Pakeha' appears only once in the Treaty, the question of whom it refers to is by no means straightforward, and it would be unwise to presume that it had the same range of meanings in 1840 as it does in present-day biculturalism. This point is demonstrated by a re-reading of historical material concerning the parties present at or implicated in the signing of the Treaty, including the so-called Pakeha Maori.

text: Translated identities: 'Pakeha' as subjects of the Treaty of Waitangi The politics of translation is clearly a perennial focus of debate in New Zealand, as shown by thematic links between the New Zealand social anthropology conferences at Waikato in 1990 and Auckland in 2004. Of the many issues of translation swirling around ongoing attempts to interpret the Treaty of Waitangi, a surprisingly neglected one concerns the identities of the people on behalf of whom the Crown signed the Treaty. The term 'Pakeha' appears only once in the Treaty, the question of whom it refers to is by no means straightforward, and it would be unwise to presume that it had the same range of meanings in 1840 as it does in present-day biculturalism. This point is demonstrated by a re-reading of historical material concerning the parties present at or implicated in the signing of the Treaty, including the so-called Pakeha Maori.

year: 2005