title: Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics

authors: Kalnins, Ernie G.

subjects: mathematics

abstract: We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

text: Coupling constant metamorphosis and Nth-order symmetries in classical and quantum mechanics We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the momenta to polynomials in the momenta. We study specializations of these actions which preserve polynomials and also the structure of the symmetry algebras in both the classical and quantum cases. We give several examples of non-constant curvature third- and fourth-order superintegrable systems in two space dimensions obtained via CCM, with some details on the structure of the symmetry algebras preserved by the transform action.

year: 2010

title: Thermostable proteases from thermophilic microorganisms

authors: Toogood, Helen S.

abstract: Two metallo-proteases, EA1 and YP-T proteases from Bacillus st. EA1 and B. caldolyticus st. YP-T, respectively, differ in amino acid sequence by only one residue (Val61 = Gly61 in EA1 and YP-T respectively). Yet EA1 protease has a higher thermostability than YP-T protease. An analysis of the half lives of the two proteases at 85°C at different Ca²⁺ concentrations shows that at low Ca²⁺ levels, autolysis is the most significant cause of loss of activity, while at higher Ca²⁺ levels denaturation is most significant.

A comparison of the sequences of the two proteases and thermolysin shows that this amino acid difference is located within the third Ca²⁺ binding site (based on the known structure of thermolysin). The residues are not directly involved in binding to the Ca²⁺, but are located within this pocket. Molecular modelling studies of EA1 and YP-T proteases, based on the structure of thermolysin, propose that the stabilisation of EA1 over YP-T protease could be due to extra interaction/s of the side chain of Val 61 of EA1 protease with the benzene ring of Tyr 27. YP-T protease has Gly in this position. As the “side chain” of Gly is only a hydrogen, there is unlikely to be any such interaction with Tyr 27. This possible extra interaction/s could increase the bonding of the amino acids within the calcium binding pocket, which may stabilise the pocket.

Bacillus st. Ak.1 produces a thermostable serine protease (subtilisin). The 16S rRNA analysis closely groups Bacillus st. Ak.1 and B. thermoglucosidasius. However, the organisms have different growth requirements. Bacillus st. Ak.1 has a requirement for glutamate, while B. thermoglucosidasius has a requirement for a compound found in yeast extract and tryptone, but not glutamate (possibly maltose). RAPD-PCR analysis of twelve organisms show that the banding patterns of the organisms are all unique, though the closest two were between Bacillus st. EA1 and B. caldolyticus. Escherichia coli clone PB5517 produces Ak.1 protease constitutively at 35°C. a 10 1 fermentor run was conducted, and 51 mg of the protease was purified to homogeneity.

Ak.1 protease is dramatically stabilised by Ca²⁺ ions. The half life at 70°C increases by four orders of magnitude in the presence of 5 mM Ca²⁺, as compared to the  thermostability in the absence of Ca²⁺. As the concentration of Ca²⁺ ions increased, the degree of denaturation decreased. At high Ca²⁺ concentrations, the major cause of loss of activity was due to autolysis.

Based on the structural and enzymatic data, the extra degree of stabilisation of Ak.1 protease by Ca²⁺ above that of thermitase-Ca²⁺ could be due to the presence of an extra Ca²⁺-binding site in Ak.1 protease. This new site is located close to Ca(1), and could therefore change the binding properties of this site also. Another possibility is that the binding constants of one or more of the Ca²⁺-binding sites could be higher for Ak.1 protease, as compared to thermitase. 

Lanthanide ions stabilised the protease, though to a much smaller degree than Ca²⁺. Like Ca²⁺, they stabilised the protease by the prevention of denaturation. Other cations stabilised the protease to a small degree, especially Sr²⁺. Different cations had different effects on the stability of the enzyme. Other significant stabilisers were 90% solutions of sorbitol, trehalose and glycerol. At 105°C, 90% sorbitol increased the thermostability of the protease from <<1 minute to 104 minutes. It did so by the prevention of autolysis.

The protease has a limited substrate specificity, preferring to cleave substrates containing neutral or hydrophobic amino acids, such as valine, alanine or phenylalanine, at the P₁ site. It has a preference for proline at the P₂ site, and alanine at the P₁-P₄ sites. It also has esterase activity, being able to cleave methyl, ethyl and p-nitrophenyl esters. Studies with Suc-Alaₙ-pNA substrates (n=2-5) shows that the specific activity of the protease increases with increasing chain length, though such a substrate containing 5 alanine residues appears to be being cleaved significantly at more than one site. A comparison of the Kₘ and Vₘₐₓ of the protease to the substrates Suc-Ala-Ala-Pro-Xaa-pNA, where Xaa = Phe, Leu or Ala, shows that the larger and more hydrophobic the P₁ amino acid is, the higher the specificity of the protease for that substrate.

An analysis of the effect of temperature on the Kₘ and Vₘₐₓ of Ak.1 protease with several substrates revealed that the specificity of the protease (Vₘₐₓ/Kₘ) changes with temperature. The Kₘ and Vₘₐₓ decreased with decreasing temperature, but not to the same degree with all substrates. If the protease is assayed with substrates in the presence of 50% methanol, the Kₘ tends to increase dramatically. This is due to hydrophobic partitioning of the solvent. The Vₘₐₓ of the protease decreases under these conditions.

The active site is a cleft, composed of hydrophobic amino acids m the substrate-binding cleft. It is similar to other subtilisins, but differs in the presence of a disulphide bond. The space-filling model of the protease with the substrate SAAPFpNA in the active site shows the cleft ‘bends’ at the P₂ site. This is easily accomidated for by proline at this position, as proline causes a bend in the substrate. This can explain the preference for proline at the P₂ site.

The sequence of Ak.1 protease indicates the presence of two cysteine residues, separated by only one amino acid. The 3D structure showed that these cysteine residues exist in a disulphide bond. Tests (e.g. Ellman assay) confirmed the presence of not only two cysteine residues, but that in native conditions (i.e. in solution) these residues exist as a disulphide bond.

Reductants, such as dithiothreitol (DTI) typically reduce disulphide bonds into their constituent cysteine residues. The lower thermostability in the presence of DTT indicates that it appears to have opened a disulphide bond as disulphide bonds are known to increase the thermostability of proteins. It is proposed that the reduction of the disulphide bond causes a localised opening of the substrate binding cleft at the P₄ site, due to the location of the disulphide bond in this position. This was supported by the results that showed that the larger the substrate, the greater the effect of DTT on the Kₘ of the protease. With that substrate. For example, the Kₘ was unchanged with DTT with a substrate occupying only sites P₂-P₁', while a substrate which occupies sites P₅-P₁' showed a significant increase of the Kₘ, suggesting it binds weaker to the binding cleft.

Heavy metals such as Hg²⁺ and Pb²⁺ bind to Ak.1 protease, causing a decrease in the specific activity of the protease. The effects of the heavy metals on activity is much smaller than with DTT. In general, the Kₘ and Vₘₐₓ were only changed to a small degree. Fluorescein mercuric acetate (FMA) binds to Ak.1 protease, causing the inherent fluorescence of FMA to increase. The presence of DTT caused a decrease in the thermostability of Ak.1 protease of 9.3 fold at 85°C.

In conclusion, the disulphide bond has a dual role, that of maintaining the integrity of the substrate-binding cleft and increasing the thermostability of the protease.

text: Thermostable proteases from thermophilic microorganisms Two metallo-proteases, EA1 and YP-T proteases from Bacillus st. EA1 and B. caldolyticus st. YP-T, respectively, differ in amino acid sequence by only one residue (Val61 = Gly61 in EA1 and YP-T respectively). Yet EA1 protease has a higher thermostability than YP-T protease. An analysis of the half lives of the two proteases at 85°C at different Ca²⁺ concentrations shows that at low Ca²⁺ levels, autolysis is the most significant cause of loss of activity, while at higher Ca²⁺ levels denaturation is most significant.

A comparison of the sequences of the two proteases and thermolysin shows that this amino acid difference is located within the third Ca²⁺ binding site (based on the known structure of thermolysin). The residues are not directly involved in binding to the Ca²⁺, but are located within this pocket. Molecular modelling studies of EA1 and YP-T proteases, based on the structure of thermolysin, propose that the stabilisation of EA1 over YP-T protease could be due to extra interaction/s of the side chain of Val 61 of EA1 protease with the benzene ring of Tyr 27. YP-T protease has Gly in this position. As the “side chain” of Gly is only a hydrogen, there is unlikely to be any such interaction with Tyr 27. This possible extra interaction/s could increase the bonding of the amino acids within the calcium binding pocket, which may stabilise the pocket.

Bacillus st. Ak.1 produces a thermostable serine protease (subtilisin). The 16S rRNA analysis closely groups Bacillus st. Ak.1 and B. thermoglucosidasius. However, the organisms have different growth requirements. Bacillus st. Ak.1 has a requirement for glutamate, while B. thermoglucosidasius has a requirement for a compound found in yeast extract and tryptone, but not glutamate (possibly maltose). RAPD-PCR analysis of twelve organisms show that the banding patterns of the organisms are all unique, though the closest two were between Bacillus st. EA1 and B. caldolyticus. Escherichia coli clone PB5517 produces Ak.1 protease constitutively at 35°C. a 10 1 fermentor run was conducted, and 51 mg of the protease was purified to homogeneity.

Ak.1 protease is dramatically stabilised by Ca²⁺ ions. The half life at 70°C increases by four orders of magnitude in the presence of 5 mM Ca²⁺, as compared to the  thermostability in the absence of Ca²⁺. As the concentration of Ca²⁺ ions increased, the degree of denaturation decreased. At high Ca²⁺ concentrations, the major cause of loss of activity was due to autolysis.

Based on the structural and enzymatic data, the extra degree of stabilisation of Ak.1 protease by Ca²⁺ above that of thermitase-Ca²⁺ could be due to the presence of an extra Ca²⁺-binding site in Ak.1 protease. This new site is located close to Ca(1), and could therefore change the binding properties of this site also. Another possibility is that the binding constants of one or more of the Ca²⁺-binding sites could be higher for Ak.1 protease, as compared to thermitase. 

Lanthanide ions stabilised the protease, though to a much smaller degree than Ca²⁺. Like Ca²⁺, they stabilised the protease by the prevention of denaturation. Other cations stabilised the protease to a small degree, especially Sr²⁺. Different cations had different effects on the stability of the enzyme. Other significant stabilisers were 90% solutions of sorbitol, trehalose and glycerol. At 105°C, 90% sorbitol increased the thermostability of the protease from <<1 minute to 104 minutes. It did so by the prevention of autolysis.

The protease has a limited substrate specificity, preferring to cleave substrates containing neutral or hydrophobic amino acids, such as valine, alanine or phenylalanine, at the P₁ site. It has a preference for proline at the P₂ site, and alanine at the P₁-P₄ sites. It also has esterase activity, being able to cleave methyl, ethyl and p-nitrophenyl esters. Studies with Suc-Alaₙ-pNA substrates (n=2-5) shows that the specific activity of the protease increases with increasing chain length, though such a substrate containing 5 alanine residues appears to be being cleaved significantly at more than one site. A comparison of the Kₘ and Vₘₐₓ of the protease to the substrates Suc-Ala-Ala-Pro-Xaa-pNA, where Xaa = Phe, Leu or Ala, shows that the larger and more hydrophobic the P₁ amino acid is, the higher the specificity of the protease for that substrate.

An analysis of the effect of temperature on the Kₘ and Vₘₐₓ of Ak.1 protease with several substrates revealed that the specificity of the protease (Vₘₐₓ/Kₘ) changes with temperature. The Kₘ and Vₘₐₓ decreased with decreasing temperature, but not to the same degree with all substrates. If the protease is assayed with substrates in the presence of 50% methanol, the Kₘ tends to increase dramatically. This is due to hydrophobic partitioning of the solvent. The Vₘₐₓ of the protease decreases under these conditions.

The active site is a cleft, composed of hydrophobic amino acids m the substrate-binding cleft. It is similar to other subtilisins, but differs in the presence of a disulphide bond. The space-filling model of the protease with the substrate SAAPFpNA in the active site shows the cleft ‘bends’ at the P₂ site. This is easily accomidated for by proline at this position, as proline causes a bend in the substrate. This can explain the preference for proline at the P₂ site.

The sequence of Ak.1 protease indicates the presence of two cysteine residues, separated by only one amino acid. The 3D structure showed that these cysteine residues exist in a disulphide bond. Tests (e.g. Ellman assay) confirmed the presence of not only two cysteine residues, but that in native conditions (i.e. in solution) these residues exist as a disulphide bond.

Reductants, such as dithiothreitol (DTI) typically reduce disulphide bonds into their constituent cysteine residues. The lower thermostability in the presence of DTT indicates that it appears to have opened a disulphide bond as disulphide bonds are known to increase the thermostability of proteins. It is proposed that the reduction of the disulphide bond causes a localised opening of the substrate binding cleft at the P₄ site, due to the location of the disulphide bond in this position. This was supported by the results that showed that the larger the substrate, the greater the effect of DTT on the Kₘ of the protease. With that substrate. For example, the Kₘ was unchanged with DTT with a substrate occupying only sites P₂-P₁', while a substrate which occupies sites P₅-P₁' showed a significant increase of the Kₘ, suggesting it binds weaker to the binding cleft.

Heavy metals such as Hg²⁺ and Pb²⁺ bind to Ak.1 protease, causing a decrease in the specific activity of the protease. The effects of the heavy metals on activity is much smaller than with DTT. In general, the Kₘ and Vₘₐₓ were only changed to a small degree. Fluorescein mercuric acetate (FMA) binds to Ak.1 protease, causing the inherent fluorescence of FMA to increase. The presence of DTT caused a decrease in the thermostability of Ak.1 protease of 9.3 fold at 85°C.

In conclusion, the disulphide bond has a dual role, that of maintaining the integrity of the substrate-binding cleft and increasing the thermostability of the protease.

year: 1998

title: How usable is a smartphone with a Māori-language interface?

authors: Mato, Paora James

subjects: Mäori

abstract: Major languages dominate contemporary technologies. For Mäori, there is opportunity to engage with some technologies using their language and to participate within Mäori- language communities in various digital media. A smartphone launched by Two Degrees Mobile Limited provides a Mäori- language interface option. An initial pilot study indicated users will engage with this interface, but when pushed for time will switch the interface to the English- language option. This paper reports on a study undertaken to test the usability of the smartphone Mäorilanguage interface. Participants reported diffi culties and some frustration as they struggled with new words and unfamiliar uses of words. They also expressed disappointment at poor translations and arbitrary truncations. The feedback highlights perceived shortcomings encountered when technologies that are normally developed and used in a major language are translated for use in minority Indigenous languages. Mäori-language strategies that consider using translated application interfaces should be cognisant of such issues.

text: How usable is a smartphone with a Māori-language interface? Major languages dominate contemporary technologies. For Mäori, there is opportunity to engage with some technologies using their language and to participate within Mäori- language communities in various digital media. A smartphone launched by Two Degrees Mobile Limited provides a Mäori- language interface option. An initial pilot study indicated users will engage with this interface, but when pushed for time will switch the interface to the English- language option. This paper reports on a study undertaken to test the usability of the smartphone Mäorilanguage interface. Participants reported diffi culties and some frustration as they struggled with new words and unfamiliar uses of words. They also expressed disappointment at poor translations and arbitrary truncations. The feedback highlights perceived shortcomings encountered when technologies that are normally developed and used in a major language are translated for use in minority Indigenous languages. Mäori-language strategies that consider using translated application interfaces should be cognisant of such issues.

year: 2016