Reflection Groups and Differential Forms

We study differential forms invariant under a finite reflection group over a field of arbitrary characteristic. In particular, we prove an analogue of Saito's freeness criterion for invariant differential 1-forms. We also discuss how twisted wedging endows the invariant forms with the structure of a free exterior algebra in certain cases. Some of the results are extended to the case of relative invariants with respect to a linear character.Comment: 16 page

Quadratic forms and linear algebraic groups

Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties, as well as some arithmetic aspects pertaining to the theory of quadratic forms over function fields over local fields

Local-global principles for Galois cohomology

This paper proves local-global principles for Galois cohomology groups over function fields $F$ of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for $H^n(F, Z/mZ(n-1))$, for all $n>1$. This is motivated by work of Kato and others, where such principles were shown in related cases for $n=3$. Using our results in combination with cohomological invariants, we obtain local-global principles for torsors and related algebraic structures over $F$. Our arguments rely on ideas from patching as well as the Bloch-Kato conjecture.Comment: 32 pages. Some changes of notation. Statement of Lemma 2.4.4 corrected. Lemma 3.3.2 strengthened and made a proposition. Some proofs modified to fix or clarify specific points or to streamline the presentatio

Analysis of the molecular mechanisms of prestin-mediated cochlear amplification via a cysteine accessibility study

Prestin is the protein being responsible for electromotility in mammals. It is a member of the SLC26 (Solute Carrier) family, which function as anion transporters. In contrast to the other members, mammalian prestin does not function as an anion transporter but produces electromotility. Non-mammalian prestin orthologues such as zebrafish prestin are anion-exchangers with a stoichiometry of 1:1, where a chloride anion is transported in exchange for a divalent anion. Based on the bacterial uracil transporter UraA, a structural homology model of prestin with a 7+7 inverted repeat architecture was predicted. The mechanism of the SLC26-mediated transport is not fully understood. A potential role of this transport mechanism in the electromotile properties of prestin is elusive, but based on the high sequence similarity of transport-capable and electromotile prestin orthologues the idea arose that both are related and electromotility evolved from transport. This is further supported by the finding that the motor protein prestin interacts with and only undergoes conformational rearrangements in the presence of intracellular monovalent anions. Furthermore, it is not completely understood whether electromotile prestin undergoes structural dynamics that are similar to those of transport-capable members of the SLC26 family. The aim of the present study is to elucidate whether the function of the SCL26 transporters and voltage-driven motors follows common structural principles. To achieve this aim, two members of the SLC26 family were chosen as model systems: the non-mammalian zebrafish prestin and the mammalian rat prestin. The method mainly used in this study is a cysteine accessibility study. It allows insights into structures that should change their accessibility to the aqueous medium according to their movement during a transport cycle. The membrane-impermeable MTS reagents were either applied from the intracellular or extracellular side. In rat and zebrafish prestin positions were identified which were sensitive to MTS applications and in consequence accessible. The presumptive anion-binding site and the anion translocation pathway are mainly located in the transmembrane domains 3 and 10. The data here presented are consistent with the structural models derived from experimental structures. Positions within transmembrane domain 10 are mainly accessibly from the intracellular side and positions within transmembrane domain 3 from the extracellular side. Furthermore, there are central positions in zebrafish prestin, which are accessible from both sides. This indicates an alternating-access transport consistent with elevator movement of the core domain. The lack of extracellular access of the homologous positions in rat prestin shows that the extracellular-exposed conformation is not obtained in mammalian prestin. This points towards an incomplete transport mechanism performed by mammalian prestin. The rat prestin mutant V139C is accessible from both sides. This two-sided accessibility suggests an outward movement of the core domain within an incomplete transport transition. This mutant shows that V139 faces the translocation pathway in the inward-open as well as in the occluded conformation and thus stays rigid and does not undergo a conformational rearrangement. An alternating-access transport in elevator mode is characterised by a relatively rigid immobile gate domain, a mobile core domain, which contains the anion-binding site, and a vertical displacement of the bound substrate. The results of the scanning support this mode of transport that was also proposed for a prokaryotic SLC26 family member. While crystal structures record a protein in a certain conformation cysteine labelling provides the opportunity to study the full conformational changes. The model derived from the scanning results present alternate conformations determined by the extracellular accessibilities of positions of the respective prestin orthologue. To what extent the core domain opens to the extracellular side can be deduced by the positions V139 within transmembrane domain 3 in rat prestin and M400 and S400 within transmembrane domain 10 in zebrafish prestin. There is an obvious difference between the alternate conformation of rat and zebrafish prestin. Zebrafish prestin undergoes a full transport cycle from an inward-open to an outward-open conformation, whereas rat prestin alternates between the inward-open and the intermediate (occluded) conformation. The results of the scanning show that the elevator mode of transport is mainly realised by zebrafish prestin. Rat prestin fails to reach the outward-open conformation, thus it performs an incomplete transport mechanism in an elevator-like manner. Additionally, rat prestin V139C shows a combination of mechano- and redox-sensitivity. The activity of rat prestin V139C is dependent on the application of fluid-flow. This flow-dependency of activity seems to be correlated with the microenvironment of the mutant - the more inflexible the side chain the more distinct the flow-sensitivity of activity. On the basis of the presented data the applied fluid-flow does not cause membrane tension in V139C. The mechanosensitivity of V139C seems to be provoked by pure shear stress. Furthermore, it is different from the intrinsic tension-sensitivity of prestin wild type. Finally, the phenomenon of the mechano- and redoxsensitivity could not yet be clarified

Lipase activity in Swedish raw milk

Bovine milk contains several enzymes which can affect the quality of milk. One of these enzymes are lipases which hydrolyse the triacylglycerides in milk. In this process off-flavours, odour and product defects are generated. By controlling the enzymes activity, milk quality can be increased and therefore milk and dairy products can be stored for a longer time. This is desirable since the world demand for long shelf-life milk and milk products is increasing. To monitor the quality of raw milk and control the enzyme activity, a well-functioning method to detect lipase activity is desired. Thus, the aim of this thesis was to investigate and improve an existing method to determine lipolytic activity which is based on a fluorescent approach. With this method, a sensitive fluorescent measurement of the lipase activity directly in the natural milk environment is possible. Once the method was evolved, raw milk samples from different regions in Sweden and from different origins, i.e. farm and dairy, were investigated and evaluated for possible differences in lipase activity. No significant difference was found between samples from farm and dairy origins. Between the different regions a significant difference was discovered. The lowest lipase activity in milk was found in milk from the south (Skånemejerier) followed by milk from the mid region of Sweden (Arla) and the highest lipase activity was seen in milk from the north (Norrmejerier). The lipase activity was also correlated to other previously measured properties of the milk. A significant negative correlation to some long chain fatty acids could be seen. This indicates that long chain fatty acids inhibit lipase activity in the milk which has previously been observed in the adipose tissue of rats and in goats milk. The long chain fatty acid content in milk can be influenced by the feed. Thus, the results of this thesis indicate that the raw milk quality could be improved by increasing the amount of long chain fatty acids in the milk through the feed and thereby reduce lipase activity.Lipases are enzymes that split the fat in milk. This reaction is called lipolysis and results in the release of free fatty acids. These free fatty acids give off-flavours, odour, and product defects to the milk. By controlling the enzyme activity, milk quality can therefore be increased and the shelf life of milk and dairy products can be extended. This is desirable since the world’s demand for long shelf-life milk and milk products is increasing. Hence, it is useful to have a well-functioning method which can detect lipase activity to monitor the quality of raw milk. There are some existing methods to measure the lipase activity. However, the optimal assay for routinely measurements of dairy products for predictive purposes is still not devised. One method was published that measures the lipase activity in the natural milk environment, which has a limited number of experimental steps and has a high sensitivity. However, previous attempts to repeat this method failed. Therefore, the scope of this project was to further investigate that method and improve it. The theory behind this method is to add a substrate to the milk and let it incubate for a specified time. This substrate consists of a fatty acid that is attached to a molecule called 4-methylumbelliferyl. This compound is non-fluorescent unless a lipase splits off the fatty acid to yield one molecule of highly fluorescent 4-methylumbellifery and one molecule fatty acid. Thus, if there is more lipase activity present, more fatty acids are split off and the fluorescence is higher. A fluorescence measurement is not possible in a turbid media like milk and therefore the turbidity needs to be decreased before a fluorescence measurement can be carried out. In milk, the fat droplets and proteins that are present in form of casein micelles cause the turbidity. The basic procedure to remove turbidity is a defatting step, followed by the addition of two solutions to remove the turbidity of the milk by unfolding the protein and make it go into solution. Furthermore, these added solutions stop the enzyme conversion by lowering the pH and thereby denature the lipase. Fluorescence intensity is highly dependent on pH and thus the last solution also rises the pH to a near neutral pH where acceptable fluorescence intensities are seen. By adjusting the pH as it was specified in the previously published method, the method to detect the lipolytic activity showed to be working. However, the variation between data was high and thus further investigation on optimal pH and experimental procedures finally resulted in a lower variation. Also, the centrifugation step and incubation temperature were optimized to attain a more reliable method. It was possible to reduce the limit of detection and quantification of lipase activity and thereby not just attain a more robust but also more sensitive method in comparison to the previously published method. The newly developed method was validated by incubating the substrate in the milk for different times and checked for a linear relation. Also, a comparison of a fresh milk and the same fresh milk which was frozen for different times showed that there is no difference in lipase activity between a fresh and frozen sample. This is important since the measurements carried out later were done on frozen samples. With the developed method, raw milk samples from different regions of Sweden were examined and evaluated for possible differences. The samples were taken both on dairy and farm level. No significant difference between these origins could be seen. However, all three regions were significantly different from each other - the milk from Skånemejerier (south of Sweden) exhibited the lowest lipase activity followed by milk from Arla (mid Sweden) and the highest lipase activity was detected in milk from Norrmejerier (north of Sweden). The lipase activity results were also correlated to other properties of the milk measured previously. These properties include the fat content, amount of fatty acids, and bacterial count of the milk. However, none of the properties had a significant correlation except for some long chain fatty acids which showed a negative correlation to the enzyme activity. This indicates that a high amount of certain long chain fatty acids reduces the lipolytic activity. This effect has been seen in the adipose tissue of rats and in goat’s milk before. Since the amount of long chain fatty acids in the milk can be influenced by the feed, a hypothesis is that the lipase activity could be reduced by changing the feed of the cows