Multiple Couplings and Renormalization Scheme Ambiguities

The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the beta-functions can be chosen to vanish beyond a certain order in perturbation theory, but that the beta-functions always contain ambiguities beyond first order. We examine how the coupling constants depend on the coefficients of the beta-function beyond one loop order. A way of characterizing renormalization schemes that doesn't use coefficients of the beta-function is considered for models with either one or two couplings. The renormalization scheme ambiguities of physical quantities computed to finite order in perturbation theory are also examined. We demonstrate how summation of the logarithms that have explicit dependence on the renormalization scale parameter mu in a physical quantity R leads to a cancellation with the implicit dependence of R on mu through the running couplings. It is also shown that there exists a renormalization scheme in which all radiative effects beyond lowest order are incorporated into the behaviour of the running couplings

Light Front Quantization with the Light Cone Gauge

The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a 2 + 1 dimensional target space

Renormalization Scheme Ambiguities in the Models with More than One Coupling

The process of renormalization to eliminate divergences arising in quantum field theory is not uniquely defined; one can always perform a finite renormalization, rendering finite perturbative results ambiguous. The consequences of making such finite renormalizations have been examined in the case of there being one or two couplings. In this paper we consider how finite renormalizations can affect more general models in which there are more than two couplings. In particular, we consider the Standard Model in which there are essentially five couplings. We show that in this model (when neglecting all mass parameters) if we use mass independent renormalization, then the renormalization group beta-functions are not unique beyond one loop order, that it is not in general possible to eliminate all terms beyond certain order for all these beta-functions, but that for a physical process all contributions beyond one loop order can be subsumed into the beta-functions

Funktionelle Rekonstitution des menschlichen lysosomale Peptid-Transporter TAPL zeigt die Substratspezifität

The transporter associated with antigen processing-like (TAPL) acts as a lysosomal ATP-dependent polypeptide transporter with broad length selectivity. To characterize in detail its substrate specificity, a procedure for solubilization, purification and functional reconstitution of human TAPL was developed. TAPL was expressed in Sf9 insect cells with the baculovirus expression system and solubilized from crude membranes. By intensive screening of detergents, the mild non-ionic detergents digitonin and dodecylmaltoside were found to be ideal for solubilization with respect to efficiency, long term stability, and functionality of TAPL. TAPL was isolated in a two-step procedure with a yield of 500 micro g/L cell culture and, subsequently, reconstituted into proteoliposomes. The KM(pep) for the peptide RRYCfKSTEL (f refers to fluorescence label) and KM(ATP) were determined to be 10.5 ± 2.3 micro M and 97.6 ± 27.5 micro M, respectively, which are in the same range as the Michaelis-Menten constants determined in the membranes. The peptide transport activity of the reconstituted TAPL strongly depends on the lipid composition. Interestingly, the E. coli lipids are prefered over other tested natural lipids extracts. Moreover, phosphatidylcholine, the most abundant phospholipid in eukaryotic cells influenced TAPL activity in a dose dependent manner. In addition, some negatively charged lipids like DOPA and DOPS increased peptide transport activity with preference for DOPS. However, DOPE or egg PG which are also negatively charged had no effect. It seems not only the charge but also the specific head group of phospholipids that has impact on the function of TAPL. With the help of combinatorial peptide libraries containing D-amino acid residues at defined positions as well as bulky fluorescein labeled peptides, the key positions of the peptides were localized to the N- and C-terminal residues with respect to peptide transport. The C-terminal position has the strongest selectivity since modification at this position shows strongest impact on peptide transport. Additionally, positions 2 and 3 of the peptide also have weak influence on peptide selectivity. Subsequently, the residue preferences at the key positions were systematically investigated by combinatorial peptide libraries with defined residues at certain positions. At both ends, TAPL favors positively charged, aromatic, or hydrophobic residues and disfavors negatively charged residues as well as asparagine and methionine. The residue preferences at the key positions are valid for peptide substrates with different length, indicating a general rule for TAPL selectivity. Besides specific interactions of both terminal residues, electrostatic interactions are important, since peptides with positive net charge are more efficiently transported than negatively charged ones. By size exclusion chromatography (SEC) and blue native PAGE, TAPL purified in the presence of digitonin or dodecylmaltoside had an apparent molecular weight of 200 kDa which is close to the theoretical molecular mass of the TAPL homodimer (172 kDa). The purified and reconstituted TAPL showed specific ATP hydrolysis activity which can be inhibited by orthovanadate. TAPL in proteoliposomes showed 6-fold higher ATP hydrolysis than digitonin solubilized protein, indicating the phospholipids impact on TAPL function. However, no peptide substrate stimulated ATPase activity was observed. For site-specific labeling of TAPL, eight cysteines in each half transporter were replaced by alanine or valine. The TAPL cys-less mutant showed the same peptide transport activity as TAPL wt. Based on the functional TAPL cys-less mutant, seven single cysteine mutants were introduced into strategic positions. All single cysteine mutants in the TMD did not influence peptide transport, whereas the mutant L701C, which is close to the conserved H-loop motif, displayed impaired transport. TAPL orthologs Haf-4 and Haf-9 from Caenorhabditis elegans possess around 40% sequence identities with TAPL and 50% with each other. Both proteins are putative half transporters and reported to be involved in the intestinal granule formation (Bauer, 2006; Kawai et al., 2009). To further understand the physiological functions of these two proteins, they were expressed in Sf9 insect cells. Haf-4 and Haf-9 showed weak but specific ATP- and peptide-dependent peptide transport activity for the given peptide RRYCfKSTEL. Therefore, it was proposed that the physiological roles for Haf-4 and Haf-9 might be related to their peptide transport activity. Besides forming functional homodimeric complex as estimated by the peptide transport activities, both half transporter could also form heteromers which was confirmed by coimmunoprecipitation. However, the heteromers showed decreased transport activity.Der humane ABC Transportkomplex ABCB9 wurde als lysosomaler Polypeptidtransporter identifiziert. ABCB9 hat eine hohe Sequenzidentität zu TAP1 ("transporter associated with antigen processing 1") und TAP2 und wird deshalb "TAP-Like" (TAPL) genannt. In lysosomalen Membranen organisiert sich TAPL als Homodimer, wobei sich das Monomer aus der N-terminalen Transmembrandomänen mit 10 putativen Transmembranhelices fusioniert mit der C-terminalen Nukleotidbindedomänen zusammensetzt. Von humanem TAPL wurden Orthologe in Invetrebraten, wie Caenorhaditis elegans und Pflanzen, nachgeweisen, was auf ein hohes evolutionäres Alter von TAPL hindeutet. Humanes TAPL wird in verschiedenen Geweben exprimiert, u.a. im Herz. Die zentrale Frage auf dem TAPL-Forschungsgebiet beschäftigt sich momentan damit, die physiologische Bedeutung aufzuklären. Um diese Fragestellung beantworten zu können ist die Kenntnis der Substratspezifität von essentieller Bedeutung. Die Ziele meiner Doktorarbeit waren (i) die funktionale Solubilisierung, Reinigung und Rekonstitution von humanem TAPL in Liposomen. (ii) Des weiteren sollte die Substratspezifität detailliert entschlüsselt werden. (iii). Die Generierung und Charakterisierung einer Cystein-freien TAPL Variante sollte den Grundstein legen, um den Translokationsmechanismus und die Struktur aufzuklären. (iv) Weiterhin sollten Orthologe von TAPL aus Caenorhabditis elegans, biochemisch charakterisiert. Da es nicht möglich war, an isolierten TAPL-haltigen Membranen die Substratspezifität von TAPL zu entschlüsseln, wurde eine Prozedur bestehend aus Expresssion in Sf9 Insektenzellen, Solubilisierung, Reinigung und funktionaler Rekonstitution in Liposomen etabliert. Durch intensives "Screening" von Detergenzien zur Solubilisierung von TAPL kristallisierten sich die nicht-ionischen Detergenzien Digitonin und n-Dodecyl-ß-D-maltosid (DDM) bezüglich Langzeitstabilität und Funktionalität von TAPL heraus. Nach Solubilisierung wurde TAPL in einem zwei Stufen Prozess, bestehend aus Kationenaustauscher und Metall-Affinitätschromatographie gereinigt. Der Oligomerisierungszustand von TAPL in der Digitionin- bzw. DDM-Mizelle wurde durch Größenausschlußchromatographie und "blue native" PAGE untersucht. TAPL bildete einen Komplex mit einem apparenten Molekulargewicht von 200 kDa aus, was auf einen Homodimer mit einem theoretischen Molekulargewicht von 172 kDa hinweist. Zur Charakterisierung des Peptidtransports wurde eine Rekonstitution von TAPL in Liposomen etabliert. Nach der funktinonalen Rekonstitution wies TAPL die gleichen kinetischen Parameter wie TAPL in Membranen von Insektenzellen auf. Für den Peptidtransport konnte eine starke Abhängigkeit für die Lipidzusammensetzung detektiert werden. Interessanterweise stellten sich Lipide von E. coli im Vergleich zu Lipidextrakten aus Säugerzellen als bevorzugt heraus. Des weiteren zeigte sich, dass Phosphatidylcholin, das meist verbreitete Lipid in eukaryontischen Zellen, einen Dosisabhängigen Effekt auf die Transportaktivität von TAPL hat. Die höchste Peptidtransporteffizienz wurde in Liposomen bestehend aus 70% E .coli Lipidextrakt und 30% (w/w) 1,2-dioleoyl-sn-glycero-3-phosphocholin (DOPC) nachgewiesen, höhere Konzentationen von DOPC reduzierten die Pepitdtransporteffizienz. Rekonstitutiertes TAPL zeigte eine spezifische ATP-Hydrolyseaktivität, welche durch ortho-Vanadat inhibiert werden konnte. Des Weiteren konnte eine durch Peptid stimulierte ATP-Hydrolyseaktivität nicht nachgewiesen werden. Nach funktionaler Rekonstitution und Charakterisierung von TAPL in Liposomen wurden mit Hilfe von kombinatorischen D-Amino Peptidbibliotheken die Schlüsselpositionen für die Substraterkennung identifiziert. Die C-terminale Position innerhalb des Peptids hat den stärksten Einfluss auf die Substraterkennung, da kovalente Modifikationen den Peptidtransport drastisch reduzieren. Zusätzlich wiesen die N-terminalen Positionen 2 und 3 einen Einfluss auf die Peptidselektivität auf. Die weitere Charakterisierung der Schlüsselpositionen mittels detaillierten Peptidbibliotheken ergab, dass TAPL sowohl bei der N- als auch bei der C-terminalen Position positiv geladene, aromatische oder hydrophobe Aminosäuren bevorzugt. Negativ geladene Aminosäuren sind nicht präferiert. Diese Selektivitätsregel für die Peptiderkennung durch TAPL konnte für Peptide mit verschiedener Länge verifiziert werden. Ein wichtiger Grundstein, um den Translokationsmechnismus und die Struktur von TAPL aufzuklären, ist die Generierung einer Cystein-freien TAPL Variante. Durch gezielte Mutagenese wurden acht Cysteine im TAPL Monomer ersetzt. Die Cystein-freie TAPL Mutante zeigte eine gleiche Peptidtransportaktivität wie TAPL Wildtyp. Nach der Gewährleistung der Funktionalität von Cystein-freiem TAPL wurden einzelne Cysteine an strategischen Positionen wieder eingeführt. Die eingeführten Cysteine hatten keinen Einfluss auf die Expression und den Peptidtransport. Eine Ausnahme bildete die TAPL-Variante L701C, welche nahe der konservierten H-Schleife in der NBD lokalisiert ist und eine signifikant reduzierte Transportaktivität aufweist. Die orthologen TAPL Varianten in Caenorhabditis elegans, Half-4 und Haf-9, besitzen eine Sequenzidentität von 40% mit humanem TAPL. Für eine detaillierte Charakterisierung der physiologischen Funktion und deren Substrate wurden Half-4 und Haf-9 in Sf9-Insektenzellen exprimiert. Beide Proteine transportieren in Abhängigkeit von ATP das Modelpeptid. Interessanterweise scheinen diese Halbtransporter sowohl als Homodimere wie auch als Heterodimere die Funktion als Peptidtransporter erfüllen zu können

Selected Topics in Quantization and Renormalization of Gauge Fields

My thesis covers several topics in the quantization and renormalization of gauge fields, ranging from the application of Dirac constraint procedure on the light front, to the manipulation of Faddeev-Popov method to enable use of the transverse-traceless gauge in first order gravity. Last, I study renormalization group ambiguities and carry out a new characterization method for models with one, two and five couplings. In chapter 2 we apply the Dirac constraint procedure to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets are found. These gauge conditions are not used to eliminate degrees of freedom from the action prior to applying the Dirac constraint procedure. This approach is illustrated by considering Yang-Mills theory and the superparticle in a $2 + 1$ dimensional target space. We consider the first order form of the Einstein-Hilbert action and quantize it using the path integral in chapter 3. Two gauge fixing conditions are imposed so that the graviton propagator is both traceless and transverse. It is shown that these two gauge conditions result in two complex Fermionic vector ghost fields and one real Bosonic vector ghost field. All Feynman diagrams to any order in perturbation theory can be constructed from two real Bosonic fields, two Fermionic ghost fields and one real Bosonic ghost field that propagate. These five fields interact through just five three point vertices and one four point vertex. Finally in chapter 4 we study the ambiguities inherent in renormalization when using mass independent renormalization in massless theories that involve two coupling constants. We review how unlike models in which there is just one coupling constant there is no renormalization scheme in which the $\beta$-functions can be chosen to vanish beyond a certain order in perturbation theory, and also the $\beta$-functions always contain ambiguities beyond first order. We examine how the coupling constants depend on the coefficients of the $\beta$-functions beyond one loop order. A way of characterizing renormalization schemes that doesn\u27t use coefficients of the $\beta$-function is considered for models with one, two and five couplings. The renormalization scheme ambiguities of physical quantities computed to finite order in perturbation theory are also examined. The renormalization group equation makes it possible to sum the logarithms that have explicit dependence on the renormalization scale parameter $\mu$ in a physical quantity R and this leads to a cancellation with the implicit dependence of R on $\mu$ through the running couplings, thereby removing the ambiguity associated with the renormalization scale parameter $\mu$. It is also shown that there exists a renormalization scheme in which all radiative contributions beyond lowest order to R are incorporated into the behavior of the running couplings and the perturbative expansion for R is a finite series

GOGO: An Improved Algorithm to Measure the Semantic Similarity Between Gene Ontology Terms

Measuring the semantic similarity between Gene Ontology (GO) terms is an essential step in functional bioinformatics research. We implemented a software named GOGO for calculating the semantic similarity between GO terms. GOGO has the advantages of both information-content-based and hybrid methods, such as Resnik’s and Wang’s methods. Moreover, GOGO is relatively fast and does not need to calculate information content (IC) from a large gene annotation corpus but still has the advantage of using IC. This is achieved by considering the number of children nodes in the GO directed acyclic graphs when calculating the semantic contribution of an ancestor node giving to its descendent nodes. GOGO can calculate functional similarities between genes and then cluster genes based on their functional similarities. Evaluations performed on multiple pathways retrieved from the saccharomyces genome database (SGD) show that GOGO can accurately and robustly cluster genes based on functional similarities. We release GOGO as a web server and also as a stand-alone tool, which allows convenient execution of the tool for a small number of GO terms or integration of the tool into bioinformatics pipelines for large-scale calculations. GOGO can be freely accessed or downloaded from http://dna.cs.miami.edu/GOGO/

Short Distance Modification of a Gravitational System and its Optical Analog

Motivated by developments in string theory, such as T-duality, it has been proposed that the geometry of spacetime should have an intrinsic minimal length associated with it. This would modify the short distance behavior of quantum systems studied on such a geometry, and an optical analog for such a short distance modification of quantum system has also been realized by using non-paraxial nonlinear optics. As general relativity can be viewed as an effective field theory obtained from string, it is expected that this would also modify the short distance behavior of general relativity. Now the Newtonian approximation is a valid short distance approximation to general relativity, and Schrodinger-Newton equation can be obtained as a non-relativistic semi-classical limit of such a theory, we will analyze the short distance modification of Schrodinger-Newton equation from an intrinsic minimal length in the geometry of spacetime. As an optical analog of the Schrodinger-Newton equation has been constructed, it is possible to optically realize this system. So, this system is important, and we will numerical analyze the solutions for this system. It will be observed that the usual Runge-Kutta method cannot be used to analyze this system. However, we will use a propose and use a new numerical method, which we will call as the two step Runge-Kutta method, for analyzing this system.Comment: 21 pages, 3 figures, 2 table

Robust Safety for Mixed-Autonomy Traffic with Delays and Disturbances

Various control strategies and field experiments have been designed for connected and automated vehicles (CAVs) to stabilize mixed traffic that contains both CAVs and Human-driven Vehicles (HVs). The effect of these stabilizing CAV control strategies on traffic safety is still under investigation. In an effort to prioritize safety over stability, a safety-critical filter via control barrier functions (CBFs) can be designed by modifying the stabilizing nominal control input in a minimal fashion and imparting collision-free driving behaviors for CAVs and HVs. However, such formal safety guarantees can be violated if there are delays in the actuation and communication channels of the CAV. Considering both actuator and sensor delays, and disturbances, we propose robust safety-critical traffic control (RSTC) design to ensure ``robust safety'' of the mixed traffic. While predictor-based CBF has been developed to compensate for the actuator delay, uncertain speed disturbances from the head vehicle cause prediction error and require novel robust CBF design. Besides, safety-critical control with sensor delay also remains an open question. In RSTC, a state predictor with bounded error is designed, and robust CBF constraints are constructed to guarantee safety under actuator delay and disturbances. When there is a sensor delay, a state observer is designed and integrated with a predictor-based CBF to ensure robust safety. Numerical simulations demonstrate that the proposed RSTC avoids rear-end collisions for two unsafe traffic scenarios in the presence of actuator, sensor delays and disturbances