Two-dimensional lattice gauge theories with superconducting quantum circuits.

A quantum simulator of [Formula: see text] lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories.

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at nonzero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.

Atomic quantum simulation of dynamical gauge fields coupled to fermionic matter: from string breaking to evolution after a quench.

Using a Fermi-Bose mixture of ultracold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.

Width of the confining string in Yang-Mills theory.

We investigate the transverse fluctuations of the confining string connecting two static quarks in (2+1)D SU(2) Yang-Mills theory using Monte Carlo calculations. The exponentially suppressed signal is extracted from the large noise by a very efficient multilevel algorithm. The resulting width of the string increases logarithmically with the distance between the static quark charges. Corrections at intermediate distances due to universal higher-order terms in the effective string action are calculated analytically. They accurately fit the numerical data.

From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.

We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.

Nested cluster algorithm for frustrated quantum antiferromagnets.

Frustrated antiferromagnets are important materials whose quantum Monte Carlo simulation suffers from a severe sign problem. We construct a nested cluster algorithm which uses a powerful strategy to address this problem. For the spin 1/2 Heisenberg antiferromagnet on a kagome and on a frustrated square lattice the sign problem is eliminated for large systems. The method is applicable to general lattice geometries but limited to moderate temperatures.

Study of CP(N-1) theta-vacua by cluster simulation of SU(N) quantum spin ladders.

D-theory provides an alternative lattice regularization of the 2D CP(N-1) quantum field theory in which continuous classical fields emerge from the dimensional reduction of discrete SU(N) quantum spins. Spin ladders consisting of n transversely coupled spin chains lead to a CP(N-1) model with a vacuum angle theta=npi. In D-theory no sign problem arises and an efficient cluster algorithm is used to investigate theta-vacuum effects. At theta=pi there is a first order phase transition with spontaneous breaking of charge conjugation symmetry for CP(N-1) models with N>2.

Screening for renal carcinoma associated mutations in the von Hippel-Lindau tumor suppressor gene by temperature gradient gel electrophoresis.

Renal cell carcinoma is the most common neoplastic disease of the adult kidney and occurs in its sporadic and hereditary form. Approximately 57% of all renal carcinomas of the clear cell type analyzed revealed a mutation in the von Hippel-Lindau disease (VHL) gene. In the present work, temperature gradient gel electrophoresis (TGGE) is presented as a rapid and precise polymerase chain reaction (PCR)-employing methodology for the detection of mutations in the VHL gene. The theoretical efficiency of TGGE to detect mutations in every base pair of the gene was calculated. According to computer analysis, at least 92% of all known mutations in the VHL gene are detectable. This calculated figure appears to be in agreement with the experimental results. Primary difficulties in analyzing exon 1 of the VHL gene were overcome by the employment of psoralen-cross-linked PCR fragments. In addition, TGGE analysis was used in screening for possible mutations in thirteen renal carcinoma samples. With this protocol TGGE is successfully added to the array of methods for the screening of VHL mutations.

Scanning for mutations in the human prion protein open reading frame by temporal temperature gradient gel electrophoresis.

Gerstmann-Sträussler-Scheinker syndrome (GSS), fatal familial insomnia (FFI) and familial Creutzfeldt-Jakob disease (CJD) are caused by point mutations or octarepeat insertions in the prion protein (PrP) gene. In the present work a method was established that is appropriate for a thorough screening for mutations in the PrP gene and is generally applicable to screenings of any given gene. Temperature gradient gel electrophoresis (TGGE) was modified at two critical steps by UV cross-linking of the DNA strands and by replacing the spatial gradient with a temporal one. The shift of a DNA band in temporal temperature gradient gel electrophoresis (tTGGE) due to a mutation can be calculated as a function of the position of the mutation in the sequence. Appropriate DNA fragments were selected for polymerase chain reaction (PCR) amplification and analysis by tTGGE on the basis that the predicted band shifts amount to more than 10% of the migration distance for all possible mutations. The accuracy of the prediction was tested experimentally with ten known mutations in the human PrP gene, and quantitative agreement between theory and experiment was achieved. Thus, this screening method is also a suitable means to verify the absence of mutations in a given gene segment.

Prions and nucleic acids: search for "residual" nucleic acids and screening for mutations in the PrP-gene.

Studies on prions involve nucleic acid chemistry under two headings: i) do infectious prion particles contain nucleic acids? ii) is it possible by a simple procedure to screen the prion protein (PrP)-gene for mutations? The return refocusing gel electrophoresis technique was developed to detect by sensitive silver staining homogeneous and heterogeneous nucleic acids extracted from highly purified scrapie prion preparations. With this method all kinds of nucleic acids from a length of 13 nucleotides up to several thousand could be recovered and detected with a yield over 90%. Despite extensive nuclease digestion some small polynucleotides remained. The results define clear restrictions for a hypothetical scrapie-specific nucleic acid. If homogeneous in size, such a molecule would be smaller than 80 nucleotides in length at a particle-to-infectivity ratio near unity; if heterogeneous, scrapie-specific nucleic acids would have to include molecules smaller than 240 nucleotides. To detect mutations in the PrP-gene, either known mutations from human prion diseases or artificial ones in transgenic animals, or to screen for not yet identified mutations in patients, a method is required which guarantees detection of mutations which might occur in every single position of the whole PrP-ORF. It will be shown that a combination of PCR and temperature-gradient gel electrophoresis fulfils these requirements. By thermodynamic calculations the shift in the gel electrophoresis due to a mutation can be calculated depending on the position of the mutation. The theoretical results were tested with the mutations known so far.

Differential expression of growth-associated protein (GAP-43) mRNA in rat primary sensory neurons after peripheral nerve lesion: a non-radioactive in situ hybridisation study.

An alkaline phosphatase-labelled anti-sense oligodeoxynucleotide probe specific for growth-associated protein messenger RNA (GAP-43 mRNA) was used for non-radioactive in situ hybridisation histochemistry to follow relative changes in GAP-43 mRNA content in lumbar primary sensory neurons (L4-6) after unilateral ligation of the sciatic nerve. In normal dorsal root ganglia (DRG) 16% of neurons expressed GAP-43 mRNA, and these cells belonged to a sub-group of intermediate-sized (32-50 microns diameter) and large (> 50 microns) neurons. The hybridisation signal detected in these cells was weak to moderate. One day after nerve ligature a significant increase in the number of GAP-43 mRNA expressing neurons in the ipsilateral DRG was detected involving particularly the very small (12-20 microns) cells, and small cell population (20-32 microns), though the hybridisation signal was less pronounced in this latter cell group. A significant increase in the cellular content of GAP-43 mRNA was detected in both cell groups when compared to the normal DRG by 2 days after the lesion. At later times (4, 7, and 10 days postinjury) the intermediate-sized and large cell subpopulations also showed an increase in the number of GAP-43 mRNA positive neurons, followed by a significant rise in their content of GAP-43 mRNA. However, they did not reach the same intensity of hybridisation signal as seen in the small and very small neurons. All DRG neurons showed a maximum of GAP-43 mRNA expression by 10 days postsurgery. At longer times there was a slight decrease in the content of GAP-43 mRNA towards 14 days postinjury, but mRNA levels remained elevated up to 28 days after nerve ligature, the longest time point examined in this study. The different onset and levels of GAP-43 gene expression in the rat primary sensory neurons after lesion of their peripheral branch axons further characterize the different subclasses of these cells and may reflect their different involvement in the plastic changes following peripheral nerve injury.

Temperature-gradient gel electrophoresis for the detection of polymorphic DNA and for quantitative polymerase chain reaction.

In order to detect mutations in a gene, either known mutations from human diseases or artificial ones in transgenic animals, or to screen for not yet identified mutations in patients, a method is required which guarantees detection of mutations which might occur in every single position of the whole open reading frame (ORF). It will be shown that a combination of polymerase chain reaction (PCR) and temperature gradient gel electrophoresis (TOGE) fulfills these requirements. By thermodynamic calculations the shift in the gel electrophoresis due to a mutation can be calculated in dependence on the position of the mutation. The theoretical results were tested with the mutations known so far. The quantitative determination of the copy number of a specific DNA or RNA sequence in a biological specimen (quantitative PCR) can be performed precisely and easily by combining PCR and TGGE. The system uses a quantification strategy of a new type of internal standardization. TGGE is applied to separate homo- and heteroduplexes which correspond respectively to standard and template sequences. The accuracy of this quantification strategy is very high, with a variability of < 15%. In addition to quantification, PCR/TGGE detects PCR artifacts and template mutants.

GAP-43 mRNA in Rat Spinal Cord and Dorsal Root Ganglia Neurons: Developmental Changes and Re-expression Following Peripheral Nerve Injury.

The expression of growth-associated protein GAP-43 mRNA in spinal cord and dorsal root ganglion (DRG) neurons has been studied using an enzyme linked in situ hybridization technique in neonatal and adult rats. High levels of GAP-43 mRNA are present at birth in the majority of spinal cord neurons and in all dorsal root ganglion cells. This persists until postnatal day 7 and then declines progressively to near adult levels (with low levels of mRNA in spinal cord motor neurons and 2000 - 3000 DRG cells expressing high levels) at postnatal day 21. A re-expression of GAP-43 mRNA in adult rats is apparent, both in sciatic motor neurons and the majority of L4 and L5 dorsal root ganglion cells, 1 day after sciatic nerve section. High levels of the GAP-43 mRNA in the axotomized spinal motor neurons persist for at least 2 weeks but decline 5 weeks after sciatic nerve section, with the mRNA virtually undetectable after 10 weeks. The initial changes after sciatic nerve crush are similar, but by 5 weeks GAP-43 mRNA in the sciatic motor neurons has declined to control levels. In DRG cells, after both sciatic nerve section or crush, GAP-43 mRNA re-expression persists much longer than in motor neurons. There was no re-expression of GAP-43 mRNA in the dorsal horn of the spinal cord after peripheral nerve lesions. Our study demonstrates a similar developmental regulation in spinal cord and DRG neurons of GAP-43 mRNA. We show moreover that failure of re-innervation does not result in a maintenance of GAP-43 mRNA in axotomized motor neurons.

Production and characterization of an anti-peptide antibody specific for the growth-associated protein, GAP-43.

In an attempt to raise specific anti-GAP-43 antibodies, a C-terminal tetradecapeptide was synthesized based on the predicted rat GAP-43 amino acid sequence using the F-moc polyamide solid phase procedure. The synthesized carboxy-terminal peptide was purified by reverse phase HPLC, conjugated to bovine serum albumin (BSA) and used as an immunogen. Polyclonal antipeptide antibodies raised in rabbits were affinity purified and their specificity for GAP-43 tested by Western blotting. Brain and spinal cord homogenates and GAP-43 enriched synaptosomal membrane fractions were analysed either by SDS-PAGE or reverse phase HPLC. The anti-GAP-43 antibodies detected a major immunoreactive band at 43 kDa (B-50), and a minor immunoreactive band at 38 kDa (B-60) together with an additional protein-band at 68 kDa, which was related to the peptide carrier, BSA. Immunohistochemical studies using these carboxy-terminal antipeptide antibodies revealed a widespread distribution of GAP-43 immunoreactivity throughout the adult rat brain and spinal cord, in a pattern generally consistent with earlier histochemical studies. It is concluded that the C-terminal GAP-43 specific tetradecapeptide is a potent immunogen and provides a convenient tool for the production of sequence specific anti-GAP-43 antibodies.

Intraspinal cellular responses after spinal cord transection in rats: neuronal expression of growth-associated protein (GAP-43).

The methods of non-radioisotopic in situ hybridization and immunocytochemistry were used to visualize sites of GAP-43 expression after a mid-thoracic spinal cord transection in adult rats. Neurons which expressed moderate to high levels of GAP-43 mRNA and showed strong GAP-43-like immunoreactivity were located immediately above the lesion site as well as at greater distances from the lesion site in the lower cervical and mid-lumbar spinal cord. The results of this study suggest a widespread occurrence of lesion-induced neuroplastic changes and may indicate that the increase in GAP-43 expression can be caused by axotomy, deafferentation and increased compensatory motor activity in the spinal cord of paraplegic rats.