Continuous measurements of two qubits

We develop a theory of coherent quantum oscillations in two, in general interacting, qubits measured continuously by a mesoscopic detector with arbitrary non-linearity and discuss an example of SQUID magnetometer that can operate as such a detector. Calculated spectra of the detector output show that the detector non-linearity should lead to mixing of the oscillations of the two qubits. For non-interacting qubits oscillating with frequencies $\Omega_1$ and $\Omega_2$, the mixing manifests itself as spectral peaks at the combination frequencies $\Omega_1\pm \Omega_2$. Additional nonlinearity introduced by the qubit-qubit interaction shifts all the frequencies. In particular, for identical qubits, the interaction splits coherent superposition of the single-qubit peaks at $\Omega_1=\Omega_2$. Quantum mechanics of the measurement imposes limitations on the height of the spectral peaks.Comment: 14 pages, 6 figure

Determination of the primary structure and carboxyl pKAs of heparin-derived oligosaccharides by band-selective homonuclear-decoupled two-dimensional 1H NMR

Determination of the structure of heparin-derived oligosaccharides by 1H NMR is challenging because resonances for all but the anomeric protons cover less than 2 ppm. By taking advantage of increased dispersion of resonances for the anomeric H1 protons at low pD and the superior resolution of band-selective, homonuclear-decoupled (BASHD) two-dimensional 1H NMR, the primary structure of the heparin-derived octasaccharide ∆UA(2S)-[(1 → 4)-GlcNS(6S)-(1 → 4)-IdoA(2S)-]3-(1 → 4)-GlcNS(6S) has been determined, where ∆UA(2S) is 2-O-sulfated ∆4,5-unsaturated uronic acid, GlcNS(6S) is 6-O-sulfated, N-sulfated β-d-glucosamine and IdoA(2S) is 2-O-sulfated α-l-iduronic acid. The spectrum was assigned, and the sites of N- and O-sulfation and the conformation of each uronic acid residue were established, with chemical shift data obtained from BASHD-TOCSY spectra, while the sequence of the monosaccharide residues in the octasaccharide was determined from inter-residue NOEs in BASHD-NOESY spectra. Acid dissociation constants were determined for each carboxylic acid group of the octasaccharide, as well as for related tetra- and hexasaccharides, from chemical shift–pD titration curves. Chemical shift–pD titration curves were obtained for each carboxylic acid group from sub-spectra taken from BASHD-TOCSY spectra that were measured as a function of pD. The pKAs of the carboxylic acid groups of the ∆UA(2S) residues are less than those of the IdoA(2S) residues, and the pKAs of the carboxylic acid groups of the IdoA(2S) residues for a given oligosaccharide are similar in magnitude. Relative acidities of the carboxylic acid groups of each oligosaccharide were calculated from chemical shift data by a pH-independent method

Reheating in the Presence of Inhomogeneous Noise

Explosive particle production due to parametric resonance is a crucial feature of reheating in an inflationary cosmology. Coherent oscillations of the inflaton field lead to a periodically varying mass in the evolution equation of matter and gravitational fluctuations and often induce a parametric resonance instability. In a previous paper (hep-ph/9709273) it was shown that homogeneous (i.e. space independent) noise leads to an increase of the generalized Floquet exponent for all modes, at least if the noise is temporally uncorrelated. Here we extend the results to the physically more realistic case of spatially inhomogeneous noise. We demonstrate - modulo some mathematical fine points which are addressed in a companion paper - that the Floquet exponent is a non- decreasing function of the amplitude of the noise. We provide numerical evidence for an even stronger statement, namely that in the presence of inhomogeneous noise, the Floquet exponent of each mode is larger than the maximal Floquet exponent of the system in the absence of noise.Comment: 21 pages, 4 figure

Residual dipolar coupling investigation of a heparin tetrasaccharide confirms the limited effect of flexibility of the iduronic acid on the molecular shape of heparin

The solution conformation of a fully sulfated heparin-derived tetrasaccharide, I, was studied in the presence of a 4-fold excess of Ca2+. Proton–proton and proton–carbon residual dipolar couplings (RDCs) were measured in a neutral aligning medium. The order parameters of two rigid hexosamine rings of I were determined separately using singular value decomposition and ab initio structures of disaccharide fragments of I. The order parameters were very similar implying that a common order tensor can be used to analyze the structure of I. Using one order tensor, RDCs of both hexosamine rings were used as restraints in molecular dynamics simulations. RDCs of the inner iduronic acid were calculated for every point of the molecular dynamics trajectory. The fitting of the calculated RDCs of the two forms of the iduronic acid to the experimental values yielded a population of 1C4 and 2So conformers of iduronic acid that agreed well with the analysis based on proton–proton scalar coupling constants. The glycosidic linkage torsion angles in RDC-restrained molecular dynamics (MD) structures of I are consistent with the interglycosidic three-bond proton–carbon coupling constants. These structures also show that the shape of heparin is not affected dramatically by the conformational flexibility of the iduronic acid ring. This is in line with conclusions of previous studies based on MD simulations and the analysis of 1H-1H NOEs. Our work therefore demonstrates the effectiveness of RDCs in the conformational analysis of glycosaminoglycans

Slow Dissociation of a Charged Ligand: Analysis of the Primary Quinone QA Site of Photosynthetic Bacterial Reaction Centers

Reaction centers (RCs) are integral membrane proteins that undergo a series of electron transfer reactions during the process of photosynthesis. In the QA site of RCs from Rhodobacter sphaeroides, ubiquinone-10 is reduced, by a single electron transfer, to its semiquinone. The neutral quinone and anionic semiquinone have similar affinities, which is required for correct in situ reaction thermodynamics. A previous study showed that despite similar affinities, anionic quinones associate and dissociate from the QA site at rates ≈104 times slower than neutral quinones indicating that anionic quinones encounter larger binding barriers (Madeo, J.; Gunner, M. R. Modeling binding kinetics at the QA site in bacterial reaction centers. Biochemistry2005, 44, 10994–11004). The present study investigates these barriers computationally, using steered molecular dynamics (SMD) to model the unbinding of neutral ground state ubiquinone (UQ) and its reduced anionic semiquinone (SQ–) from the QA site. In agreement with experiment, the SMD unbinding barrier for SQ– is larger than for UQ. Multi Conformational Continuum Electrostatics (MCCE), used here to calculate the binding energy, shows that SQ– and UQ have comparable affinities. In the QA site, there are stronger binding interactions for SQ– compared to UQ, especially electrostatic attraction to a bound non-heme Fe2+. These interactions compensate for the higher SQ– desolvation penalty, allowing both redox states to have similar affinities. These additional interactions also increase the dissociation barrier for SQ– relative to UQ. Thus, the slower SQ– dissociation rate is a direct physical consequence of the additional binding interactions required to achieve a QA site affinity similar to that of UQ. By a similar mechanism, the slower association rate is caused by stronger interactions between SQ– and the polar solvent. Thus, stronger interactions for both the unbound and bound states of charged and highly polar ligands can slow their binding kinetics without a conformational gate. Implications of this for other systems are discussed

NMR methods to monitor the enzymatic depolymerization of heparin

Heparin and the related glycosaminoglycan, heparan sulfate, are polydisperse linear polysaccharides that mediate numerous biological processes due to their interaction with proteins. Because of the structural complexity and heterogeneity of heparin and heparan sulfate, digestion to produce smaller oligosaccharides is commonly performed prior to separation and analysis. Current techniques used to monitor the extent of heparin depolymerization include UV absorption to follow product formation and size exclusion or strong anion exchange chromatography to monitor the size distribution of the components in the digest solution. In this study, we used 1H nuclear magnetic resonance (NMR) survey spectra and NMR diffusion experiments in conjunction with UV absorption measurements to monitor heparin depolymerization using the enzyme heparinase I. Diffusion NMR does not require the physical separation of the components in the reaction mixture and instead can be used to monitor the reaction solution directly in the NMR tube. Using diffusion NMR, the enzymatic reaction can be stopped at the desired time point, maximizing the abundance of larger oligosaccharides for protein-binding studies or completion of the reaction if the goal of the study is exhaustive digestion for characterization of the disaccharide composition. In this study, porcine intestinal mucosa heparin was depolymerized using the enzyme heparinase I. The unsaturated bond formed by enzymatic cleavage serves as a UV chromophore that can be used to monitor the progress of the depolymerization and for the detection and quantification of oligosaccharides in subsequent separations. The double bond also introduces a unique multiplet with peaks at 5.973, 5.981, 5.990, and 5.998 ppm in the 1H-NMR spectrum downfield of the anomeric region. This multiplet is produced by the proton of the C-4 double bond of the non-reducing end uronic acid at the cleavage site. Changes in this resonance were used to monitor the progression of the enzymatic digestion and compared to the profile obtained from UV absorbance measurements. In addition, in situ NMR diffusion measurements were explored for their ability to profile the different-sized components generated over the course of the digestion

Kissing G Domains of MnmE Monitored by X-Ray Crystallography and Pulse Electron Paramagnetic Resonance Spectroscopy

The authors of this research article demonstrate the nature of the conformational changes MnmE was previously suggested to undergo during its GTPase cycle, and show the nucleotide-dependent dynamic movements of the G domains around two swivel positions relative to the rest of the protein. These movements are of crucial importance for understanding the mechanistic principles of this GAD

HIV-1 gp41 and TCRα Trans-Membrane Domains Share a Motif Exploited by the HIV Virus to Modulate T-Cell Proliferation

Viruses have evolved several strategies to modify cellular processes and evade the immune response in order to successfully infect, replicate, and persist in the host. By utilizing in-silico testing of a transmembrane sequence library derived from virus protein sequences, we have pin-pointed a nine amino-acid motif shared by a group of different viruses; this motif resembles the transmembrane domain of the α-subunit of the T-cell receptor (TCRα). The most striking similarity was found within the immunodeficiency virus (SIV and HIV) glycoprotein 41 TMD (gp41 TMD). Previous studies have shown that stable interactions between TCRα and CD3 are localized to this nine amino acid motif within TCRα, and a peptide derived from it (TCRα TMD, GLRILLLKV) interfered and intervened in the TCR function when added exogenously. We now report that the gp41 TMD peptide co-localizes with CD3 within the TCR complex and inhibits T cell proliferation in vitro. However, the inhibitory mechanism of gp41 TMD differs from that of the TCRα TMD and also from the other two known immunosuppressive regions within gp41