Collagen processing and cuticle formation is catalysed by the astacin metalloprotease DPY-31 in free-living and parasitic nematodes

The exoskeleton or cuticle performs many key roles in the development and survival of all nematodes. This structure is predominantly collagenous in nature and requires numerous enzymes to properly fold, modify, process and cross-link these essential structural proteins. The cuticle structure and its collagen components are conserved throughout the nematode phylum but differ from the collagenous matrices found in vertebrates. This structure, its formation and the enzymology of nematode cuticle collagen biogenesis have been elucidated in the free-living nematode Caenorhabditis elegans. The dpy-31 gene in C. elegans encodes a procollagen C-terminal processing enzyme of the astacin metalloprotease or bone morphogenetic protein class that, when mutated, results in a temperature-sensitive lethal phenotype associated with cuticle defects. In this study, orthologues of this essential gene have been identified in the phylogenetically diverse parasitic nematodes Haemonchus contortus and Brugia malayi. The DPY-31 protein is expressed in the gut and secretory system of C. elegans, a location also confirmed when a B. malayi transcriptional dpy-31 promoter-reporter gene fusion was expressed in C. elegans. Functional conservation between the nematode enzymes was supported by the fact that heterologous expression of the H. contortus dpy-31 orthologue in a C. elegans dpy-31 mutant resulted in the full rescue of the mutant body form. This interspecies conservation was further established when the recombinant nematode enzymes were found to have a similar range of inhibitable protease activities. In addition, the recombinant DPY-31 enzymes from both H. contortus and B. malayi were shown to efficiently process the C. elegans cuticle collagen SQT-3 at the correct C-terminal procollagen processing site

Optimal estimation of qubit states with continuous time measurements

We propose an adaptive, two steps strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given $n$ identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions. We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits. The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large $n$, the statistical model described by $n$ identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator. The term `local' refers to a shrinking neighborhood around a fixed state $\rho_{0}$. An essential result is that the neighborhood radius can be chosen arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by which we first localize the state within a smaller neighborhood of radius $n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.Comment: 32 pages, 3 figures, to appear in Commun. Math. Phy

Local asymptotic normality for finite dimensional quantum systems

We extend our previous results on local asymptotic normality (LAN) for qubits, to quantum systems of arbitrary finite dimension $d$. LAN means that the quantum statistical model consisting of $n$ identically prepared $d$-dimensional systems with joint state $\rho^{\otimes n}$ converges as $n\to\infty$ to a statistical model consisting of classical and quantum Gaussian variables with fixed and known covariance matrix, and unknown means related to the parameters of the density matrix $\rho$. Remarkably, the limit model splits into a product of a classical Gaussian with mean equal to the diagonal parameters, and independent harmonic oscillators prepared in thermal equilibrium states displaced by an amount proportional to the off-diagonal elements. As in the qubits case, LAN is the main ingredient in devising a general two step adaptive procedure for the optimal estimation of completely unknown $d$-dimensional quantum states. This measurement strategy shall be described in a forthcoming paper.Comment: 64 page