When does a Bounded Domain Cover a Projective Manifold? (Survey)

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and Technology

Editorial overview:new protein production tools for structural biology

Full text: The idea of producing proteins from recombinant DNA hatched almost half a century ago. In his PhD thesis, Peter Lobban foresaw the prospect of inserting foreign DNA (from any source, including mammalian cells) into the genome of a λ phage in order to detect and recover protein products from Escherichia coli [ 1 and 2]. Only a few years later, in 1977, Herbert Boyer and his colleagues succeeded in the first ever expression of a peptide-coding gene in E. coli — they produced recombinant somatostatin [ 3] followed shortly after by human insulin. The field has advanced enormously since those early days and today recombinant proteins have become indispensable in advancing research and development in all fields of the life sciences. Structural biology, in particular, has benefitted tremendously from recombinant protein biotechnology, and an overwhelming proportion of the entries in the Protein Data Bank (PDB) are based on heterologously expressed proteins. Nonetheless, synthesizing, purifying and stabilizing recombinant proteins can still be thoroughly challenging. For example, the soluble proteome is organized to a large part into multicomponent complexes (in humans often comprising ten or more subunits), posing critical challenges for recombinant production. A third of all proteins in cells are located in the membrane, and pose special challenges that require a more bespoke approach. Recent advances may now mean that even these most recalcitrant of proteins could become tenable structural biology targets on a more routine basis. In this special issue, we examine progress in key areas that suggests this is indeed the case. Our first contribution examines the importance of understanding quality control in the host cell during recombinant protein production, and pays particular attention to the synthesis of recombinant membrane proteins. A major challenge faced by any host cell factory is the balance it must strike between its own requirements for growth and the fact that its cellular machinery has essentially been hijacked by an expression construct. In this context, Bill and von der Haar examine emerging insights into the role of the dependent pathways of translation and protein folding in defining high-yielding recombinant membrane protein production experiments for the common prokaryotic and eukaryotic expression hosts. Rather than acting as isolated entities, many membrane proteins form complexes to carry out their functions. To understand their biological mechanisms, it is essential to study the molecular structure of the intact membrane protein assemblies. Recombinant production of membrane protein complexes is still a formidable, at times insurmountable, challenge. In these cases, extraction from natural sources is the only option to prepare samples for structural and functional studies. Zorman and co-workers, in our second contribution, provide an overview of recent advances in the production of multi-subunit membrane protein complexes and highlight recent achievements in membrane protein structural research brought about by state-of-the-art near-atomic resolution cryo-electron microscopy techniques. E. coli has been the dominant host cell for recombinant protein production. Nonetheless, eukaryotic expression systems, including yeasts, insect cells and mammalian cells, are increasingly gaining prominence in the field. The yeast species Pichia pastoris, is a well-established recombinant expression system for a number of applications, including the production of a range of different membrane proteins. Byrne reviews high-resolution structures that have been determined using this methylotroph as an expression host. Although it is not yet clear why P. pastoris is suited to producing such a wide range of membrane proteins, its ease of use and the availability of diverse tools that can be readily implemented in standard bioscience laboratories mean that it is likely to become an increasingly popular option in structural biology pipelines. The contribution by Columbus concludes the membrane protein section of this volume. In her overview of post-expression strategies, Columbus surveys the four most common biochemical approaches for the structural investigation of membrane proteins. Limited proteolysis has successfully aided structure determination of membrane proteins in many cases. Deglycosylation of membrane proteins following production and purification analysis has also facilitated membrane protein structure analysis. Moreover, chemical modifications, such as lysine methylation and cysteine alkylation, have proven their worth to facilitate crystallization of membrane proteins, as well as NMR investigations of membrane protein conformational sampling. Together these approaches have greatly facilitated the structure determination of more than 40 membrane proteins to date. It may be an advantage to produce a target protein in mammalian cells, especially if authentic post-translational modifications such as glycosylation are required for proper activity. Chinese Hamster Ovary (CHO) cells and Human Embryonic Kidney (HEK) 293 cell lines have emerged as excellent hosts for heterologous production. The generation of stable cell-lines is often an aspiration for synthesizing proteins expressed in mammalian cells, in particular if high volumetric yields are to be achieved. In his report, Buessow surveys recent structures of proteins produced using stable mammalian cells and summarizes both well-established and novel approaches to facilitate stable cell-line generation for structural biology applications. The ambition of many biologists is to observe a protein's structure in the native environment of the cell itself. Until recently, this seemed to be more of a dream than a reality. Advances in nuclear magnetic resonance (NMR) spectroscopy techniques, however, have now made possible the observation of mechanistic events at the molecular level of protein structure. Smith and colleagues, in an exciting contribution, review emerging ‘in-cell NMR’ techniques that demonstrate the potential to monitor biological activities by NMR in real time in native physiological environments. A current drawback of NMR as a structure determination tool derives from size limitations of the molecule under investigation and the structures of large proteins and their complexes are therefore typically intractable by NMR. A solution to this challenge is the use of selective isotope labeling of the target protein, which results in a marked reduction of the complexity of NMR spectra and allows dynamic processes even in very large proteins and even ribosomes to be investigated. Kerfah and co-workers introduce methyl-specific isotopic labeling as a molecular tool-box, and review its applications to the solution NMR analysis of large proteins. Tyagi and Lemke next examine single-molecule FRET and crosslinking following the co-translational incorporation of non-canonical amino acids (ncAAs); the goal here is to move beyond static snap-shots of proteins and their complexes and to observe them as dynamic entities. The encoding of ncAAs through codon-suppression technology allows biomolecules to be investigated with diverse structural biology methods. In their article, Tyagi and Lemke discuss these approaches and speculate on the design of improved host organisms for ‘integrative structural biology research’. Our volume concludes with two contributions that resolve particular bottlenecks in the protein structure determination pipeline. The contribution by Crepin and co-workers introduces the concept of polyproteins in contemporary structural biology. Polyproteins are widespread in nature. They represent long polypeptide chains in which individual smaller proteins with different biological function are covalently linked together. Highly specific proteases then tailor the polyprotein into its constituent proteins. Many viruses use polyproteins as a means of organizing their proteome. The concept of polyproteins has now been exploited successfully to produce hitherto inaccessible recombinant protein complexes. For instance, by means of a self-processing synthetic polyprotein, the influenza polymerase, a high-value drug target that had remained elusive for decades, has been produced, and its high-resolution structure determined. In the contribution by Desmyter and co-workers, a further, often imposing, bottleneck in high-resolution protein structure determination is addressed: The requirement to form stable three-dimensional crystal lattices that diffract incident X-ray radiation to high resolution. Nanobodies have proven to be uniquely useful as crystallization chaperones, to coax challenging targets into suitable crystal lattices. Desmyter and co-workers review the generation of nanobodies by immunization, and highlight the application of this powerful technology to the crystallography of important protein specimens including G protein-coupled receptors (GPCRs). Recombinant protein production has come a long way since Peter Lobban's hypothesis in the late 1960s, with recombinant proteins now a dominant force in structural biology. The contributions in this volume showcase an impressive array of inventive approaches that are being developed and implemented, ever increasing the scope of recombinant technology to facilitate the determination of elusive protein structures. Powerful new methods from synthetic biology are further accelerating progress. Structure determination is now reaching into the living cell with the ultimate goal of observing functional molecular architectures in action in their native physiological environment. We anticipate that even the most challenging protein assemblies will be tackled by recombinant technology in the near future.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Quaternion Extensions of Order 16

2000 Mathematics Subject Classification: 12F12

Gas analysis of sediment cores from the Batumi seep area

Detailed knowledge of the extent of post-genetic modifications affecting shallow submarine hydrocarbons fueled from the deep subsurface is fundamental for evaluating source and reservoir properties. We investigated gases from a submarine high-flux seepage site in the anoxic Eastern Black Sea in order to elucidate molecular and isotopic alterations of low-molecular-weight hydrocarbons (LMWHC) associated with upward migration through the sediment and precipitation of shallow gas hydrates. For this, near-surface sediment pressure cores and free gas venting from the seafloor were collected using autoclave technology at the Batumi seep area at 845 m water depth within the gas hydrate stability zone. Vent gas, gas from pressure core degassing, and from hydrate dissociation were strongly dominated by methane (>99.85 mol.% of Sum[C1-C4, CO2]). Molecular ratios of LMWHC (C1/[C2 + C3] > 1000) and stable isotopic compositions of methane (d13C = -53.5 per mill V-PDB; D/H around -175 per mill SMOW) indicated predominant microbial methane formation. C1/C2+ ratios and stable isotopic compositions of LMWHC distinguished three gas types prevailing in the seepage area. Vent gas discharged into bottom waters was depleted in methane by >0.03 mol.% (Sum[C1-C4, CO2]) relative to the other gas types and the virtual lack of 14C-CH4 indicated a negligible input of methane from degradation of fresh organic matter. Of all gas types analyzed, vent gas was least affected by molecular fractionation, thus, its origin from the deep subsurface rather than from decomposing hydrates in near-surface sediments is likely. As a result of the anaerobic oxidation of methane, LMWHC in pressure cores in top sediments included smaller methane fractions [0.03 mol.% Sum(C1-C4, CO2)] than gas released from pressure cores of more deeply buried sediments, where the fraction of methane was maximal due to its preferential incorporation in hydrate lattices. No indications for stable carbon isotopic fractionations of methane during hydrate crystallization from vent gas were found. Enrichments of 14C-CH4 (1.4 pMC) in short cores relative to lower abundances (max. 0.6 pMC) in gas from long cores and gas hydrates substantiates recent methanogenesis utilizing modern organic matter deposited in top sediments of this high-flux hydrocarbon seep area.

Mining dynamic databases for frequent closed itemsets

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

In-situ examination of the selective etching of an alkanethiol monolayer covered Au{111} surface

An examination of the selective etching mechanism of a 1-alkanethiol self-assembled monolayer (SAM) covered Au{111} surface using in-situ atomic force microscopy (AFM) and molecular resolution scanning tunnelling microscopy (STM) is presented. The monolayer self-assembles on a smooth Au{111} surface and typically contains nanoscale non-uniformities such as pinholes, domain boundaries and monatomic depressions. During etching in a ferri/ferrocyanide water-based etchant, selective and preferential etching occurs at SAM covered Au(111) terrace and step edges where a lower SAM packing density is observed, resulting in triangular islands being relieved. The triangular islands are commensurate with the Au(111) lattice with their long edges parallel to its [11-0] direction. Thus, SAM etching is selective and preferential attack is localized to defects and step edges at sites of high molecular density contrast.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

Mining dynamic databases for frequent closed itemsets

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Non-Gaussian distribution of collective operators in quantum spin chains

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on thesame curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators.

On the positive approximation property

Using a different approach to that of Popa, we arrive at an alternative definition
of the positive approximation property for order complete Banach lattices.
Some results associated with this new approach may be of independent interest. We
also prove a Banach lattice analogue of an old characterization, due to Palmer, of
the metric approximation property in terms of the continuous bidual of the ideal of
approximable operators.

On the regularity of homomorphisms between Riesz subalgebras of L^r(X).

We investigate the automatic regularity of continuous algebra homomorphisms between Riesz algebras of regular operators on Banach lattices.