Synthesis of galactofuranose-containing acceptor substrates for mycobacterial galactofuranosyltransferases

The major structural component of the cell wall in Mycobacterium tuberculosis, infection by which causes tuberculosis, is the mycolyl-arabinogalactan (mAG) complex. This large glycoconjugates has at its core a backbone of approximately 30 D-galactofuranose (Gal(f)) residues that are linked to peptidoglycan by way of a linker disaccharide containing L-rhamnose and 2-acetamido-2-deoxy-D-glucose. Recent studies have supported a model of galactan biosynthesis in which the entire structure is assembled by the action of two bifunctional galactofuranosyltransferases. These biochemical investigations were made possible, in part, by access to a panel of oligosaccharide fragments of the mAG complex (1-12), the synthesis of which we describe here. An early key finding in this study was that the iodine-promoted cyclization of galactose diethyl dithioacetal (19) in the presence of an alcohol solvent led to the formation Gal(f) glycosides contaminated with no pyranoside isomer, thus allowing the efficient preparation of furanoside derivatives of this monosaccharide. The synthesis of disaccharide targets 1, 2, 11 and 12 proceeded without difficulty through the use of thioglycoside donors and octyl glycoside acceptors, both carrying benzoyl protection. In the synthesis of the tri- and tetrasaccharides 3-6, we explored routes in which the molecule was assembled from the reducing to nonreducing end, and the reverse. The latter approach was found to be preferable for the preparation of 6, and in the case of 3 and 4, this strategy allowed the development of efficient one-pot methods for their synthesis. We have also carried out the first synthesis of three mAG fragments (8-10) consisting of the linker disaccharide further elaborated with one, two or three Gal(f) residues. A key step in the synthesis of these target compounds was the coupling of a protected linker disaccharide derivative (58) with a mono-, di-, or trigalactofuranosyl thioglycoside (17, 54, or 53, respectively).     

Development of a planar multibody model of the human knee joint

The aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur cannot be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous nonlinear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as nonlinear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system’s equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study.     

Vacuum moulding of a superplastic in two dimensions

A mathematical model is proposed for the process of vacuum superplasticforming. The model exploits the fact that in most industrialapplications the sheet aspect ratio (thickness/sheet width)is small. After an initial consideration of some of the moregeneral properties and the literature of superplastic materials,the elastic/plastic deformation of an internally-inflated thin-walledcylinder is examined. Plates of arbitrary geometry are thenconsidered. A quasisteady model in which the sheet moves througha sequence of steady states is developed. Some simplified closed-formsolutions are examined, but for general cases a system of nonlinearpartial differential equations must be solved numerically. Anefficient and accurate semi-explicit numerical scheme is proposedand a simplified stability analysis is presented; the methodis then used to compute properties of superplastic vacuum mouldedsheets in a number of practically motivated cases.     

Modulated optical lattice as an atomic fabry-perot interferometer

We propose to engineer the atomic band structure in optical lattices in order to design a Fabry-Perot interferometer with large mode spacing and strong nonlinear coupling to be employed in atom optics. The use of an optical lattice allows for a significant reduction of the atomic effective mass, while the slow modulation of its parameters spatially confines the matter waves on a length scale of a few dozen optical wavelengths. As a consequence, the mode spacing in such a cavity would be as high as one-tenth of the recoil energy, allowing for a very efficient filter action, while the nonlinear coupling due to interatomic interactions could lead to bistability and limiting effects in the transmission of the atomic beam.