Degenerate mechanisms

Hollyfield, JG, Salomon, RG, and Crabb, JW, 2003. Proteomic approaches to understanding age-related macular degeneration, In LaVail, MM, Anderson, RE, and Hollyfield, JG (Eds.), Retinal Degenerations Mechanisms and Experimental Therapy. Kluwer Academic/Plenum Publishers, New York, pp. 83-89. 

Coleman, M. Axonal degeneration mechanisms Commonality and diversity. Nat. Rev. 

Degenerate Mechanisms, "Catastrophic Cyclic Paths, and the Unique Path Assunyjtion... 

Both these cases lead to identical temperature distributions. Fortunately, kinetic techniques can frequently be used to distinguish between such degenerate mechanisms. ... 

The definition of a unique path for the vibrational temperatures purposes can now be developed. Such paths are simply those that produce a stable long-lived vibrational temperature distribution. These include all degenerate mechanisms leading to the same temperature distribution. Catastrophic cyclic paths are in principle excluded from such a unique path nevertheless, if there is a slow kinetic step in such a catastrophic path, this step can be identified and removed thus producing a stable unique temperature distribution. While the steady-state vibrational temperature picture can correctly identify the presence of a catastrophic cycle, such a description provides no insight into the time scale required for catastrophe (or decay) to occur. 

The one-dimensional cases discussed above illustrate many of die qualitative features of quantum mechanics, and their relative simplicity makes them quite easy to study. Motion in more than one dimension and (especially) that of more than one particle is considerably more complicated, but many of the general features of these systems can be understood from simple considerations. Wliile one relatively connnon feature of multidimensional problems in quantum mechanics is degeneracy, it turns out that the ground state must be non-degenerate. To prove this, simply assume the opposite to be true, i.e. 

Figure A3.13.1 illustrates our general understanding of intramolecular energy redistribution in isolated molecules and shows how these processes are related to intemiolecular processes, which may follow any of the mechanisms discussed in the previous section. The horizontal bars represent levels of nearly degenerate states of an isolated molecule.

One heterocyclic subunit which is an excellent donor group is the 2,6-pyrido-sub-stitutent - ". However, when 4-chloro-2,6-dicarboxypyridine was utilized as precursor to the macrocycle, the product apparently was less stable than was the corresponding nonchlorinated ester The decomposition was apparently initiated by complexation of either Sr or Ba " but the mechanism by which this degeneration occurred was not suggested nor is it obvious to the present authors, especially in the absence of any commentary concerning the products of decomposition. The synthesis of the apparently unstable system is illustrated below. 

Isotope effect between the HH, HD, DH, and DD isotopomers was used as an important tool to determine the mechanism of the double-proton transfer. For concerted degenerate double-proton transfers in the absence of tunneling, the rule of the geometrical mean (RGM) should hold in good approximation, which states that /chh/ hd = /cdh/ dd-Tunneling may lead to a breakdown of this rule but the relation /chh > hd = dh > dd should remain valid. In the absence of secondary isotope effects the relation /chh HD = DH = 2 /cdd sliould liold for a stepwise pathway, even if tunneling is involved. 

These rules follow directly from the quantum-mechanical theory of perturbations and the resolution of the secular equations for the orbital interaction problem. The (small) interaction between orbitals of significantly different energ is the familiar second order type interaction, where the interaction energy is small relative to the difference between EA and EB. The (large) interaction between orbitals of same energy is the familiar first order type interaction between degenerate or nearly degenerate levels. 

The first-order perturbation theory of the quantum mechanics (4, III) is very simple when applied to a non-degenerate state of a system that is, a state for which only one eigenfunction exists. The energy change W1 resulting from a perturbation function / is just the quantum mechanics average of / for the state in question i.e., it is... 

These disorders are all acquired conditions with no evidence of an hereditary basis. Most of them involve inflammation of the skeletal muscle itself (myositis) (Figure 17), though this may sometimes occur because of initial targeting of the muscle vasculature or connective tissue. Many instances of myositis are classed as idiopathic disorders, in that the precise mechanisms of muscle degeneration are not known, but is widely accepted that these syndromes are associated with abnormal function of the immune system. The syndromes of polymyositis (PM) and derma-... 

ADM may evolve over several years, the extent of fiber atrophy provides an important indication of the chronicity of muscle degeneration. Acute muscle necrosis and phagocytosis give some indication as to how active the disease is at the time of biopsy. In most biopsies from ADM patients, the inflammatory cell foci are perivascular and perimysial rather than endomysial and are dominated by B-lymphocytes. The ratio of T4 lymphocytes (helper cells) to T8 lymphocytes (cytotoxic) generally indicates a predominance of the former. As in JDM, this is consistent with humoral mechanisms of cell damage, and vascular involvement is also apparent in the form of capillary endothelial cell abnormalities (tubular arrays) and duplication of basal lamina. Loss of myofibrillar ATPase from the central portions of fibers is a common prelude to muscle necrosis. 

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