Frobenius Solution for Legendre's Equation, Rodrigue's Formula and Normalization

The Frobenius solution to Legendre/s equation is developed in detail as is Rodrigue's formula, which is employed to normalize Legendre polynomials.

Long-term hyperexcitability of sensory and motor axons in Aplysia californica: Induction by axotomy, serotonin, and transient depolarization

Neuropathic pain is a debilitating neurological disorder that may appear after peripheral nerve trauma and is characterized by persistent, intractable pain. The well-studied phenomenon of long-term hyperexcitability (LTH), in which sensory somata become hyperexcitable following peripheral nerve injury may be important for both chronic pain and long-lasting memory formation, since similar cellular alterations take place after both injury and learning. Though axons have previously been considered simple conducting cables, spontaneous afferent signals develop from some neuromas that form at severed nerve tips, indicating intrinsic changes in sensory axonal excitability may contribute to this intractable pain. Here we show that nerve transection, exposure to serotonin, and transient depolarization induce long-lasting sensory axonal hyperexcitability that is localized to the treated nerve segment and requires local translation of new proteins. Long-lasting functional plasticity may be a general property of axons, since both injured and transiently depolarized motor axons display LTH as well. Axonal hyperexcitability may represent an adaptive mechanism to overcome conduction failure after peripheral injury, but also displays key features shared with cellular analogues of memory including: site-specific changes in neuronal function, dependence on transient, focal depolarization for induction, and requirement for synthesis of new proteins for expression of long-lasting effects. The finding of axonal hyperexcitability after nerve injury sheds new light on the clinical problem of chronic neuropathic pain, and provides more support for the hypothesis that mechanisms of long-term memory storage evolved from primitive adaptive responses to injury. ^

Modulation of carbohydrates and carbohydrate binding proteins (lectins) during retinoic acid -induced differentiation of murine embryonal carcinoma cells

The current studies were undertaken to examine the effect of retinoic acid (RA)-induced differentiation of the murine embryonal carcinoma cell line, F-9, on the glycosylation of specific cellular glycoproteins and on the expression of two members of the family of endogenous lactoside-binding lectins. It was found that RA-induced differentiation of these cells into cells with the properties of primitive endoderm results in the increased fucosylation of 3 glycoproteins with molecular weights of 175 (gp175), 250 (gp250), and 400 (pg400) kDa. These three fucose-containing glycoproteins can be considered as new markers of differentiation in this system. The increased fucosylation of these glycoproteins preceded the 3-fold increase in fucosyltransferase (FT) activity that was seen upon RA-induced differentiation of these cells, indicating that an increase in fucosyltransferase activity alone cannot explain the increased fucosylation of these glycoproteins.^ The effect of RA and Ch55, a chalcone carboxylic acid with retinoid-like properties, induced differentiation of a variety of murine embryonal carcinoma cell lines on the activities of both FT and sialyltransferase (ST) was examined. The effect of differentiation on the activities of both glycosyltransferases was modulated and most probably is dependent upon the differentiation pathway that is triggered by the retinoids for each of the embryonal carcinoma cell lines.^ Two glycoproteins, Lysosomal Associated Membrane Glycoproteins 1 and 2 (LAMP-1 and LAMP-2) were examined in more detail during the course of RA-induced differentiation of F-9 cells. Both the levels and glycosylation of both glycoproteins are increased following differentiation of these cells. Differentiation results in the increased binding of $\sp{125}$l-labelled L-phytohemagglutinin to bind to LAMP-1 which indicates increased GlcNAc $\beta$1,6 branching of the oligosaccharide side chains.^ We found that RA-induced differentiation of F-9 cells results in the decreased expression of the 34 kDa lectin 24 h after addition of the retinoid to the medium. Additionally, 48 h of RA-treatment results in the increased expression of the 14.5 kDa lectin. By indirect immunofluorescence we were able to colocalize the 14.5 kDa lectin and laminin which suggests that laminin may be a ligand for the lectin in the F-9 cells. (Abstract shortened with permission of author.) ^

Cloning and molecular analysis of paraxis: A {\it trans\/}-acting factor required for somite maturation

During vertebrate embryogenesis, cells from the paraxial mesoderm coalesce in a rostral-to-caudal progression to form the somites. Subsequent compartmentalization of the somites yields the sclerotome, myotome and dermatome, which give rise to the axial skeleton, axial musculature, and dermis, respectively. Recently, we cloned a novel basic-Helix-Loop-Helix (bHLH) protein, called scleraxis, which is expressed in the sclerotome, in mesenchymal precursors of bone and cartilage, and in connective tissues. This dissertation focuses on the cloning, expression and functional analysis of a bHLH protein termed paraxis, which is nearly identical to scleraxis within the bHLH region but diverges in both its amino and carboxyl termini. During the process of mouse embryogenesis, paraxis transcripts are first detected at about day 7.5 post coitum within the primitive mesoderm lying posterior to the head and heart primordia. Subsequently, paraxis expression progresses caudally through the paraxial mesoderm, immediately preceding somite formation. Paraxis is expressed at high levels in newly formed somites before the first detectable expression of the myogenic bHLH genes, and as the somite becomes compartmentalized, paraxis becomes downregulated within the myotome.^ To determine the function of paraxis during mammalian embryogenesis, mice were generated with a null mutation in the paraxis locus. Paraxis null mice survived until birth, but exhibited severe foreshortening along the anteroposterior axis due to the absence of vertebrae caudal to the midthoracic region. The phenotype also included axial skeletal defects, particularly shortened bifurcated ribs which were detached from the vertebral column, fused vertebrae and extensive truncation and disorganization caudal to the hindlimbs. Mutant neonates also lacked normal levels of trunk muscle and exhibited defects in the dermis as well as the stratification of the epidermis. Analysis of paraxis -/- mutant embryos has revealed a failure of the somites to both properly epithelialize and compartmentalize, resulting in defects in somite-derived cell lineages. These results suggest that paraxis is an essential component of the genetic pathway regulating somitogenesis. ^

Element concentrations of plagioclase and clinopyroxene in poikilitic olivine gabbros from ODP Hole 153-923A (Table 4)

Ocean Drilling Program Hole 923A, located on the western flank of the Mid-Atlantic Ridge south of the Kane Fracture Zone, recovered primitive gabbros that have mineral trace element compositions inconsistent with growth from a single parental melt. Plagioclase crystals commonly show embayed anorthitic cores overgrown by more albitic rims. Ion probe analyses of plagioclase cores and rims show consistent differences in trace element ratios, indicating variation in the trace element characteristics of their respective parental melts. This requires the existence of at least two distinct melt compositions within the crust during the generation of these gabbros. Melt compositions calculated to be parental to plagioclase cores are depleted in light rare earth elements, but enriched in yttrium, compared to basalts from this region of the Mid-Atlantic Ridge, which are normal mid-ocean ridge basalt (N-MORB). Clinopyroxene trace element compositions are similar to those predicted to be in equilibrium with N-MORB. However, primitive clinopyroxene crystals are much more magnesian than those produced in one-atmosphere experiments on N-MORB, suggesting that the major element composition of the melt was unlike N-MORB. These data require that the diverse array of melt compositions generated within the mantle beneath mid-ocean ridges are not always fully homogenised during melt extraction from the mantle and that the final stage of mixing can occur efficiently within crustal magma chambers. This has implications for the process of melt extraction from the mantle and the liquid line of descent of MORB

Appendix A. Whole-rock major, trace and rare earth element analyses of the Ulubey volcanics, Appendix B. Analytical standards and detection limits for analyses

Collisional and post-collisional volcanic rocks in the Ulubey (Ordu) area at the western edge of the Eastern Pontide Tertiary Volcanic Province (EPTVP) in NE Turkey are divided into four suites; Middle Eocene (49.4-44.6 Ma) aged Andesite-Trachyandesite (AT), Trachyandesite-Trachydacite-Rhyolite (TTR), Trachydacite-Dacite (TD) suites, and Middle Miocene (15.1 Ma) aged Trachybasalt (TB) suite. Local stratigraphy in the Ulubey area starts with shallow marine environment sediments of the Paleocene-Eocene time and then continues extensively with sub-aerial andesitic to rhyolitic and rare basaltic volcanism during Eocene and Miocene time, respectively. Petrographically, the volcanic rocks are composed primarily of andesites/trachyandesites, with minor trachydacites/rhyolites, basalts/trachybasalts and pyroclastics, and show porphyric, hyalo-microlitic porphyric and rarely glomeroporphyric, intersertal, intergranular, fluidal and sieve textures. The Ulubey (Ordu) volcanic rocks indicate magma evolution from tholeiitic-alkaline to calc-alkaline with medium-K contents. Primitive mantle normalized trace element and chondrite normalized rare earth element (REE) patterns show that the volcanic rocks have moderate light rare earth element (LREE)/heavy rare earth element (HREE) ratios relative to E-Type MORB and depletion in Nb, Ta and Ti. High Th/Yb ratios indicate parental magma(s) derived from an enriched source formed by mixing of slab and asthenospheric melts previously modified by fluids and sediments from a subduction zone. All of the volcanic rocks share similar incompatible element ratios (e.g., La/Sm, Zr/Nb, La/Nb) and chondrite-normalized REE patterns, indicating that the basic to acidic rocks originated from the same source. The volcanic rocks were produced by the slab dehydration-induced melting of an existing metasomatized mantle source, and the fluids from the slab dehydration introduced significant large ion lithophile element (LILE) and LREE to the source, masking its inherent HFSE-enriched characteristics. The initial 87Sr/86Sr (0.7044-0.7050) and eNd (-0.3 to +3.4) ratios of the volcanics suggest that they originated from an enriched lithospheric mantle source with low Sm/Nd ratios. Integration of the geochemical, petrological and isotopical with regional and local geological data suggest that the Tertiary volcanic rocks from the Ulubey (Ordu) area were derived from an enriched mantle, which had been previously metasomatized by fluids derived from subducted slab during Eocene to Miocene in collisional and post-collisional extension-related geodynamic setting following Late Mesozoic continental collision between the Eurasian plate and the Tauride-Anatolide platform.

Geochemistry and petrology of ODP Leg 121 basalts

Basement lavas from Sites 756, 757, and 758 on Ninetyeast Ridge are tholeiitic basalts. Lavas from Sites 756 and 757 appear to be subaerial eruptives, but the lowermost flows from Hole 758A are pillow lavas. In contrast to the compositional variation during the waning stages of Hawaiian volcanism, no alkalic lavas have been recovered from Ninetyeast Ridge and highly evolved lavas were recovered from only one of seven drill sites (DSDP Site 214). All lavas from Site 758 have relatively high MgO contents (8-10 wt%), and they are less evolved than lavas from Sites 756 and 757. Although abundances of alkali metals in these Ninetyeast Ridge basalts were significantly modified by postmagmatic alteration, abundances of other elements reflect magmatic processes. At Site 757 most of the lavas are Plagioclase cumulates, but lava compositions require two compositionally distinct, AhCb-rich parental magmas, perhaps segregated at relatively low mantle pressures. In addition, at both Sites 756 and 758 more than one compositionally distinct parental magma is required. The compositions of these Ninetyeast Ridge lavas, especially those from Site 758, require a source component with a depleted composition; specifically, the abundance ratios Th/Ta, Th/La, Ba/Nb, Ba/La, and La/Ce in these lavas are generally less than the ratios inferred for primitive mantle. Lavas from Ninetyeast Ridge and the Kerguelen Archipelago have very different chondrite-normalized REE patterns, with lower light REE/heavy REE (LREE/HREE) ratios in lavas from Ninetyeast Ridge. However, lavas from Sites 757 and 758 have Pb isotope ratios that overlap with the field defined by lavas from the Kerguelen Archipelago (Weis and Frey, this volume). Therefore, these Ninetyeast Ridge lavas contain more of a component that is relatively depleted in LREE and other highly incompatible elements, but have similar amounts of the component that controls radiogenic Pb isotopes. A model involving mixing between components related to a depleted source and an enriched plume source has been proposed for the oldest Kerguelen Archipelago basalts and Ninetyeast Ridge lavas. Although the incompatible element characteristics of the Ninetyeast Ridge lavas are intermediate between depleted MORB and Kerguelen Archipelago basalts, these data are not consistent with a simple two-component mixing process. A more complex model is required.

Element abundances and Nd isotopic composition in boninite and tholeiite from DSDP Hole 60-458

Boninites are unusual high MgO-high SiO2 volcanic rocks found in several western Pacific island arcs. Their high Mg/(Mg + total Fe) (0.55-0.83) and compatible element contents (Ni = 70-450 ppm, Cr = 200-1800 ppm) indicate equilibration with mantle peridotite, but their low TiO2 contents (0.1-0.5%) indicate severe depletion of this source. K, Rb, Sr and Ba abundances in boninites are typical of primitive arc basalts, but ratios such as Ti/Zr and La/Yb are variable (Ti/Zr = 23-67, (La/Yb)e.f. = 0.6-4.7). Evidence for both enrichment and depletion of incompatible elements suggests that boninites are derived from refractory peridotite which has been metasomatically enriched in LREE, Zr, Sr, Ba and alkalis. Wide variations in 143Nd/144Nd (0.51262-0.51296) are correlated with La/Sm, Sm/Nd and Ti/Zr, which enables identification of components in the boninite source. Possible LREE depleted components have relative REE and Ti abundances like those in depleted peridotites and high 143Nd/144Nd ratios which reach MORB-like values. Possible LREE enriched components have relative REE abundances similar to those in metasomatized mantle peridotite nodules, and low 143Nd/144Nd ratios which indicate either sedimentary sources or mantle sources with recent to ancient LREE enrichment. Relative abundances of Ba and Sr in boninites decrease with increasing LREE enrichment and suggest a non-sedimentary source for the LREE enriched material. Enrichment in Ba, Sr and alkalis may result from a third component derived from subducted oceanic crust. Two models can account for the successive generation of boninites and arc tholeiites within a single area: 1) boninites can be derived from the peridotite residue of earlier arc tholeiite generation which is metasomatically enriched in LREE before boninite volcanism, or 2) arc tholeiites and boninites can be derived from a variably depleted peridotite source which has been pervasively enriched in LREE. Areas of fertile peridotite would yield tholeiites while refractory areas would yield boninites.

Major, trace and rare earth elements and minerals at DSDP Legs 69-70 Holes

We obtained major and trace element data on 113 samples from basalts drilled during DSDP Legs 69 and 70 in the Costa Rica Rift area. The majority have major and trace element characteristics typical of ocean-ridge tholeiities. Most of the basalts are relatively MgO rich (MgO > 8 wt.%) and have Mg values (MgO/MgO + 0.85FeO x 100) of about 53, characteristics that clearly indicate that the various magmas underwent only a small amount of crystal fractionation before being erupted onto the seafloor. According to their normative mineralogies, the rocks are olivine tholeiites. A few samples plot close to the diopside-hypersthene join of the projected basalt tetrahedron. Except for basalts from two thin intervals in Hole 504B, which differ significantly from all the other basalts of the hole, practically no chemical downhole variation could be established. In the two exceptional intervals, both TiO2 and P2O5 contents are markedly enriched among the major oxides. The trace elements in these intervals are distinguished by relatively high contents of magmatophile elements and have flat to enriched chondrite-normalized distribution patterns of light rare earth elements (LREE). Most of the rocks outside these intervals are strongly depleted in large-ionlithophile (LIL) elements and LREE. We offer no satisfactory hypothesis for the origin of these basalts at this time. They might have originated within pockets of mantle materials that were more primitive than the LIL-element-depleted magmas that were the source of the other basalts. A significant change with depth in the type of alteration occurs in the 561 meters of basalt cored in Hole 504B. According to the behavior of such alteration-sensitive species as K2O, H2O-, CO2, S, Tl, and the iron oxidation ratio, the alteration is oxidative in the upper part and nonoxidative or even reducing in the lower part. The oxidative alteration may have resulted from low temperature basalt/seawater interaction, whereas hydrothermal solutions may be responsible for the nonoxidative alteration.

Major and trace element abundances of igneous rocks from DSDP Site 37-334

REE abundances in gabbros and peridotites from Site 334 of DSDP Leg 37 show that these rocks are cumulates produced by fractional crystallization of a primitive oceanic tholeiite magma. They may be part of a layered oceanic complex. The REE distributions in the residual liquids left after such a fractionation are similar to those of incompatible element-depleted oceanic tholeiites. The REE data indicate that the basalts which overlie the gabbro-peridotite complex, are not genetically related to plutonic rocks.

Mineral composition and major element oxides of gabbros from ODP Hole 179-1105A, southwest Indian Ridge

Hole 1105A penetrated 158 m of gabbros at a site offset 1.3 km east-northeast from Hole 735B on the Atlantis Bank near the Atlantis II Fracture Zone. A total of 118 m of dominantly medium- to coarse-grained intercalated Fe-Ti oxide gabbro and olivine gabbro was recovered from Hole 1105A that shows many petrographic features similar to those recovered from the upper part of Hole 735B. The main rock types are distinguished based on the constituent cumulus phases, with the most primitive gabbros consisting of olivine, plagioclase, and clinopyroxene. The inferred crystallization order is subsequently Fe-Ti oxides (ilmenite and titanomagnetite), followed by orthopyroxene, then apatite, and finally biotite. Orthopyroxene appears to replace olivine in a narrow middle interval. The magmatic evolution is likewise reflected in the mineral compositions. Plagioclase varies from An66 to An28. Olivine varies from Fo78 to Fo35. The gap in olivine crystallization occurs between Fo46 and Fo40 and coincides approximately with the appearance of orthopyroxene (~En50). The clinopyroxenes show large compositional variation in Mg/(Mg + Fe total) from 0.84 to 0.51. The nonquadrilateral cations of clinopyroxene similarly show large variations with Ti increasing for the olivine gabbros and decreasing for the Fe-Ti oxide gabbros with the decrease in Mg/(Mg + Fe total). The apatites are mainly flourapatites. The compositional variation in the gabbros is interpreted as a comagmatic suite resulting from fractional crystallization. Pyroxene geothermometry suggests equilibration temperatures from 1100°C and below. The coexisting Fe-Ti oxide minerals indicate subsolidus equilibration temperatures from 900°C for olivine gabbros to 700°C for the most evolved apatite-bearing gabbros. The cryptic variation in the olivine gabbros defines two or three lenses, 40 to 60 m thick, each characterized by a distinct convex zoning with a lower segment indicating upward reverse fractionation, a central maximum, and an upper segment showing normal fractionation. The Fe-Ti oxide gabbros show cryptic variations independent of the host olivine gabbros and reveal a systematic upward normal fractionation trend transgressing host olivine gabbro boundaries. Forward fractional crystallization modeling, using a likely parental magma composition from the Atlantis II Fracture Zone (MgO = 7.2 wt%; Mg/[Mg + Fe2+] = 0.62), closely matches the compositions of coexisting olivine, plagioclase, and clinopyroxene. This modeling suggests cosaturation of olivine, plagioclase, and clinopyroxene from 1155°C and the addition of Fe-Ti oxides from 1100°C. The liquid line of descent initially shows increasing FeO with moderately increasing SiO2. After saturation of Fe-Ti oxides, the liquid strongly decreases in FeO and TiO2 and increases in SiO2, reaching dacitic compositions at ~10% liquid remaining. The calculations indicate that formation of olivine gabbros can be accounted for by <65% fractionation and that only the residual 35% liquid was saturated in Fe-Ti oxides. The modeling of the solid fractionation products shows that both the olivine gabbro and the Fe-Ti oxide gabbros contain very small amounts of trapped liquid (<5%). The implications are that the gabbros represent crystal mush that originated in a recharging and tapping subaxial chamber. Compaction and upward melt migration in the crystal mush appear to have been terminated with relatively large amounts of interstitial liquid remaining in the upper parts of the cumulate mush. This termination may have been caused by tectonic disturbances, uplift, and associated withdrawal of magma into the subaxial dike and sill system. Prolonged compaction and cooling of the trapped melt in the mush formed small differentiated bodies and lenses by pressure release migration and crystallization along syntectonic channels. This resulted in differentiation products along lateral and vertical channelways in the host gabbro that vary from olivine gabbro, to Fe-Ti oxide gabbro, gabbronorite, and apatite gabbros and show large compositional variations independent of the host olivine gabbros.