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Showing papers by "University of Cologne published in 1991"


Journal ArticleDOI
04 Apr 1991-Nature
TL;DR: The importance of the membrane form of the μ chain in B-cell development is assessed by generating mice lacking this chain by disrupting one of the membranes exons of the gene encoding the μ-chain constant region by gene targeting in mouse embryonic stem cells.
Abstract: OF the various classes of antibodies that B lymphocytes can produce, class M (IgM) is the first to be expressed on the membrane of the developing cells. Pre-B cells, the precursors of B-lymphocytes, produce the heavy chain of IgM (μ chain), but not light chains1. Recent data suggest that pre-B cells express μ chains on the membrane together with the 'surrogate' light chains λ5 and VpreB (refs 2–7). This complex could control pre-B-cell differentiation, in particular the rearrangement of the light-chain genes8. We have now assessed the importance of the membrane form of the μ chain in B-cell development by generating mice lacking this chain. We disrupted one of the membrane exons of the gene encoding the μ-chain constant region by gene targeting9 in mouse embryonic stem cells10. From these cells we derived mice heterozygous or homozygous for the mutation. B-cell development in the heterozygous mice seemed to be normal, but in homozygous animals B cells were absent, their development already being arrested at the stage of pre-B-cell maturation.

1,826 citations


Journal ArticleDOI
01 Nov 1991-Science
TL;DR: Some but not all of the in vitro properties of IL-4 are critical for the physiology of the immune system in vivo, but the serum levels of IgG1 and IgE are strongly reduced.
Abstract: Interleukin-4 (IL-4) promotes the growth and differentiation of many hematopoietic cells in vitro; in particular, it directs the immunoglobulin (Ig) class switch to IgG1 and IgE. Mice homozygous for a mutation that inactivates the IL-4 gene were generated to test the requirement for IL-4 in vivo. In the mutant mice T and B cell development was normal, but the serum levels of IgG1 and IgE were strongly reduced. The IgG1 dominance in a T cell-dependent immune response was lost, and IgE was not detectable upon nematode infection. Thus, some but not all of the in vitro properties of IL-4 are critical for the physiology of the immune system in vivo.

1,262 citations


Journal ArticleDOI
05 Dec 1991-Nature
TL;DR: Direct evidence is reported for direct evidence that antigen-induced proliferation of B cells at another site, periarteriolar lymphocyte sheath-associated foci, was not associated with somatic hypermutation, and most represent cells of distinct B-cell clones which expanded locally, generating somatic antibody mutants at high rate.
Abstract: The generation and selection of somatic antibody mutants are key elements of acquired immunity, essential for the affinity maturation of antibody responses dependent on T cells. The mutants are generated through a mechanism that introduces point mutations at high rate into rearranged variable (V) region genes in the course of cell proliferation. Their appearance coincides with the generation of germinal centres, which are characterized by oligoclonal B-cell proliferation and have been suggested to be the microenvironment in which antibody mutants are generated. We report here direct evidence for this hypothesis. Rearranged V-region genes were amplified from the genomic DNA of cells picked from individual germinal centres. The sequence analysis of these genes revealed that most represent cells of distinct B-cell clones which expanded locally, generating somatic antibody mutants at high rate. By contrast, antigen-induced proliferation of B cells at another site, periarteriolar lymphocyte sheath-associated foci, was not associated with somatic hypermutation.

1,076 citations


Book
01 Jan 1991
TL;DR: In this article, the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement, which includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations.
Abstract: The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables as well as unsharp pointers.

793 citations


Journal ArticleDOI
TL;DR: The data indicate that the recruitment of newly generated B cells into the long-lived peripheral B cell pool is mediated through positive selection by internal and/or external antigens, different from the selection of memory B cells in T cell-dependent immune responses.
Abstract: Using amplified cDNA and genomic libraries, we have analyzed the VH gene repertoire of pre-B cells and various B cell subsets of conventional mice at the level of VH genes belonging to the J558 VH gene family. The sequence data were evaluated on the basis of a newly established list of 67 J558 VH genes that comprise approximately two-thirds of the J558 VH genes of the murine IgHb haplotype. The results of the analysis demonstrate that VH gene utilization in pre-B cells, although biased to some extent by B cell autonomous VH gene selection, scatters over the whole range of J558 VH genes present in the germline. In contrast, in mature, peripheral B cells comprising long-lived mu + delta high B cells as well as Ly-1 B cells, small overlapping sets of germline VH genes are dominantly expressed. The data indicate that the recruitment of newly generated B cells into the long-lived peripheral B cell pool is mediated through positive selection by internal and/or external antigens. Because of the absence of immunoglobulin class switching and somatic hypermutation, this process is different from the selection of memory B cells in T cell-dependent immune responses.

404 citations


Journal ArticleDOI
TL;DR: In this article, an improved version of the empirical geothermometer for spinel peridotites derived from the evaluation of the solubilities of Ca and Al in orthopyroxene was presented.
Abstract: Geothermometric equations for spinel peridotites by Fujii (1976), Gasparik and Newton (1984), and Chatterjee, and Terhart (1985) based on the reaction enstatite (en)+spinel (sp)→Mg−Tschermaks (mats)+forsterite (fo) were tested using a nearly isothermal suite of mantle xenoliths from the Eifel, West Germany. In spite of using activities of MgAl2O4, en, and mats to allow for the non-ideal solution behaviour of the constituent phases, temperatures calculated from these equations systematically change as a function of Cr/(Cr+AL+Fe3+) in spinel. We propose an improved version of the empirical geothermometer for spinel peridotites of Sachtleben and Seck (1981) derived from the evaluation of the solubilities of Ca and Al in orthopyroxene from more than 100 spinel peridotites from the Rhenish Volcanic Province. A least squares regression yielded a smooth correlation between $${\text{(}}X_{{\text{Ca}}} {\text{)}}^{{\text{opx}}} {\text{ and 1n K}}_{\text{D}} = 1n\frac{{(x_{{\text{Fo}}}^{{\text{Ol}}} )^2 {\text{ * }}(x_{{\text{Al}}}^{{\text{Ml}}} )^{opx} }}{{(x_{{\text{Al}}}^{{\text{Sp}}} )^2 {\text{ * }}(x_{{\text{Mg}}}^{{\text{Sp}}} )^2 {\text{ * }}(x_{{\text{Mg}}}^{{\text{M1}}} )^{opx} }}$$ as measure of Al in orthopyroxene, if the mole fraction of (Mg,Fe)Cr2O4 [Y Sp Cr ] in spinel is allowed for. Fitting (X Al)opx and (X Cr)opx or ln KD to temperatures derived from the new thermometer of Brey and Koehler (1990) based on (X Ca)opx leads to the following equations: $$\begin{gathered} T{\text{(}}^\circ {\text{C)}} = 2248.25 + 991.58*1n{\text{ K}}_{\text{D}} + 153.32*(1n{\text{ K}}_{\text{D}} )^2 + 539.05*y_{Cr}^{Sp} \hfill \\ {\text{ }} - 2005.74*(y_{Cr}^{Sp} )^2 \hfill \\ T{\text{(}}^\circ {\text{C)}} = 636.54 + 2088.21*x_{{\text{Al}}}^{{\text{M1}}} + 14527.32*x_{{\text{Cr}}}^{{\text{M1}}} \hfill \\ \end{gathered}$$ The last of these is more suitable for practical use but is applicable only over a limited range of (X Al)M1 and (X Cr)M1 in orthopyroxene. The lack of steady-state equilibrium conditions due to young thermal perturbations or fast cooling may lead to discrepancies of temperatures calculated from (X Ca)opx and (X Al)opx. Spinel peridotite xenoliths from Central Asia are shown to demonstrate this.

316 citations


Journal ArticleDOI
01 Oct 1991-Virology
TL;DR: Restriction enzyme analysis revealed that HHV-6 isolates from roseola, bone marrow transplant, leukopenia, and an HIV-1-positive AIDS patient from Zaire (Z-29) were closely related but distinct from GS type HHVs, suggesting that, like herpes simplex virus types 1 and 2, the 15 isolates analyzed can be divided into group A and group B.

308 citations


Journal ArticleDOI
Stefan Grond1, D. Zech1, Stephan A. Schug, J. Lynch1, Klaus A. Lehmann1 
TL;DR: This study shows that cancer pain can be treated satisfactorily until death, with the World Health Organization's guidelines for cancer pain relief examined in 401 dying patients.

235 citations


Journal ArticleDOI
TL;DR: The main emphasis is on the concept of the multiple level of significance (controlling the experiment, or family error in the strong sense) which can be achieved by applying the principle of closed tests.
Abstract: The basic ideas of multiple testing are outlined and the problem of how to control the probability of erroneous decisions is discussed. The main emphasis is on the concept of the multiple level of significance (controlling the experiment, or family error in the strong sense) which can be achieved by applying the principle of closed tests. Various practical situations encountered in multiple testing in clinical trials are considered: more than one end point; more than two treatments, such as comparisons with a single control, comparisons using ordered alternatives, all pairwise comparisons and contrast methods; and more than one trial. Tests based on global statistics, the union intersection principle and other criteria are discussed. The application of the multiple test concept in sequential sampling is investigated. Finally some comments are made on multiple power, multiple confidence intervals and directed decisions.

222 citations


Journal ArticleDOI
TL;DR: The ability to construct five-arm and six-arm junctions vastly increases the number of structures and networks that can be built from branched DNA components.
Abstract: DNA branched junctions have been constructed that contain either five arms or six arms surrounding a branch point These junctions are not as stable as junctions containing three or four arms; unlike the smaller junctions, they cannot be shown to migrate as a single band on native gels when each of their arms contains eight nucleotide pairs However, they can be stabilized if their arms contain 16 nucleotide pairs Ferguson analysis of these junctions in combination with three-arm and four-arm junctions indicates a linear increase in friction constant as the number of arms increases, with the four-arm junction migrating anomalously The five-arm junction does not appear to have any unusual stacking structure, and all strands show similar responses to hydroxyl radical autofootprinting analysis By contrast, one strand of the six-arm junction shows virtually no protection from hydroxyl radicals, suggesting that it is the helical strand of a preferred stacking domain Both junctions are susceptible to digestion by T4 endonuclease VII, which resolves Holliday junctions However, the putative helical strand of the six-arm junction shows markedly reduced cleavage, supporting the notion that its structure is largely found in a helical conformation Branched DNA molecules can be assembled into structures whose helix axes form multiply connected objects and networks The ability to construct five-arm and six-arm junctions vastly increases the number of structures and networks that can be built from branched DNA components Icosahedral deltahedra and 11 networks with 432 symmetry, constructed from Platonic and Archimedean solids, are among the structures whose construction is feasible, now that these junctions can be made

207 citations


Journal ArticleDOI
05 Apr 1991-Cell
TL;DR: Evidence is obtained that membrane-bound D mu signals arrest of differentiation, presumably by preventing VH-DHJH joining in areas of sequence homology further enforces RF1 usage.

Journal ArticleDOI
TL;DR: The identification and characterization of the cDNA of another member of the cadherin family, M-cadherin (M for muscle), from differentiating muscle cells is reported, indicating that M- cadher in is part of the myogenic program and may provide a trigger for terminal muscle differentiation.
Abstract: Cadherins, a multigene family of transmembrane glycoproteins, mediate Ca(2+)-dependent intercellular adhesion. They are thought to be essential for the control of morphogenetic processes, including myogenesis. Here we report the identification and characterization of the cDNA of another member of the cadherin family, M-cadherin (M for muscle), from differentiating muscle cells. The longest open reading frame of the cDNAs isolated contains almost the entire coding region of the mature M-cadherin as determined by sequence homology to the known cadherins. M-cadherin mRNA is present at low levels in myoblasts and is upregulated in myotube-forming cells. In mouse L cells (fibroblasts), M-cadherin mRNA is undetectable. This expression pattern indicates that M-cadherin is part of the myogenic program and may provide a trigger for terminal muscle differentiation.


Journal ArticleDOI
TL;DR: P phenotypic interactions of Ser alleles with the neurogenic genes Notch and Delta coupled with the structural similarity of the proteins encoded by these three genes suggest close interactions at the protein level.
Abstract: We describe the molecular characterization of the Drosophila gene Serrate (Ser), which encodes an integral membrane protein. The extracellular domain contains two cysteine-rich regions, one of which is organized in a tandem array of 14 EGF-like repeats. Antibodies directed against part of the extracellular region confirm the localization of the protein in the membrane. In the wing imaginal discs, the protein is detected in those regions that are affected in the wings of two dominant mutations, SerD and SerBd. Both mutations as well as three out of eight newly induced revertants of SerD could be mapped molecularly to the transcribed region, confirming the identity between the gene Ser and the transcription unit characterized. During embryonic development, RNA and protein exhibit a complex expression pattern, which is, however, not correlated with an appropriate embryonic phenotype. Phenotypic interactions of Ser alleles with the neurogenic genes Notch and Delta coupled with the structural similarity of the proteins encoded by these three genes suggest close interactions at the protein level.

Journal ArticleDOI
TL;DR: In combination, the stimulatory effects of Sh1 exon 1 and intron 1 are multiplicative in monocot protoplasts resulting in a final enhancement of up to 1000-fold compared to the unmodified CAT or luciferase marker genes.
Abstract: Both exon 1 and intron 1 of the maize Shrunken-1 (Sh1) gene individually stimulate expression of reporter genes in transient gene expression experiments if present within the transcription unit. The Sh1 exon 1 mediates a 10-fold increase in activity when inserted at the 5′ end of the bacterial chloramphenicol transacetylase (CAT) marker gene in both monocot and dicot protoplasts. The Sh1 intron 1 enhances chimeric gene expression in rice and maize protoplasts approximately 100-fold but inhibits CAT expression in tobacco protoplasts. In combination, the stimulatory effects of Sh1 exon 1 and intron 1 are multiplicative in monocot protoplasts resulting in a final enhancement of up to 1000-fold compared to the unmodified CAT or luciferase marker genes.


Journal ArticleDOI
TL;DR: In this article, the authors generalize the topological massive gauge model of gravity to a three-dimensional Riemann-Cartan spacetime with torsion, and derive an exact vacuum solution with purely axial torsions and constant curvature.

Journal ArticleDOI
TL;DR: Many of the molecular mechanisms involved in the cell fate choices are shared in the development of the CNS and PNS, and the analysis of the cellular decisions that lead to the formation of the PNS is discussed.
Abstract: In insects, neurons in the central nervous system (CNS) are generated by progenitor cells called neuroblasts derived from a region of the ectoderm called the neurogenic region or neuroectoderm. In the neuroectoderm of Drosophila melanogaster, neighboring cells take on one of two alternative fates and develop either as neuroblasts or as epidermoblasts (progenitor cells of the epidermis). The neuroblasts move to deeper levels of the embryo to build up the central neural primordium, whereas the epidermoblasts remain at the surface to build up part of the epidermal sheath. The peri­ pheral nervous system (PNS) of insects develops from progenitor cells located within the epidermis. Thus, development of the PNS involves another choice by the epidermal cells between neural and nonneural fates, i.e. to develop as sensory progenitor cells versus non sensory epidermal cells. As is discussed in this review, many of the molecular mechanisms involved in the cell fate choices are shared in the development of the CNS and PNS. The analysis of the cellular decisions that lead to the formation of the

Book
01 Jan 1991
TL;DR: The author’s aim has been to contribute towards the humanizing of English by promoting a more positive image of the language and its role in the lived experience.
Abstract: The period between 1500 and 1700 was the most decisive one in the formation of standard modern English, yet no really comprehensive account of Early Modern English has been available. Manfred Gorlach's Introduction to Early Modern English fills a very real need. It provides a thorough and linguistically informed synchronic description of Early Modern English, dealing with its varieties, with writing and orthography, phonetics and phonology, syntax and the lexicon, including sections on problems of language contact and the lexicographical tradition. In addition, it provides a valuable anthology of texts from a wide range of sources: the texts exemplify features from Early Modern English discussed in the main body of the book, and have also been effectively chosen so as to provide something of the cultural background to the processes of linguistic change of the period. This textbook is admirably suited to undergraduate courses, and will be welcomed by all students of English language and literature studying the Early Modern period.

Journal ArticleDOI
Paul Busch1
TL;DR: In this paper, the notion of informational completeness is formulated within the convex state (or operational) approach to statistical physical theories and employed to introduce a type of statistical metrics, and a criterion for a set of physical quantities to be informationally complete is proven.
Abstract: The notion of informational completeness is formulated within the convex state (or operational) approach to statistical physical theories and employed to introduce a type of statistical metrics. Further, a criterion for a set of physical quantities to be informationally complete is proven. Some applications of this result are given within the algebraic and Hilbert space formulations of quantum theory.

Journal ArticleDOI
TL;DR: Systemic effects of Co-Cr alloy/polyethylene hip joint prostheses were investigated using instrumental neutron activation to determine the concentrations of up to 16 elements and showed massive Co enrichments as a consequence of implant corrosion.
Abstract: Systemic effects of Co-Cr alloy/polyethylene hip joint prostheses were investigated using instrumental neutron activation to determine the concentrations of up to 16 elements. First, in a prospective study whole blood and serum taken from 10 patients from 1 day before to 90 days after implantation were analyzed. Secondly, in a retrospective study whole blood and serum from 23 patients who had had prostheses in place for up to 18 years were analyzed. For comparison, normal trace element levels in humans were determined by analyzing whole blood and serum from 21 patients. Finally, various tissues and organs from two deceased implant patients were analyzed and compared with normal concentrations obtained from the analysis of five “normal” patients without implants. In agreement with other recent investigations, our analyses of normal serum, whole blood, tissues, and organs show that most previously defined “normal” trace element concentrations were too high, chiefly owing to contamination and insufficient blanks. A detailed discussion shows that for many elements the ranges of normal concentrations have to be revised. This conclusion is of particular importance with respect to the sometimes conflicting earlier reports of systemic effects of metal prostheses. In the work reported here, both the prospective and the retrospective investigations of serum and whole blood showed massive Co enrichments as a consequence of implant corrosion. The data show a wide range of individual burdening, ranging from practically no effect to the most extreme values. The analyses of tissues from the vicinity of the implants in the two deceased implant patients showed strong local effects of Co, Cr, Zr, and Hf, the latter two elements originating from the X-ray contrast media in the bone cement. The analyses of organs revealed significant Co and Cr enrichment in several tissues and organs. Consequently, it can be seen that implant corrosion is not an occurrence of merely local significance, but one that affects the trace element status of the entire organism.

Journal ArticleDOI
TL;DR: The similarity in degrees of folding among hominoids is consistent with interpretations that, given its small cranial capacity, the lunate sulcus of the Taung specimen is in a pongid position.

Journal ArticleDOI
TL;DR: It is shown that a 61-amino-acid peptide sequence containing only the bipartite basic motif/helix-loop-helix domain of Myc is necessary and sufficient for dimerization and sequence-specific DNA binding of v-Myc recombinant proteins.
Abstract: Myc proteins have a tripartite carboxyl-terminal domain containing specific amino acid sequence motifs: a basic motif, a helix-loop-helix motif, and a leucine heptad repeat. Similar sequence motifs have been identified in several eukaryotic transcription factors and were shown to facilitate protein-DNA and protein-protein interactions. By using recombinant v-Myc proteins obtained by bacterial expression of full-length or partially deleted avian v-myc alleles, the functional relevance of these sequence motifs for Myc protein oligomerization and for DNA binding was investigated. All recombinant v-Myc proteins that have retained the carboxyl-terminal domain dimerize and specifically bind to double-stranded DNA containing the palindromic core sequence CACGTG. This and a closely related DNA sequence element have been defined previously as part of the binding sites for human transcription factors USF and TFE3, which specifically bind to the adenovirus major late promoter or the muE3 motif within the immunoglobulin heavy-chain enhancer, respectively. It is shown that a 61-amino-acid peptide sequence containing only the bipartite basic motif/helix-loop-helix domain of Myc is necessary and sufficient for dimerization and sequence-specific DNA binding of v-Myc recombinant proteins.

Book ChapterDOI
01 Jan 1991
TL;DR: In this paper, the behavior of elementary particles in special relativity (SR), such as electrons, protons, or neutrons, is discussed in order to get ideas of the underlying principles of the gravitational interaction of fermions.
Abstract: In these two lectures we want to provide information on the behavior of elementary particles in special relativity (SR), such as electrons, protons, or neutrons, in order to get ideas of the underlying principles of the gravitational interaction of fermions. For tangible matter and for the electromagnetic field, Einstein’s gravitational theory, general relativity (GR), describes all phenomena very well and has been verified experimentally with ever increasing accuracy. In contrast therefrom, not too much is known experimentally for fermions and their gravitational interaction, apart from the celebrated Colella-Overhauser-Werner (or COW) experiment [21] using a neutron interferometer in a gravitational field.

Journal ArticleDOI
TL;DR: In this paper, a tropopause fold and cut-off low developed over Europe at the end of April 1982 and enhanced the exchange of air between the stratosphere and troposphere.

Journal ArticleDOI
TL;DR: This work investigates the stability of general-relativistic boson stars by classifying singularities of differential mappings and compares their results with those of perturbation theory.
Abstract: We investigate the stability of general-relativistic boson stars by classifying singularities of differential mappings and compare our results with those of perturbation theory. Depending on the particle number, the star has the following regimes of behavior: stable, metastable, pulsation, and collapse.

Journal ArticleDOI
TL;DR: The evaluation of the sedation score showed that sedation of artifically ventilated infants and young children can be established by continuous intravenous infusion of midazolam.
Abstract: Twenty-four patients in a paediatric intensive care unit mostly undergoing cardiac surgery, received a midazolam dosage between 50-400 micrograms/kg per hour as a continuous intravenous infusion partly in combination with fentanyl [0,5-2,5 micrograms/kg per hour] for analgesia and sedation. The mean duration of midazolam infusion was 11.6 days (range 38 h-40 days). Blood samples for the HPLC assay of serum midazolam concentration were taken and the clearance estimated. The efficiency of sedation in correlation to the midazolam concentration was evaluated by a clinical sedation score. Serum midazolam concentrations between 100-400 micrograms/l were sufficient for sedation. Dosage had to be increased during therapy according to an increased midazolam clearance. The evaluation of the sedation score showed that sedation of artificially ventilated infants and young children can be established by continuous intravenous infusion of midazolam.

Journal ArticleDOI
TL;DR: As these five plant families are not closely related, the ability to generate a pressurized ventilation by thermo-osmosis of gas can be seen as a special adaptation of the wetland plants to the anoxic environment.

Journal Article
TL;DR: The proposals in this review are based on experimental work on the integration of foreign DNA in mammalian cells, on the establishment of specific de novo patterns of DNA methylation, and on the inhibition of transcription by the sequence-specific methylation of promoter sequences.
Abstract: The proposals in this review are based on experimental work on the integration of foreign DNA in mammalian cells, on the establishment of specific de novo patterns of DNA methylation, and on the inhibition of transcription by the sequence-specific methylation of promoter sequences. It is suggested that eukaryotic cells have developed several mechanisms of defense against the uptake, integration, and continued expression of foreign DNA. In the course of evolution and continuing at present, cells have been exposed to foreign DNA, entire genomes or fragments of them. A particularly problematic organ system in that respect must be digestive tract in higher organisms. The defense mechanisms are thought to be the following: (i) degradation and/or excretion of foreign DNA; (ii) excision and loss of previously integrated DNA from the host genome; (iii) targeted inactivation of foreign genes by sequence-specific methylation. Genes whose products could be advantageous to the transformed cells can somehow be selectively excluded from this silencing mechanism. In part, the specificity of de novo methylation must reside in the DNA methyltransferase systems of the host cell. However, nucleotide sequence, structure, and chromatin arrangement in the foreign DNA could also play an important role. Since defense processes must have been activated many times in evolution, patterns of DNA methylation as they can be observed today, may represent vestiges of evolution, i.e. the sum total of selective de novo methylations, possibly demethylations, and mutations.(ABSTRACT TRUNCATED AT 250 WORDS)

Journal ArticleDOI
TL;DR: In this article, the lifetime of low-lying levels in 90, 92, 94, 96, and 96Sr were measured using a recently developed βγγ fast timing method, which provided evidence for a strong Z = 38 subshell effect extending from N = 50 to N = 58.