Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

Reversibility and "pH-T phase diagrams" of Rapana venosa hemocyanin and its structural subunits

We have studied the stability and reassociation behaviour of native molecules of Rapana venosa hemocyanin and its two subunits, termed RvH1 and RvH2. In the presence of different concentrations of Ca(2+) and Mg(2+) ions and pH values, the subunits differ not only in their reassociation behaviour, but also in their formation of helical tubules and multidecamers. RvH1 revealed a greater stability at higher pH values compared to RvH2. Overall, the stability of reassociated RvH and its structural subunits was found to be pH-dependent. The increasing stability of native Hc and its subunits, shown by pH-induced CD transitions (acid and alkaline denaturation), can be explained with the formation of quaternary structure. The absence of a Cotton effect at temperatures 20-40 degrees C in the pH-transition curves of RvH2 indicates that this subunit is stabilized by additional "factors", e.g.: non-ionic/hydrophobic stabilization and interactions of carbohydrate moieties. A similar behaviour was observed for the T-transition curves in a wide pH interval for RvH and its structural subunits. At higher temperatures, many of the secondary structural elements are preserved especially at neutral pH, even at extreme high temperatures above 90 degrees C the protein structures resemble a "globule state".     

Genetic determinants for intramuscular fat content and water-holding capacity in mice selected for high muscle mass

Intramuscular fat content and water-holding capacity are important traits in livestock as they influence meat quality, nutritive value of the muscle, and animal health. As a model for livestock, two inbred lines of the Berlin Muscle Mouse population, which had been long-term selected for high muscle mass, were used to identify genomic regions affecting intramuscular fat content and water-holding capacity. The intramuscular fat content of the Musculus longissimus was on average 1.4 times higher in BMMI806 than in BMMI816 mice. This was accompanied by a 1.5 times lower water-holding capacity of the Musculus quadriceps in BMMI816 mice. Linkage analyses with 332 G₃ animals of reciprocal crosses between these two lines revealed quantitative trait loci for intramuscular fat content on chromosome 7 and for water-holding capacity on chromosome 2. In part, the identified loci coincide with syntenic regions in pigs in which genetic effects for the same traits were found. Therefore, these muscle-weight-selected mouse lines and the produced intercross populations are valuable genetic resources to identify genes that could also contribute to meat quality in other species.     

Sperm number trumps sperm size in mammalian ejaculate evolution

Postcopulatory sexual selection is widely accepted to underlie the extraordinary diversification of sperm morphology. However, why does it favour longer sperm in some taxa but shorter in others? Two recent hypotheses addressing this discrepancy offered contradictory explanations. Under the sperm dilution hypothesis, selection via sperm density in the female reproductive tract favours more but smaller sperm in large, but the reverse in small, species. Conversely, the metabolic constraint hypothesis maintains that ejaculates respond positively to selection in small endothermic animals with high metabolic rates, whereas low metabolic rates constrain their evolution in large species. Here, we resolve this debate by capitalizing on the substantial variation in mammalian body size and reproductive physiology. Evolutionary responses shifted from sperm length to number with increasing mammalian body size, thus supporting the sperm dilution hypothesis. Our findings demonstrate that body-size-mediated trade-offs between sperm size and number can explain the extreme diversification in sperm phenotypes.     

Drosophila p24 homologues eclair and baiser are necessary for the activity of the maternally expressed Tkv receptor during early embryogenesis

p24 proteins are assumed to play an important role in the transport of secreted and transmembrane proteins into membranes. However, only few cargo proteins are known that partially, but in no case completely require p24 proteins for membrane transport. Here, we show that two p24 proteins are essential for dorsoventral patterning of Drosophila melanogaster embryo. Mutations in the genes, eclair (eca) and baiser (bai), encoding two p24 proteins reduce signalling by the TGF-beta homologue, Dpp, in early embryos. This effect is strictly maternal and specific to early embryogenesis, as Dpp signalling in other contexts is not notably affected. We provide genetic evidence that in the absence of eca or bai function in the oocyte, the maternally expressed type I TGF-beta receptor Tkv is not active. We propose that during early embryogenesis eca and bai are specifically required for the activity of the maternal Tkv, while the zygotic Tkv is not affected in the mutant embryos. Mutations in either eca or bai are sufficient for the depletion of Tkv activity and no enhancement of the phenotypes was observed in embryos derived from oocytes mutant for both genes. The dependence of maternal Tkv protein on the products of p24 genes may serve as an in vivo model for studying p24 proteins.     

The upper cytokine-binding module and the Ig-like domain of the leukaemia inhibitory factor (LIF) receptor are sufficient for a functional LIF receptor complex.

To elucidate the function of the two cytokine-binding modules (CBM) of the leukemia inhibitory factor receptor (LIFR), receptor chimeras of LIFR and the interleukin-6 receptor (IL-6R) were constructed. Either the NH(2)-terminal (chimera RILLIFdeltaI) or the COOH-terminal LIFR CBM (chimera RILLIFdeltaII) were replaced by the structurally related CBM of the IL-6R which does not bind LIF. Chimera RILLIFdeltaI is functionally inactive, whereas RILLIFdeltaII binds LIF and mediates signalling as efficiently as the wild-type LIFR. Deletion mutants of the LIFR revealed that both the NH(2)-terminal CBM and the Ig-like domain of the LIFR are involved in LIF binding, presumably via the LIF site III epitope. The main function of the COOH-terminal CBM of the LIFR is to position the NH(2)-terminal CBM and the Ig-like domain, so that these can bind to LIF. In analogy to a recently published model of the IL-6R complex, a model of the active LIFR complex is suggested which positions the COOH-terminal CBM at LIF site I and the NH(2)-terminal CBM and the Ig-like domain at site III. An additional contact is postulated between the Ig-like domain of gp130 and the NH(2)-terminal CBM of the LIFR.     

Recent advances in chlorophyll biosynthesis and breakdown in higher plants

Chlorophyll (Chl) has unique and essential roles in photosynthetic light-harvesting and energy transduction, but its biosynthesis, accumulation and degradation is also associated with chloroplast development, photomorphogenesis and chloroplast-nuclear signaling. Biochemical analyses of the enzymatic steps paved the way to the identification of their encoding genes. Thus, important progress has been made in the recent elucidation of almost all genes involved in Chl biosynthesis and breakdown. In addition, analysis of mutants mainly in Arabidopsis, genetically engineered plants and the application of photo-reactive herbicides contributed to the genetic and regulatory characterization of the formation and breakdown of Chl. This review highlights recent progress in Chl metabolism indicating highly regulated pathways from the synthesis of precursors to Chl and its degradation to intermediates, which are not longer photochemically active.     

Cellular recognition of trimyristoylated peptide or enterobacterial lipopolysaccharide via both TLR2 and TLR4

Evidence for specific and direct bacterial product recognition through toll-like receptors (TLRs) has been emphasized recently. We analyzed lipopeptide analogues and enterobacterial lipopolysaccharide (eLPS) for their potential to activate cells through TLR2 and TLR4. Whereas bacterial protein palmitoylated at its N-terminal cysteine and N-terminal peptides derived thereof are known to induce TLR2-mediated cell activation, a synthetic acylhexapeptide mimicking a bacterial lipoprotein subpopulation for which N-terminal trimyristoylation is characteristic (Myr(3)CSK(4)) activated cells not only through TLR2 but also through TLR4. Conversely, highly purified eLPS triggered cell activation through overexpressed TLR2 in the absence of TLR4 expression if CD14 was coexpressed. Accordingly, TLR2(-/-) macrophages prepared upon gene targeting responded to Myr(3)CSK(4) challenge, whereas TLR2(-/-)/TLR4(d/d) cells were unresponsive. Through interferon-gamma (IFNgamma) priming, macrophages lacking expression of functional TLR4 and/or MD-2 acquired sensitivity to eLPS, whereas TLR2/TLR4 double deficient cells did not. Not only TLR2(-/-) mice but also TLR4(-/-) mice were resistant to Myr(3)CSK(4) challenge-induced fatal shock. d-Galactosamine-sensitized mice expressing defective TLR4 or lacking TLR4 expression acquired susceptibility to eLPS-driven toxemia upon IFNgamma priming, whereas double deficient mice did not. Immunization toward ovalbumin using Myr(3)CSK(4) as adjuvant was ineffective in TLR2(-/-)/TLR4(-/-) mice yet effective in wild-type, TLR2(-/-), or TLR4(-/-) mice as shown by analysis of ovalbumin-specific serum Ig concentration. A compound such as Myr(3)CSK(4) whose stimulatory activity is mediated by both TLR2 and TLR4 might constitute a preferable adjuvant. On the other hand, simultaneous blockage of both of the two TLRs might effectively inhibit infection-induced pathology.     

His499 Regulates Dimerization and Prevents Oncogenic Activation by Asparagine Mutations of the Human Thrombopoietin Receptor

Ligand binding to the extracellular domain of the thrombopoietin receptor (TpoR) imparts a specific orientation on the transmembrane (TM) and intracellular domains of the receptors that is required for physiologic activation via receptor dimerization. To map the inactive and active dimeric orientations of the TM helices, we performed asparagine (Asn)-scanning mutagenesis of the TM domains of the murine and human TpoR. Substitution of Asn at only one position (S505N) activated the human receptor, whereas Asn substitutions at several positions activated the murine receptor. Second site mutational studies indicate that His⁴⁹⁹ near the N terminus of the TM domain is responsible for protecting the human receptor from activation by Asn mutations. Structural studies reveal that the sequence preceding His⁴⁹⁹ is helical in the murine receptor but non-helical in peptides corresponding to the TM domain of the inactive human receptor. The activating S505N mutation and the small molecule agonist eltrombopag both induce helix in this region of the TM domain and are associated with dimerization and activation of the human receptor. Thus, His⁴⁹⁹ regulates the activation of human TpoR and provides additional protection against activating mutations, such as oncogenic Asn mutations in the TM domain.