Population growth in random environments

This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.     

On the role of Ca2+-calmodulin-dependent and cAMP-dependent protein phosphorylation in the circadian rhythm ofNeurospora crassa

Summary Pulses of some Ca²⁺ channel blockers (dantrolene, Co²⁺, nifedipine) and calmodulin inhibitors (chlorpromazine) lead to medium (maximally 5–9 h) phase shifts of the circadian conidiation rhythm ofNeurospora crassa. Pulses of high Ca²⁺, or of low Ca²⁺, a Ca²⁺ ionophore (A23187) together with Ca²⁺, and other Ca²⁺ channel blockers (La³⁺, diltiazem), however, caused only minor phase shifts. The effect of these substances (A 23187) and of different temperatures on the Ca²⁺ release from isolated vacuoles was analyzed by using the fluorescent dye Fura-2. A 23187 and higher temperatures increased the release drastically, whereas dantrolene decreased the permeation of Ca²⁺ (Cornelius et al., 1989).Pulses of 8-PCTP-cAMP, IBMX and of the cAMP antagonist RP-cAMPS, also caused medium (maximally 6–9 h) phase shifts of the conidiation rhythm. The phase response curve of the agonist was almost 180° out of phase with the antagonist PRC. In spite of some variability in the PRCs of these series of experiments all showed maximal shifts during ct 0–12. The variability of the response may be due to circadian changes in the activity of phosphodiesterases: After adding cAMP to mycelial extracts HPLC analysis of cAMP metabolites showed significant differences during a circadian period with a maximum at ct 0.Protein phosphorylation was tested mainly in an in vitro phosphorylation system (with³⁵S-thio -ATP). The results showed circadian rhythmic changes predominantly in proteins of 47/48 kDa. Substances and treatments causing phase-shifts of the conidiation rhythm also caused changes in the phosphorylation of these proteins: an increase was observed when Ca²⁺ or cAMP were added, whereas a decrease occurred upon addition of a calmodulin inhibitor (TFP) or pretreatment of the mycelia with higher (42° C) temperatures.Altogether, the results indicate that Ca²⁺-calmodulin-dependent and cAMP-dependent processes play an important, but perhaps not essential, role in the clock mechanism ofNeurospora. Ca²⁺ calmodulin and the phosphorylation state of the 47/48-kDa proteins may have controlling or essential functions for this mechanism.     

Catalytic Turnover Triggers Exchange of Subunits of the Magnesium Chelatase AAA+ Motor Unit

The ATP-dependent insertion of Mg²⁺ into protoporphyrin IX is the first committed step in the chlorophyll biosynthetic pathway. The reaction is catalyzed by magnesium chelatase, which consists of three gene products: BchI, BchD, and BchH. The BchI and BchD subunits belong to the family of AAA+ proteins (ATPases associated with various cellular activities) and form a two-ring complex with six BchI subunits in one layer and six BchD subunits in the other layer. This BchID complex is a two-layered trimer of dimers with the ATP binding site located at the interface between two neighboring BchI subunits. ATP hydrolysis by the BchID motor unit fuels the insertion of Mg²⁺ into the porphyrin by the BchH subunit. In the present study, we explored mutations that were originally identified in semidominant barley (Hordeum vulgare L.) mutants. The resulting recombinant BchI proteins have marginal ATPase activity and cannot contribute to magnesium chelatase activity although they apparently form structurally correct complexes with BchD. Mixing experiments with modified and wild-type BchI in various combinations showed that an exchange of BchI subunits in magnesium chelatase occurs during the catalytic cycle, which indicates that dissociation of the complex may be part of the reaction mechanism related to product release. Mixing experiments also showed that more than three functional interfaces in the BchI ring structure are required for magnesium chelatase activity.     

Harvesting in a random environment: Itô or Stratonovich calculus?

We extend to harvesting stochastic differential equation (SDE) models in a random environment our previous work on models without harvesting concerning the resolution of the It?-Stratonovich controversy. The resolution is obtained for the very general class of models dN/dt=N (r(N)-h(N)+sigmaepsilon(t)), where N=N(t) is the population size at time t, r(N) is the (density-dependent) "mean" per capita growth rate, h(N) is the (density-dependent) harvesting effort, epsilon(t) is a standard white noise (representing environmental random fluctuations), and sigma is a noise intensity parameter. It? and Stratonovich calculus in the resolution of SDEs apparently give different qualitative and quantitative results, leading to controversy on which calculus is more appropriate and creating an obstacle on the use of this modeling approach. We show that the apparent difference between the two calculi is due to a semantic confusion based on the fallacious assumption that we are working with the same type of mean rates. After clearing the confusion, the two calculi yield exactly the same results and we obtain important common conditions for extinction and for existence of a stationary density. The resolution of the controversy is intertwined with and sheds light on the estimation issues.     

Iron overload of the bone marrow by trimethylhexanoyl-ferrocene in rats.

Iron-deficient female Wistar rats were fed a diet which contained 0.5% 3,5,5-trimethylhexanoyl (TMH)-ferrocene over a 57-week period. The state of iron deficiency was characterized by means of the absence of stainable iron in the bone marrow. After the first days on the iron-enriched diet, ferritin-containing siderosomes were found, in numerous erythroblasts up to orthochromatic normoblasts and in reticulocytes, i.e. the dispensed iron was used for haemoglobin synthesis. After 1 week the first macrophages showed a positive Perls' Prussian blue reaction. In the cytoplasm they stored the iron in the form of free ferritin molecules and lysosomally as aggregated ferritin and/or haemosiderin. The iron loading of the macrophages increased in both of the storage qualities proportionally with duration of the feeding period and reached a maximum after 38 weeks. Final stages showed extremely iron-loaded macrophages with high concentrations of free ferritin molecules and large siderosomes, partially flowing together to still greater units. Iron deposits within endothelial cells of bone marrow sinusoids can be observed for the first time after 4 weeks. In these cells the iron is stored as ferritin in siderosomes of relatively small and uniform size; free ferritin molecules in the cytosol were of only slight concentration. The TMH-ferrocene model of iron overload shows in the bone marrow: (1) an unimpeded utilization of the iron component for erythropoiesis, (2) development of excessive iron overload of the bone marrow in macrophages and endothelial cells of sinusoids and (3) a pattern of distribution of iron as seen in secondary haemochromatosis.     

Induced Variations in Brassinosteroid Genes Define Barley Height and Sturdiness,and Expand the Green Revolution Genetic Toolkit

Reduced plant height and culm robustness are quantitative characteristics important for assuring cereal crop yield and quality under adverse weather conditions. A very limited number of short-culm mutant alleles were introduced into commercial crop cultivars during the Green Revolution. We identified phenotypic traits, including sturdy culm, specific for deficiencies in brassinosteroid biosynthesis and signaling in semidwarf mutants of barley (Hordeum vulgare). This set of characteristic traits was explored to perform a phenotypic screen of near-isogenic short-culm mutant lines from the brachytic, breviaristatum, dense spike, erectoides, semibrachytic, semidwarf, and slender dwarf mutant groups. In silico mapping of brassinosteroid-related genes in the barley genome in combination with sequencing of barley mutant lines assigned more than 20 historic mutants to three brassinosteroid-biosynthesis genes (BRASSINOSTEROID-6-OXIDASE, CONSTITUTIVE PHOTOMORPHOGENIC DWARF, and DIMINUTO) and one brassinosteroid-signaling gene (BRASSINOSTEROID-INSENSITIVE1 [HvBRI1]). Analyses of F2 and M2 populations, allelic crosses, and modeling of nonsynonymous amino acid exchanges in protein crystal structures gave a further understanding of the control of barley plant architecture and sturdiness by brassinosteroid-related genes. Alternatives to the widely used but highly temperature-sensitive uzu1.a allele of HvBRI1 represent potential genetic building blocks for breeding strategies with sturdy and climate-tolerant barley cultivars.The introduction of dwarfing genes to increase culm sturdiness of cereal crops was crucial for the first Green Revolution (Hedden, 2003). The culms of tall cereal crops were not strong enough to support the heavy spikes of high-yielding cultivars, especially under high-nitrogen conditions. As a result, plants fell over, a process known as lodging. This caused losses in yield and grain-quality issues attributable to fungal infections, mycotoxin contamination, and preharvest germination (Rajkumara, 2008). Today, a second Green Revolution is on its way, to revolutionize the agricultural sector and to ensure food production for a growing world population. Concurrently, global climate change is expected to cause more frequent occurrences of extreme weather conditions, including thunderstorms with torrential rain and strong winds, thus promoting cereal culm breakage (Porter and Semenov, 2005; National Climate Assessment Development Advisory Committee, 2013). Accordingly, plant architectures that resist lodging remain a major crop-improvement goal and identification of genes that regulate culm length is required to enhance the genetic toolbox in order to facilitate efficient marker-assisted breeding. The mutations and the corresponding genes that enabled the Green Revolution in wheat (Triticum aestivum) and rice (Oryza sativa) have been identified (Hedden, 2003). They all relate to gibberellin metabolism and signal transduction. It is now known that other plant hormones such as brassinosteroids are also involved in the regulation of plant height. Knowledge of the molecular mechanisms underlying the effects of the two hormones on cell elongation and division has mainly come from studies in Arabidopsis (Arabidopsis thaliana; Bai et al., 2012). Mutant-based breeding strategies to fine-tune brassinosteroid metabolism and signaling pathways could improve lodging behavior in modern crops (Vriet et al., 2012) such as barley (Hordeum vulgare), which is the fourth most abundant cereal in both area and tonnage harvested (http://faostat.fao.org).A short-culm phenotype in crops is often accompanied by other phenotypic changes. Depending on the penetrance of such pleiotropic characters, but also the parental background and different scientific traditions and expertise, short-culmed barley mutants were historically divided into groups, such as brachytic (brh), breviaristatum (ari), dense spike (dsp), erectoides (ert), semibrachytic (uzu), semidwarf (sdw), or slender dwarf (sld; Franckowiak and Lundqvist, 2012). Subsequent mutant characterization was limited to intragroup screens and very few allelism tests between mutants from different groups have been reported (Franckowiak and Lundqvist, 2012). Although the total number of short-culm barley mutants exceeds 500 (Franckowiak and Lundqvist, 2012), very few have been characterized at the DNA level (Helliwell et al., 2001; Jia et al., 2009; Chandler and Harding, 2013; Houston et al., 2013). One of the first identified haplotypes was uzu barley (Chono et al., 2003). The Uzu1 gene encodes the brassinosteroid hormone receptor and is orthologous to the BRASSINOSTEROID-INSENSITIVE1 (BRI1) gene of Arabidopsis, a crucial promoter of plant growth (Li and Chory, 1997). The uzu1.a allele has been used in East Asia for over a century and is presently distributed in winter barley cultivars in Japan, the Korean peninsula, and China (Saisho et al., 2004). Its agronomic importance comes from the short and sturdy culm that provides lodging resistance, and an upright plant architecture that tolerates dense planting.Today, more than 50 different brassinosteroids have been identified in plants (Bajguz and Tretyn, 2003). Most are intermediates of the complex biosynthetic pathway (Shimada et al., 2001). Approximately nine genes code for the enzymes that participate in the biosynthetic pathway from episterol to brassinolide (Supplemental Fig. S1). Brassinosteroid deficiency is caused by down-regulation of these genes, but it can also be associated with brassinosteroid signaling. The first protein in the signaling network is the brassinosteroid receptor encoded by BRI1 (Li and Chory, 1997; Kim and Wang, 2010). In this work, we show how to visually identify brassinosteroid-mutant barley plants and we describe more than 20 relevant mutations in four genes of the brassinosteroid biosynthesis and signaling pathways that can be used in marker-assisted breeding strategies.     

Linking stem cell function and growth pattern of intestinal organoids

Intestinal stem cells (ISCs) require well-defined signals from their environment in order to carry out their specific functions. Most of these signals are provided by neighboring cells that form a stem cell niche, whose shape and cellular composition self-organize. Major features of this self-organization can be studied in ISC-derived organoid culture. In this system, manipulation of essential pathways of stem cell maintenance and differentiation results in well-described growth phenotypes.We here provide an individual cell-based model of intestinal organoids that enables a mechanistic explanation of the observed growth phenotypes. In simulation studies of the 3D structure of expanding organoids, we investigate interdependences between Wnt- and Notch-signaling which control the shape of the stem cell niche and, thus, the growth pattern of the organoids. Similar to in vitro experiments, changes of pathway activities alter the cellular composition of the organoids and, thereby, affect their shape. Exogenous Wnt enforces transitions from branched into a cyst-like growth pattern; known to occur spontaneously during long term organoid expansion. Based on our simulation results, we predict that the cyst-like pattern is associated with biomechanical changes of the cells which assign them a growth advantage. The results suggest ongoing stem cell adaptation to in vitro conditions during long term expansion by stabilizing Wnt-activity.Our study exemplifies the potential of individual cell-based modeling in unraveling links between molecular stem cell regulation and 3D growth of tissues. This kind of modeling combines experimental results in the fields of stem cell biology and cell biomechanics constituting a prerequisite for a better understanding of tissue regeneration as well as developmental processes.     

Semi-dwarf barley (<Emphasis Type="Italic">Hordeum vulgare</Emphasis> L.) <Emphasis Type="Italic">brh2</Emphasis> and <Emphasis Type="Italic">ari-l</Emphasis> mutants are deficient in a U-box E3 ubiquitin ligase

Lodging is the process where crop plants fall over and lie on the ground due to strong winds and heavy precipitation. This problem reduces yield and increases the risk of fungal infections and pre-harvest germination. In order to avoid lodging, plant breeders utilize short-culm mutants, which often have a robust culm that can support the weight of a heavy spike. In barley (Hordeum vulgare L.), thousands of short-culm mutants have been isolated in breeding programs around the world. Our long-term goal is to reveal the genetic network underlying culm length, with the objective to provide an enlarged repertoire of genes and alleles suitable for future breeding of lodging resistant barley. In the present work we studied a group of allelic brh2 and ari-l mutants, which have a relatively strong semi-dwarf phenotype and are phenotypically similar to previously identified mutants deficient in brassinosteroid signalling or metabolism. The Brh2 gene is located in the centromeric region of chromosome 4H and we applied a candidate gene approach to identify the gene. Brh2 is orthologous to TUD1 in rice (Orysa sativa L.), which encodes a U-box E3 ubiquitin ligase. We identified one missense mutation, one nonsense mutation and four deletions of the complete Brh2 gene. The mutants could respond to exogenously applied brassinolide, which suggests that the apparent brassinosteroid deficient phenotype of barley brh2 and ari-l mutants is related to brassinosteroid metabolism rather than signalling.     

Fate of Cyclic Nucleotides in PC12 Cell Cultures: Uptake, Metabolism, and Effects of Metabolites on Nerve Growth Factor-Induced Neurite Outgrowth

The fate of cyclic AMP (cAMP), dibutyryl-cAMP (Bt2-cAMP), and the (Sp)-isomer of adenosine 3',5'-monophosphorothioate [(Sp)-cAMPS] was studied in the PC12 culture medium by means of HPLC. In the absence of PC12 cells, cAMP and Bt2-cAMP were rapidly degraded by nonspecific esterases and cyclic nucleotide phosphodiesterase both originating from the serum commonly used as a culture medium ingredient, whereas (Sp)-cAMPS was completely stable. Since 5'-AMP, adenosine, inosine, and hypoxanthine appeared in the culture medium after incubation with cAMP or Bt2-cAMP, we have determined their effect on nerve growth factor (NGF)-induced neurite outgrowth. 5'-AMP, adenosine, and inosine were indeed potent agents in producing a potentiating effect on NGF-induced early neurite outgrowth at a concentration of 1 mM. Thus, cAMP metabolites had the capacity to induce an effect that has been described as cAMP-specific. In serum-free culture medium and in the presence of cells, all cyclic nucleotides were taken up by PC12 cells. Uptake was highly correlated with the hydrophobic nature of the compounds, and was accompanied by a simultaneous excretion of metabolites. On incubation with cAMP, NGF had a pronounced effect on the metabolic pattern found in the culture medium. In particular, dephosphorylation of 5'-AMP was specifically enhanced. This effect of NGF on the degradation of cAMP was also apparent when cAMP metabolites were incubated with PC12 cells. Whereas 5'-AMP degradation was greatly increased, NGF had no effect on the metabolism of the other purine compounds.     

Hydrolysis of cyclic nucleotides by a purified cGMP-stimulated phosphodiesterase: structural requirements for hydrolysis

Hydrolysis of cyclic AMP and cyclic GMP analogues by a purified cGMP-stimulated phosphodiesterase from bovine adrenal tissue was investigated by reversed-phase HPLC. The results indicate that both a negative charge and an equatorial oxygen atom located at the cyclic phosphate residue are absolute requirements for the process of hydrolysis. Other substituents only gradually decreased the apparent hydrolytic activity. C-8-substituted derivatives were generally poor substrates due to the limited ability of these compounds to rotate freely around the glycosidic bond. While C-6- and 0-2'-substituted analogues carrying bulky substituents were also poorly hydrolysed, all other derivatives, including different C-2-, C-6-, 0-3'- and 0-5'-modified cyclic nucleotides, were good substrates. We consistently observed that cyclic GMP and cyclic GMP analogues were better hydrolysed than the corresponding cyclic AMP analogues. Hydrolysis was correlated with neither the hydrogen bond donor/acceptor abilities nor the hydrophobicity of selected cyclic nucleotide analogues. Based on quantum-chemical calculations of the size and direction of the dipole moments of different purine bases, we propose that the polarization of inducible amino acid side-chains within the binding site is involved in the differential binding of adenine-derived and guanine-derived nucleotides. However, the size of the dipole moment alone is not sufficient to explain the observed cGMP-preference. Rather, the direction of the polarization power relative to the other molecular structures involved in binding and hydrolysis seems to be the molecular mechanism by which the enzyme is able to discriminate between cAMP- and cGMP-like structures.