On a Class of Deterministic Population Models with Stochastic Foundation

Generalising a site-based stochastic model due to Royama, Solé et al. and Sumpter et al., we investigate competition in a single species with discrete, non-overlapping generations. We show that the deterministic limit of the dynamics depends on a few easily interpretable parameters only. Further, we discuss qualitative properties and limit sets of the corresponding difference equations, and we relate these to modes of competition. Moreover, a detailed analysis of stochastic effects in some relevant scenarios indicates that the behaviour of the stochastic model is very sensitive to further details of the model.     

Mechanochemical Phosphorylation and Solubilisation of β-D-Glucan from Yeast Saccharomyces cerevisiae and Its Biological Activities

To obtain a water-soluble β-D-glucan derivative cleanly and conveniently, a highly efficient mechanochemical method, planetary ball milling, was used to phosphorylate β-D-glucan isolated from yeast Saccharomyces cerevisiae in solid state. Soluble β-D-glucan phosphate (GP) with a high degree of substitution (0.77–2.09) and an apparent PEAK molecular weight of 6.6–10.0 kDa was produced when β-D-glucan was co-milled with sodium hexametaphosphate at 139.5–186.0 rad/s for 12–20 min. The energy transferred was 3.03–11.98 KJ/g. The phosphorylation of GPs was demonstrated by Fourier transform infrared spectroscopy and ¹³C and ³¹P Nuclear magnetic resonance spectroscopy. Three GP products with different degree of substitution (DS) and degree of polymerisation (DP) were able to upregulate the functional events mediated by activated murine macrophage RAW264.7 cells, among which GP-2 with a DS of 1.24 and DP of 30.5 exerted the highest immunostimulating activity. Our results indicate that mechanochemical processing is an efficient method for preparing water-soluble and biologically active GP with high DS.     

On the Evolution of the Timing of Reproduction with Non-equilibrium Resident Dynamics

We study the evolution of an individual’s reproductive strategy in a mechanistic modeling framework. We assume that the total number of juveniles one adult individual can produce is a finite constant, and we study how this number should be distributed during the season, given the types of inter-individual interactions and mortality processes included in the model. The evolution of the timing of reproduction in this modeling framework has already been studied earlier in the case of equilibrium resident dynamics, but we generalize the situation to also fluctuating population dynamics. We find that, as in the equilibrium case, the presence or absence of inter-juvenile aggression affects the functional form of the evolutionarily stable reproductive strategy. If an ESS exists, it can have an absolutely continuous part only if inter-juvenile aggression is included in the model. If inter-juvenile aggression is not included in the model, an ESS can have no continuous parts, and only Dirac measures are possible.     

Theoretical Analysis of Time-to-Peak Responses in Biological Reaction Networks

Processing of information by signaling networks is characterized by properties of the induced kinetics of the activated pathway components. The maximal extent of pathway activation (maximum amplitude) and the time-to-peak-response (position) are key determinants of biological responses that have been linked to specific outcomes. We investigate how the maximum amplitude of pathway activation and its position depend on the input and wiring of a signaling network. For this purpose, we consider a simple reaction A→B that is regulated by a transient input and extended this to include back-reaction and additional partners. In particular, we show that a unique maximum of B(t) exists. Moreover, we prove that the position of the maximum is independent of the applied input but regulated by degradation reactions of B. Indeed, the time-to-peak-response decreases with increasing degradation rate, which we prove for small models and show in simulations for more complex ones. The identified dependencies provide insights into design principles that facilitate the realization dynamical characteristics like constant position of maximal pathway activation and thereby guide the characterization of unknown kinetics within larger protein networks.     

Effects of Whaling on the Structure of the Southern Ocean Food Web: Insights on the “Krill Surplus” from Ecosystem Modelling

The aim of this study was to examine the ecological plausibility of the “krill surplus” hypothesis and the effects of whaling on the Southern Ocean food web using mass-balance ecosystem modelling. The depletion trajectory and unexploited biomass of each rorqual population in the Antarctic was reconstructed using yearly catch records and a set of species-specific surplus production models. The resulting estimates of the unexploited biomass of Antarctic rorquals were used to construct an Ecopath model of the Southern Ocean food web existing in 1900. The rorqual depletion trajectory was then used in an Ecosim scenario to drive rorqual biomasses and examine the “krill surplus” phenomenon and whaling effects on the food web in the years 1900–2008. An additional suite of Ecosim scenarios reflecting several hypothetical trends in Southern Ocean primary productivity were employed to examine the effect of bottom-up forcing on the documented krill biomass trend. The output of the Ecosim scenarios indicated that while the “krill surplus” hypothesis is a plausible explanation of the biomass trends observed in some penguin and pinniped species in the mid-20^th century, the excess krill biomass was most likely eliminated by a rapid decline in primary productivity in the years 1975–1995. Our findings suggest that changes in physical conditions in the Southern Ocean during this time period could have eliminated the ecological effects of rorqual depletion, although the mechanism responsible is currently unknown. Furthermore, a decline in iron bioavailability due to rorqual depletion may have contributed to the rapid decline in overall Southern Ocean productivity during the last quarter of the 20^th century. The results of this study underscore the need for further research on historical changes in the roles of top-down and bottom-up forcing in structuring the Southern Ocean food web.     

Interactions Between the Immune System and Cancer: A Brief Review of Non-spatial Mathematical Models

We briefly review spatially homogeneous mechanistic mathematical models describing the interactions between a malignant tumor and the immune system. We begin with the simplest (single equation) models for tumor growth and proceed to consider greater immunological detail (and correspondingly more equations) in steps. This approach allows us to clarify the necessity for expanding the complexity of models in order to capture the biological mechanisms we wish to understand. We conclude by discussing some unsolved problems in the mathematical modeling of cancer-immune system interactions.     

Concurrence of Danish Dementia and Cataract: Insights from the Interactions of Dementia Associated Peptides with Eye Lens α-Crystallin

Familial Danish Dementia (FDD) is an autosomal disease, which is distinguished by gradual loss of vision, deafness, progressive ataxia and dementia. Cataract is the first manifestation of the disease. In this article, we demonstrate a specific correlation between the poisoning of the chaperone activity of the rat eye lens α-crystallins, loss of lens transparency in organ culture by the pathogenic form of the Danish dementia peptide, i.e. the reduced Danish dementia peptide (redADan peptide), by a combination of ex vivo, in vitro, biophysical and biochemical techniques. The interaction of redADan peptide and lens crystallins are very specific when compared with another chaperone, HSP-70, underscoring the specificity of the pathogenic form of Danish dementia peptide, redADan, for the early onset of cataract in this disease.     

Influence of Polyols on the Stability and Kinetic Parameters of Invertase from Candida utilis: Correlation with the Conformational Stability and Activity

Invertase (β-d-fructofuranoside fructohydrolase-E.C. 3.2.1.26) is a sucrose hydrolyzing enzyme found in microbial, plant and animal sources. Invertase from Candida utilis is a dimeric glycoprotein composed of two identical monomer subunits with an apparent molecular mass of 150 kDa. We investigated the mechanism of stabilization of invertase with polyols (glycerol, xylitol, and sorbitol). Activity, thermodynamic and kinetic measurements of invertase were performed as a function of polyol concentration and showed that polyols act as very effective stabilizing agents. The result from the solvent-invertase interaction shows preferential exclusion of the polyols from the protein domain leading to preferential hydration of protein. Apparent thermal denaturation temperature of the protein (T _m ) rose from 75 °C to a maximum of 85 °C in 30% glycerol. The stabilization has been attributed to the preferential hydration of the enzyme.     

On the Trails of the Proteasome Fold: Structural and Functional Analysis of the Ancestral β-Subunit Protein Anbu

The 20S proteasome is a key player in eukaryotic and archaeal protein degradation, but its progenitor in eubacteria is unknown. Recently, the ancestral β-subunit protein (Anbu) was predicted to be the evolutionary precursor of the proteasome. We crystallized Anbu from Hyphomicrobium sp. strain MC1 in four different space groups and solved the structures by SAD-phasing and Patterson search calculation techniques. Our data reveal that Anbu adopts the classical fold of Ntn-hydrolases, but its oligomeric state differs from that of barrel-shaped proteases. In contrast to their typical architecture, the Anbu protomer is a tightly interacting dimer that can assemble into a helical superstructure. Although Anbu features a catalytic triad of Thr1O^γ, Asp17O^δ1 and Lys32N^ε, it is unable to hydrolyze standard protease substrates. The lack of activity might be caused by the incapacity of Thr1NH₂ to function as a Brønsted acid during substrate cleavage due to its missing activation via hydrogen bonding. Altogether, we demonstrate that the topology of the proteasomal fold is conserved in Anbu, but whether it acts as a protease still needs to be clarified.     

Parameter Sensitivity Analysis of Stochastic Models Provides Insights into?Cardiac Calcium Sparks

We present a parameter sensitivity analysis method that is appropriate for stochastic models, and we demonstrate how this analysis generates experimentally testable predictions about the factors that influence local Ca²⁺ release in heart cells. The method involves randomly varying all parameters, running a single simulation with each set of parameters, running simulations with hundreds of model variants, then statistically relating the parameters to the simulation results using regression methods. We tested this method on a stochastic model, containing 18 parameters, of the cardiac Ca²⁺ spark. Results show that multivariable linear regression can successfully relate parameters to continuous model outputs such as Ca²⁺ spark amplitude and duration, and multivariable logistic regression can provide insight into how parameters affect Ca²⁺ spark triggering (a probabilistic process that is all-or-none in a single simulation). Benchmark studies demonstrate that this method is less computationally intensive than standard methods by a factor of 16. Importantly, predictions were tested experimentally by measuring Ca²⁺ sparks in mice with knockout of the sarcoplasmic reticulum protein triadin. These mice exhibit multiple changes in Ca²⁺ release unit structures, and the regression model both accurately predicts changes in Ca²⁺ spark amplitude (30% decrease in model, 29% decrease in experiments) and provides an intuitive and quantitative understanding of how much each alteration contributes to the result. This approach is therefore an effective, efficient, and predictive method for analyzing stochastic mathematical models to gain biological insight.     

Insights into the Aggregation Mechanism of PolyQ Proteins with Different Glutamine Repeat Lengths

Polyglutamine (polyQ) diseases, including Huntington’s disease, result from the aggregation of an abnormally expanded polyQ repeat in the affected protein. The length of the polyQ repeat is essential for the disease’s onset; however, the molecular mechanism of polyQ aggregation is still poorly understood. Controlled conditions and initiation of the aggregation process are prerequisites for the detection of transient intermediate states. We present an attenuated total reflection Fourier-transform infrared spectroscopic approach combined with protein immobilization to study polyQ aggregation dependent on the polyQ length. PolyQ proteins were engineered mimicking the mammalian N-terminus fragment of the Huntingtin protein and containing a polyQ sequence with the number of glutamines below (Q11), close to (Q38), and above (Q56) the disease threshold. A monolayer of the polyQ construct was chemically immobilized on the internal reflection element of the attenuated total reflection cell, and the aggregation was initiated via enzymatic cleavage. Structural changes of the polyQ sequence were monitored by time-resolved infrared difference spectroscopy. We observed faster aggregation kinetics for the longer sequences, and furthermore, we could distinguish β-structured intermediates for the different constructs, allowing us to propose aggregation mechanisms dependent on the repeat length. Q11 forms a β-structured aggregate by intermolecular interaction of stretched monomers, whereas Q38 and Q56 undergo conformational changes to various β-structured intermediates, including intramolecular β-sheets.     

Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey

Invasive species are a significant cause of bio-diversity loss particularly in island ecosystems. It has been suggested to release pathogenic parasites as an efficient control measure of these mostly immune-naïve populations. In order to explore the potential impacts of such bio-control approach, we construct and investigate mathematical models describing disease dynamics in a host population that acts as a predator embedded in a simple food chain. The consequences of Feline Immunodeficiency Virus (FIV) introduction into a closed ecosystem are addressed using a bi-trophic system, comprising an indigenous prey (birds) and an introduced predator (cats). Our results show that FIV is unlikely to fully eradicate cats on sub-Antarctic islands, but it can be efficient in depressing their population size, allowing for the recovery of the endangered prey. Depending on the ecological setting and disease transmission mode (we consider proportionate mixing as well as mass action), successful pathogen invasion can induce population oscillations that are not possible in the disease-free predator–prey system. These fluctuations can be seen as a mixed blessing from a management point of view. On the one hand, they may increase the extinction risk of the birds. On the other hand, they provide an opportunity to eradicate cats more easily in combination with other methods such as trapping or culling.     

Breastfeeding and Its Prospective Association with Components of the GH-IGF-Axis,Insulin Resistance and Body Adiposity Measures in Young Adulthood – Insights from Linear and Quantile Regression Analysis

Background

Breastfeeding may lower chronic disease risk by long-term effects on hormonal status and adiposity, but the relations remain uncertain.

Objective

To prospectively investigate the association of breastfeeding with the growth hormone- (GH) insulin-like growth factor- (IGF) axis, insulin sensitivity, body composition and body fat distribution in younger adulthood (18–37 years).

Design

Data from 233 (54% female) participants of a German cohort, the Dortmund Nutritional and Anthropometric Longitudinally Designed (DONALD) Study, with prospective data on infant feeding were analyzed. Multivariable linear as well as quantile regression were performed with full breastfeeding (not: ≤2, short: 3–17, long: >17 weeks) as exposure and adult IGF-I, IGF binding proteins (IGFBP) -1, -2, -3, homeostasis model assessment of insulin resistance (HOMA-IR), fat mass index, fat-free mass index, and waist circumference as outcomes.

Results

After adjustment for early life and socio-economic factors, women who had been breastfed longer displayed higher adult IGFBP-2 (p_trend = 0.02) and lower values of HOMA-IR (p_trend = 0.004). Furthermore, in women breastfeeding duration was associated with a lower mean fat mass index (p_trend = 0.01), fat-free mass index (p_trend = 0.02) and waist circumference (p_trend = 0.004) in young adulthood. However, there was no relation to IGF-I, IGFBP-1 and IGFBP-3 (all p_trend>0.05). Associations for IGFBP-2 and fat mass index were more pronounced at higher, for waist circumference at very low or high percentiles of the distribution. In men, there was no consistent relation of breastfeeding with any outcome.

Conclusions

Our data suggest that breastfeeding may have long-term, favorable effects on extremes of adiposity and insulin metabolism in women, but not in men. In both sexes, breastfeeding does not seem to induce programming of the GH-IGF-axis.