A density-dependent model of Cirsium vulgare population dynamics using field-estimated parameter values

Two versions of a stage-structured model of Cirsium vulgare population dynamics were developed. Both incorporated density dependence at one stage in the life cycle of the plant. In version 1 density dependence was assumed to operate during germination whilst in version 2 it was included at the seedling stage. Density-dependent parameter values for the model were estimated from annual census data in a factorial grazing experiment. Version 1 of the model produced significant estimates of density dependence under field conditions. The estimated values, when included in a simulation of the dynamics, produced two-point limit cycles under conditions of hard grazing. The limit cycles were most pronounced at the early rosette stage. Comparison of the effects of density dependence at the two different stages in the life cycle revealed a strong difference in predicted dynamics. This emphasizes the importance of determining where density dependence operates under field conditions and the potential problems of arbitrarily assigning it to particular life-history stages. Version 1 of the model produced a good prediction of observed mean plant density across the different grazing treatments (r ²=0.81, P<0.001).     

Evaluation of the lower protein limit in the budding yeast Saccharomyces cerevisiae using TIPI-gTOW

Background

Identifying permissible limits of intracellular parameters such as protein expression provides important information for examining robustness. In this study, we used the TEV protease-mediated induction of protein instability (TIPI) in combination with the genetic Tug-of-War (gTOW) to develop a method to measure the lower limit of protein level. We first tested the feasibility of this method using ADE2 as a marker and then analyzed some cell cycle regulators to reveal genetic interactions.

Results

Using TIPI-gTOW, we successfully constructed a strain in which GFP-^TDegFAde2 was expressed at the lower limit, just sufficient to support cellular growth under the -Ade condition by accelerating degradation by TEV protease. We also succeeded in constructing a strain in which the minimal level of GFP-^TDegFCdc20 was expressed by TIPI-gTOW. Using this strain, we studied genetic interactions between cell cycle regulators and CDC20, and the result was highly consistent with the previously identified interactions. Comparison of the experimental data with predictions of a mathematical model revealed some interactions that were not implemented into the current model.

Conclusions

TIPI-gTOW is useful for estimating changes in the lower limit of a protein under different conditions, such as different genetic backgrounds and environments. TIPI-gTOW is also useful for analyzing genetic interactions of essential genes whose deletion mutants cannot be obtained.     

Mitochondrial Colocalization with Ca2+ Release Sites is Crucial to Cardiac Metabolism

In cardiomyocyte subcellular structures, colocalization of mitochondria with Ca²⁺ release sites is implicated in regulation of cardiac energetics by facilitating Ca²⁺ influx into mitochondria to modulate the tricarboxylic acid (TCA) cycle. However, current experimental techniques limit detailed examination of this regulatory mechanism. Earlier, we developed a three-dimensional (3D) finite-element cardiomyocyte model featuring a subcellular structure that integrates excitation-contraction coupling and energy metabolism. Here, using this model, we examined the influence of distance between mitochondria and Ca²⁺ release sites by comparing a normal (50-nm) distance model and a large (200-nm) distance model (LD). The influence of distance was minimal under a low pacing rate (0.25 Hz), but under a higher pacing rate (2 Hz), lower levels of mitochondrial Ca²⁺ and NADH, elevated phosphate, and suppressed force generation became apparent in the LD model. Such differences became greater when functional impairments (reduced TCA cycle activity, uncoupling effect, and failing excitation-contraction coupling) were additionally imposed. We concluded that juxtaposition of the mitochondria and the Ca²⁺ release sites is crucial for rapid signal transmission to maintain cardiac-energy balance. The idealized 3D model of cardiac excitation-contraction and metabolism is a powerful tool to study cardiac energetics.     

A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle

Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular components and other regulators considered here. We validate the model by comparing our in silico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recovered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent consequence of the inherent characteristics of the regulatory logic proposed here. This dynamical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes.     

Multiple attractors and boundary crises in a tri-trophic food chain

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed also by relating them to their counterparts for a two-dimensional map which is invertible like the next-return map. In the global bifurcations two homoclinic or two heteroclinic orbits collide and disappear. In the food chain model two attractors coexist; a stable limit cycle where the top-predator is absent and an interior attractor. In addition there is a saddle cycle. The stable manifold of this limit cycle forms the basin boundary of the interior attractor. We will show that this boundary has a complicated structure when there are heteroclinic orbits from a saddle equilibrium to this saddle limit cycle. A homoclinic bifurcation to a saddle limit cycle will be associated with a boundary crisis where the chaotic attractor disappears suddenly when a bifurcation parameter is varied. Thus, similar to a tangent local bifurcation for equilibria or limit cycles, this homoclinic global bifurcation marks a region in the parameter space where the top-predator goes extinct. The 'Paradox of Enrichment' says that increasing the concentration of nutrient input can cause destabilization of the otherwise stable interior equilibrium of a bi-trophic food chain. For a tri-trophic food chain enrichment of the environment can even lead to extinction of the highest trophic level.     

State and Spectral Properties of Chloride Oscillations in Pollen

Pollen tube growth is a dynamic system expressing a number of oscillating circuits. Our recent work identified a new circuit, oscillatory efflux of Cl⁻ anion from the pollen tube apex. Cl⁻ efflux is the first ion signal found to be coupled in phase with growth oscillations. Functional analyses indicate an active role for Cl⁻ flux in pollen tube growth. In this report the dynamical properties of Cl⁻ efflux are examined. Phase space analysis demonstrates that the system trajectory converges on a limit cycle. Fourier analysis reveals that two harmonic frequencies characterize normal growth. Cl⁻ efflux is inhibited by the channel blocker DIDS, is stimulated by hypoosmotic treatment, and is antagonized by the signal encoded in inositol 3,4,5,6-tetrakisphosphate. These perturbations induce transitions of the limit cycle to new metastable states or cause system collapse to a static attractor centered near the origin. These perturbations also transform the spectral profile, inducing subharmonic frequencies, transitions to period doubling and tripling, superharmonic resonance, and chaos. These results indicate that Cl⁻ signals in pollen tubes display features that are characteristic of active oscillators that carry frequency-encoded information. A reaction network of the Cl⁻ oscillator coupled to two nonlinear feedback circuits that may drive pollen tube growth oscillations is considered.     

Factors limiting in time the induced pinocytotic response of amoeba proteus

The consumption of membrane reserves on the cell surface cannot be considered as universal factor limiting the pinocytotic cycle in time, because the postpinocytotic rosettes induced by heparin, Na⁺ or EDTA may immediately repeat pinocytosis under the influence of K⁺. Potassium may reactivate any postpinocytotic rosette and transform it into a smooth sphere not activable any more. The full membrane exploitation seems to be the ultimate limit reached only in high [K⁺]. In other inducers the pinocytosis stops earlier, probably when the cell membrane loses contact with the contractile cortical layer.     

Revised limit cycle oscillator model of human circadian pacemaker

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer's model has been replaced with a higher order limit cycle oscillator so that the system's amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer's model has been refined so that the peak sensitivity to light on the limit cycle now occurs approximately 4 h before the core body temperature minimum (CBTmin) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT,n now corresponds to 0.8 h after the minimum of x (x(min) in this refined model rather than to the exact timing of x(min) as in Kronauer's model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff's rule.     

Pathway of ammonia assimilation in illuminated Lemna minor

Plants of duckweed (Lemna minor) were grown under constant illumination and with a controlled supply of ammonium-N so as to maintain a constant low concentration. In two kinetic experiments (differing in illumination and N level) with ¹⁵N-ammonia, plants were periodically harvested and their free amino acids analysed for ¹⁵N abundance. Attempts were then made to fit the data by computer simulation models. Only models which had at least two or more intracellular compartments gave adequate fits. Two two-compartment models were tested fully. Both had in compartment 1 the glutamine synthetase-glutamate synthase cycle and in compartment 2 a second site of glutamine synthesis. In one model the glutamate for compartment 2 was derived by transport from compartment 1; in the second model it was synthesized from ammonia by glutamate dehydrogenase at a rate equivalent to 10% of the total N uptake. This second model was rejected after it was found that plants previously treated with methionine sulphoximine and aza-serine (inhibitors of the glutamate synthase cycle) were unable to incorporate ¹⁵N. In spite of wide differences in labelling pattern between the two experiments the first model gave acceptable fits to both when different pool sizes were allowed for. Operation of the glutamate synthase cycle was confirmed by the correspondence between model and data for labelling of glutamine amide, glutamine amino and glutamic acid. Consideration of enzyme distributions suggested that compartment 1 (the glutamate synthase system) is the chloroplasts and compartment 2 the cytosol. Analysis of asparagine and neutral amino acids made it possible to construct balance sheets for N uptake in the two experiments. They suggest that all glutamine synthesized in the chloroplast is used for glutamate and asparagine synthesis and that the cytosol enzyme meets the need of the cell for glutamine per se. The high turnover rates for asparagine indicate that this compound is an important intermediate even under steady state conditions, and carries between 20 and 50% of the products of N assimilation.     

A size dependent predator-prey interaction: who pursues whom?

We investigate the properties of an (age, size) -structured model for a population of Daphnia that feeds on a dynamical algal food source. The stability of the internal equilibrium is studied in detail and combined with numerical studies on the dynamics of the model to obtain insight in the relation between individual behaviour and population dynamical phenomena. Particularly the change in the (age, size)-relation with a change in the food availability seems to be an important behavioural mechanism that strongly influences the dynamics. This influence is partly stabilizing and partly destabilizing and leads to the coexistence of a stable equilibrium and a stable limit cycle or even coexistence of two stable limit cycles for the same parameter values. The oscillations in this case are characterized by drastic changes in the size-structure of the population during a cycle. In addition the model exhibits the usual predator-prey oscillations that characterize Lotka-Volterra models.     

On the Size of the DNA in the Mammalian Chromosome: Structural Subunits

Alkaline degradation of mammalian DNA indicates that the molecule exists in the chromosome as an array of structural subunits. The size of the subunit of single-stranded DNA is circa 5 × 10⁸ daltons, and it is of sufficient length to contain a number of synthetic units, replicons. The upper size limit of the multicomponent structure is in excess of 10¹⁰ daltons. Mammalian cells of three different origins have been shown to contain the same basic structural DNA components and these components exist throughout the cell cycle. The nature of the links between the subunits is not known.     

In vivo robustness analysis of cell division cycle genes in Saccharomyces cerevisiae

Intracellular biochemical parameters, such as the expression level of gene products, are considered to be optimized so that a biological system, including the parameters, works effectively. Those parameters should have some permissible range so that the systems have robustness against perturbations, such as noise in gene expression. However, little is known about the permissible range in real cells because there has been no experimental technique to test it. In this study, we developed a genetic screening method, named “genetic tug-of-war” (gTOW) that evaluates upper limit copy numbers of genes in a model eukaryote Saccharomyces cerevisiae, and we applied it for 30 cell-cycle related genes (CDC genes). The experiment provided unique quantitative data that could be used to argue the system-level properties of the cell cycle such as robustness and fragility. The data were used to evaluate the current computational model, and refinements to the model were suggested.     

A new mathematical approach to the metabolism of [14C]glucose, with applications to sensory ganglia of chicken embryos

Abstract— The available models of carbohydrate metabolism are not suitable for analysis of experiments on dorsal root ganglia of chicken embryos because they assume that certain products of the pentose cycle mix freely with those of glycolysis, which appears not to be true in this tissue, and because full isotopic equilibration, needed before the start of measurements, is not achieved while the excised ganglia are reasonably fresh. Therefore, new equations were developed which assume only a steady state of relevant metabolic intermediates and make use of the process of isotopic equilibration as a source of information. It is also assumed that an initially unknown but calculable fraction of the products of each pentose cycle re-enters the next cycle, the remainder leaking either to glycolysis or to the incubation medium. From measurements of the time course of output of labelled CO₂ in the presence of [1-¹⁴C]- and [6-¹⁴C]glucose and the incorporation and release in lactate of labelled C from [l-¹⁴C]glucose, the equations permit the estimation of many features of carbohydrate metabolism, such as the partitioning of material between the pentose cycle and glycolysis, the partitioning of CO₂ output between the pentose and citric acid cycles, the partitioning of the products of glycolysis between CO₂ and other destinations, such as lactate, and the degree of recycling from one pentose cycle into the next. In addition, the time course of labelled CO₂ output from [2-¹⁴C]glucose can be predicted; this, by comparison with the observed output, serves to support some variants of the basic model, while invalidating others. In dorsal root ganglia from 15-day chicken embryos, the assumption of a metabolic steady state was supported by a constant output of labelled CO² from [l-¹⁴C]glucose for 15 or more hours, except for the initial period of isotopic equilibration. By use of the new equations, it is concluded that in these ganglia (a) recycling in the pentose cycle can be 100% efficient in some incubation conditions, but not in others, (b) more CO₂ is released from the pentose cycle than from the citric acid cycle, (c) large, quantifiable differences exist between the utilization of the various carbon atoms of glucose, and (d) a pool of intermediates within the pentose cycle, with a time constant of about 1 h, explains a large delay observed in the output of C-6 of glucose into CO², which occurs with a time constant as long as 5 h under some conditions. Under conditions where recycling is complete in the pentose cycle, this cycle must operate in isolation from glycolysis, which would otherwise convert much of the output of the pentose cycle to lactate. This may explain the role of fructose-1,6-diphospha-tase in the tissue, without recourse to the oft-proposed, puzzling, and ATP-degrading‘futile cycle’between fructose-6-P and fructose-1,6-diP. It is proposed that the new equations may be suitable for similar analyses on some, but not all, other tissues.     

The oxidative TCA cycle operates during methanotrophic growth of the Type I methanotroph Methylomicrobium buryatense 5GB1

Methanotrophs are a group of bacteria that use methane as sole carbon and energy source. Type I methanotrophs are gamma-proteobacterial methanotrophs using the ribulose monophosphate cycle (RuMP) cycle for methane assimilation. In order to facilitate metabolic engineering in the industrially promising Type I methanotroph Methylomicrobium buryatense 5GB1, flux analysis of cellular metabolism is needed and ¹³C tracer analysis is a foundational tool for such work. This biological system has a single-carbon input and a special network topology that together pose challenges to the current well-established methodology for ¹³C tracer analysis using a multi-carbon input such as glucose, and to date, no ¹³C tracer analysis of flux in a Type I methanotroph has been reported. In this study, we showed that by monitoring labeling patterns of several key intermediate metabolites in core metabolism, it is possible to quantitate the relative flux ratios for important branch points, such as the malate node. In addition, it is possible to assess the operation of the TCA cycle, which has been thought to be incomplete in Type I methanotrophs. Surprisingly, our analysis provides direct evidence of a complete, oxidative TCA cycle operating in M. buryatense 5GB1 using methane as sole carbon and energy substrate, contributing about 45% of the total flux for de novo malate production. Combined with mutant analysis, this method was able to identify fumA (METBUDRAFT_1453/MBURv2__60244) as the primary fumarase involved in the oxidative TCA cycle, among 2 predicted fumarases, supported by ¹³C tracer analysis on both fumA and fumC single knockouts. Interrupting the oxidative TCA cycle leads to a severe growth defect, suggesting that the oxidative TCA cycle functions to not only provide precursors for de novo biomass synthesis, but also to provide reducing power to the system. This information provides new opportunities for metabolic engineering of M. buryatense for the production of industrially relevant products.     

The chacma baboon (<Emphasis Type="Italic">Papio</Emphasis><Emphasis Type="Italic">ursinus</Emphasis>) through time: a model of potential core habitat regions during a glacial–interglacial cycle

The aim of this research is to understand changes in the biogeography of the chacma baboon (Papio ursinus) through time, by modelling potential habitat changes through the last glacial–interglacial cycle (last interglacial, glacial maximum and current conditions). An environmental envelope model in a geographic information system is used to produce a range of habitat distribution models for the chacma baboon. Initially it is modelled as a single taxon, following which the data are further divided and explored to model predicted habitats for the chacma clades during different stages of the glacial–interglacial cycle. An area of approximately 1,044,000 km² was identified as potentially having been within the environmental core habitat at some stage of the glacial–interglacial cycle. Of this, 63,700 km² of land was predicted to have been core habitat regardless of the stage of the glacial–interglacial cycle. Additionally, rainfall appears to be the environmental variable with the most limiting effect on habitat size. This is true for the current, last glacial maximum and last interglacial environmental conditions. The largest area that remains within the core habitat throughout the last glacial–interglacial cycle is found in the northern provinces of South Africa. The chacma clades appear to interact in a cyclic pattern of expansion and contraction, each clade being more prominent under different environmental conditions. It appears that grey footed chacma habitat periodically extends northward towards the yellow baboon. These findings suggest dynamic and varied progression of the chacma baboon palaeo-distributions.     

Transient and steady state phase response curves of limit cycle oscillators

The experiment of phase shifts resulting from discrete perturbations of stable biological rhythms has been carried out to study entrainment behavior of oscillators. There are two kinds of phase response curves, which are measured in experiments, according to as one measures the phase shifts immediately or long after the perturbation. The former is the first transient phase response curve and the latter is the steady state phase response curve. We redefine both curves within the framework of dynamical system theory and homotopy theory. Several topological properties of both curves are clarified. Consequently, it is shown that we must compare the shapes of both two phase response curves to investigate the inner structures of biological oscillators. Moreover, we prove that a single limit cycle oscillator involving only two variables cannot simulate transient resetting behavior reported by Pittendrigh and Minis (1964). In other words, the circadian oscillator of Drosophila pseudoobscura does not consist of a single oscillator of two variables. Finally we show that a model which consists of two limit cycle oscillators is able to simulate qualitatively the phase response curves of Drosophila.     

p27Kip1 is required to maintain proliferative quiescence in the adult cochlea and pituitary

Cell cycle inhibitors, such as the cyclin-dependent kinase (Cdk) inhibitor proteins and retinoblastoma (Rb) family members, control exit from the cell cycle during the development of a variety of terminally differentiated tissues. It is unclear whether sustained expression of these proteins is required to prevent cell cycle re-entry in quiescent and terminally differentiated cells. The organ of Corti (cochlear sensory epithelium) and pars intermedia (intermediate lobe of the pituitary) are two tissues that share the characteristic of ongoing cell division in mice lacking either the p27^Kip1 Cdk inhibitor, Ink4 proteins or Rb. Here, we use tamoxifen-inducible mouse models to delete p27^Kip1 in postnatal animals and show this is sufficient to induce proliferation in both the organ of Corti and pars intermedia. Thus, these tissues remain sensitive to the presence of p27^Kip1 even after their developmental exit from the cell cycle. The neonatal cochlea displayed heightened sensitivity to changes in p27^Kip1 expression, with a proliferative response higher than that of constitutive null mice. In adults, the proliferative response was reduced but was accompanied by increased cell survival. In contrast, re-establishment of normal p27^Kip1 expression in animals with established pituitary tumors, in an inducible “knock-on” model, led to cessation of pituitary tumor growth, indicating the cells had maintained their susceptibility to p27-mediated growth suppression. Although restoration of p27^Kip1 did not induce apoptosis, it did lead to resolution of pathological features and normalization of gene expression. Our data underscore the importance of p27^Kip1 expression in the maintenance of cellular quiescence and terminal differentiation.Key words: proliferation, cell cycle, p27, Cdk inhibitor, auditory, cochlea, pituitary