Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.     

Factors controlling planktonic size spectral responses to autumnal circulation in a Mediterranean lake

1. Studies of planktonic size spectra have been common in recent years, but few concerning the effects of autumnal lake processes on those distributions have been reported. We carried out such a study for 93 days during early circulation in a small, mesotrophic, seepage lake with only benthivorous fish. Two distinct mixing periods occurred before full circulation in Las Madres lake (Spain). As a proxy of overall planktonic‐ and phytoplanktonic size distributions, the shape of a Pareto I power function was traced over time. The phytoplanktonic size spectrum was also used to test the hypothesis that phytoplankton might show a trophic cascade during early circulation. 2. Our results demonstrated that the overall size spectrum changed smoothly during the autumnal mixing, with sequential changes controlled by a combination of biotic and abiotic variables, albeit experiencing different temporal delays, always shorter than a week. A first combined, autogenic process, driven both by algal competition and a crustacean trophic effect, and a second physical‐forcing process, driven by the combined effect of convective cooling and decreasing irradiance on mixed layer dynamics, may be related to the overall planktonic spectrum in the first and second periods of mixing, respectively. 3. The phytoplanktonic size spectrum did not appear to be dictated by a trophic cascade in Las Madres lake, their dynamics being mostly controlled by physical forcing, along with some effect of non‐edible primary producers and cladocerans in the first and second periods of mixing, respectively. 4. Our results and others covering early circulation with longer sampling periods suggest that planktonic size spectral dynamics during lake circulation is context‐dependent (i.e. varying from one lake to another), thus preventing generalisation. However, when further studies with finer temporal resolution have been carried out, it is likely that clear‐cut patterns in the planktonic size spectrum will emerge, arising from the interplay of autogenic plankton dynamics, implying some resistance to community change because of external physical forcing, and the velocity of autumnal mixing.     

Importance of intermediate disturbances for the species composition and diversity of phytoplankton in two very different Berlin lakes

Species composition and diversity of phytoplankton were studied for several years in two lakes which differ with respect to mixing conditions and nutrient limitation: Schlachtensee regularly stratifies very stably. In contrast, size and wind-exposure predispose Lake Tegel to deeper mixing; additionally, stratification is artificially destabilized by aeration. As the duration of aeration was varied, the study period includes interannual changes in mixing conditions. For both lakes, it also covers trophic change due to restoration; this was especially pronounced in Schlachtensee.Results show that mixing conditions affect species composition on two levels: on a superordinate level, lake morphology or hydrology govern stability of stratification and susceptibility to perturbation, and hence the extent to which motile species can develop. In Schlachtensee, species with some means of actively seeking preferred depths usually dominated during summer stratification: Planktothrix agardhii during the hypertrophic phase, and flagellates since restoration. In contrast, in Lake Tegel deeper mixing as a generally prevailing condition favored non-motile species. Their seasonal pattern was remarkably constant from year to year. Although changes in the extent of mixing were pronounced during the four years studied (1987–1990), these were within a range that affected species composition only slightly: in summer, cyanobacteria and diatoms represented climax species whose dominance was not offset by additional, weather-induced increases of turbulence.On a subordinate level, and within the constraints set by nutrient limitation as well as by grazing pressure, small-scale changes in mixing conditions caused by meteorological cycles were shown to strongly affect species composition and in consequence diversity: Results for the fouryear post-restoration study period at Schlachtensee show that considerable interannual variations of species composition and diversity can be attributed to variations in the frequency of meteorological changes. In accordance with the intermediate disturbance hypothesis (IDH), diversity was lowest during 1989, the year with the longest and most pronounced cycles of fair weather (14 to 27 fair days on end). However, the mechanism for this was rarely a decline of diversity caused by competitive exclusion within single long phases of stable conditions, as conceived by the intermediate disturbance hypothesis. Instead, diversity responded to changes in mixing conditions with a variety of patterns — often with low values during phases of increased mixing and with high values under quiescent conditions, especially during the first calm days just after increased mixing. Thus, not disturbance as such, but rather the rate of change between phases of disturbance and quiescence appears to determine the frequency of high diversity indices.In Lake Tegel, high diversity indices were somewhat more frequent in 1989, the year during which thermal stratification was most stable. For species adapted to frequent or continuous mixing, interjected calm phases with unusually high stability of thermal stratification may represent a disturbance of accustomed conditions. Thus, in turbulent Lake Tegel, meteorological cycles appear to act in reversal to the IDH, in a sense which may be termed intermediate quiescence hypothesis.Phosphorus limitation due to successful restoration was found to decrease winter and vernal diversity in Schlachtensee. Presumably, without nutrient constraints, new populations could grow more rapidly in response to the rapid changes of physical parameters during this season. In contrast, restoration has increased summer diversity, as phosphorus concentrations no longer allow the virtual monocultures of Planktothrix agardhii which prevailed previously. In Lake Tegel, the reduction of phosphorus concentration down to 60 µg/l P in 1989 limited biomass, but this level was still too high to significantly alter species composition or diversity.     

Behavioural evidence that magnetic field effects in the land snail,Cepaea nemoralis,might not depend on magnetite or induced electric currents

Although extremely low frequency (ELF) magnetic fields (<300 Hz) appear to exert a variety of biological effects, the magnetic field sensing/transduction mechanism(s) remains to be established. Here, using the inhibitory effects of magnetic fields on endogenous opioid peptide-mediated “analgaesic” response of the land snail. Cepaea nemoralis, we addressed the mechanism(s) of action of ELF magnetic fields. Indirect mechanisms involving both induced electric fields and direct magnetic field detection mechanisms (e.g., magnetite, parametric resonance) were evaluated. Snails were exposed to a static magnetic field (B_DC=78±1 μT) and to a 60 Hz magnetic field (B_AC=299±1 μT peak) with the angle between the static and 60 Hz magnetic fields varied in eight steps between 0° and 90°. At 0° and 90°, the magnetic field reduced opioid-induced analgaesia by approximately 20%, and this inhibition was increased to a maximum of 50% when the angle was between 50° and 70°. Because B_AC was fixed in amplitude, direction, and frequency, any induced electric currents would be constant independent of the B_AC/B_DC angle. Also, an energy transduction mechanism involving magnetite should show greatest sensitivity at 90°. Therefore, the energy transduction mechanism probably does not involve induced electric currents or magnetite. Rather, our results suggest a direct magnetic field detection mechanism consistent with the parametric resonance model proposed by Lednev. © 1996 Wiley-Liss, Inc.     

Late Holocene climate change and human impact recorded in a south Swedish ombrotrophic peat bog

A peat core from a raised bog in southern Sweden was examined (plant macrofossils, pollen/non-pollen microfossils, colorimetric humification, carbon/nitrogen ratios, bulk densities, loss on ignition) to investigate the effects of climate change and human impact on the plant species composition and carbon accumulation of the peat forming vegetation. ¹⁴C wiggle-match dating was applied for fine-resolution dating. Cooling at the start of the Little Ice Age was reflected by a decline of thermophilous trees from the pollen record between ca. cal AD 1275–1590, coinciding with increases in atmospheric Δ¹⁴C pointing to decreases of solar activity (Wolf and Spörer minimum). Human impact also decreased. Later, the effect of human impact was clearly visible in the form of a black brown, decomposed peat layer, the top of which marks a gap of more than 300 years. Artificial drainage probably caused secondary decomposition and oxidation of the peat. From ca. cal AD 1960 the water table of the peat bog was restored following construction of a road and raised bog vegetation regenerated.     

Structural Stability of a Stage Structured Model of Fish: The Case of the Anchovy (<Emphasis Type="Italic">Engraulis Encrasicolus L</Emphasis>.) in the Bay of Biscay

A study of stage structured model of fish population is presented. This model focuse on the anchovy population in the Bay of Biscay (Engraulis encrasicolus L.) is presented. The method of study is based on an intermediate complexity mathematical model, taking into account the spatialisation, the environmental conditions and the stage-structure of the fishes. First, to test the model, we show mathematical properties, such as unicity of the solution of structural stability. Then we provide numerical simulations, to validate the model and to test the dynamics according to the variations of the parameters.     

A Temporal Mechanism for Generating the Phase Precession of Hippocampal Place Cells

The phase relationship between the activity of hippocampal place cells and the hippocampal theta rhythm systematically precesses as the animal runs through the region in an environment called the place field of the cell. We present a minimal biophysical model of the phase precession of place cells in region CA3 of the hippocampus. The model describes the dynamics of two coupled point neurons—namely, a pyramidal cell and an interneuron, the latter of which is driven by a pacemaker input. Outside of the place field, the network displays a stable, background firing pattern that is locked to the theta rhythm. The pacemaker input drives the interneuron, which in turn activates the pyramidal cell. A single stimulus to the pyramidal cell from the dentate gyrus, simulating entrance into the place field, reorganizes the functional roles of the cells in the network for a number of cycles of the theta rhythm. In the reorganized network, the pyramidal cell drives the interneuron at a higher frequency than the theta frequency, thus causing a systematic precession relative to the theta input. The frequency of the pyramidal cell can vary to account for changes in the animal's running speed. The transient dynamics end after up to 360 degrees of phase precession when the pacemaker input to the interneuron occurs at a phase to return the network to the stable background firing pattern, thus signaling the end of the place field. Our model, in contrast to others, reports that phase precession is a temporally, and not spatially, controlled process. We also predict that like pyramidal cells, interneurons phase precess. Our model provides a mechanism for shutting off place cell firing after the animal has crossed the place field, and it explains the observed nearly 360 degrees of phase precession. We also describe how this model is consistent with a proposed autoassociative memory role of the CA3 region.     

The structural identifiability of the susceptible infected recovered model with seasonal forcing

In this paper, it is shown that the SIR epidemic model, with the force of infection subject to seasonal variation, and a proportion of either the prevalence or the incidence measured, is unidentifiable unless certain key system parameters are known, or measurable. This means that an uncountable number of different parameter vectors can, theoretically, give rise to the same idealised output data. Any subsequent parameter estimation from real data must be viewed with little confidence as a result. The approach adopted for the structural identifiability analysis utilises the existence of an infinitely differentiable transformation that connects the state trajectories corresponding to parameter vectors that give rise to identical output data. When this approach proves computationally intractable, it is possible to use the converse idea that the existence of a coordinate transformation between states for particular parameter vectors implies indistinguishability between these vectors from the corresponding model outputs.     

A model for seasonal phytoplankton blooms

We analyse a generic bottom-up nutrient phytoplankton model to help understand the dynamics of seasonally recurring algae blooms. The deterministic model displays a wide spectrum of dynamical behaviours, from simple cyclical blooms which trigger annually, to irregular chaotic blooms in which both the time between outbreaks and their magnitudes are erratic. Unusually, despite the persistent seasonal forcing, it is extremely difficult to generate blooms that are both annually recurring and also chaotic or irregular (i.e. in amplitude) even though this characterizes many real time-series. Instead the model has a tendency to 'skip' with outbreaks often being suppressed from 1 year to the next. This behaviour is studied in detail and we develop analytical expressions to describe the model's flow in phase space, yielding insights into the mechanism of the bloom recurrence. We also discuss how modifications to the equations through the inclusion of appropriate functional forms can generate more realistic dynamics.     

Continuous and discrete extreme climatic events affecting the dynamics of a high-arctic reindeer population

Climate at northern latitudes are currently changing both with regard to the mean and the temporal variability at any given site, increasing the frequency of extreme events such as cold and warm spells. Here we use a conceptually new modelling approach with two different dynamic terms of the climatic effects on a Svalbard reindeer population (the Brøggerhalvøya population) which underwent an extreme icing event (“locked pastures”) with 80% reduction in population size during one winter (1993/94). One term captures the continuous and linear effect depending upon the Arctic Oscillation and another the discrete (rare) “event” process. The introduction of an “event” parameter describing the discrete extreme winter resulted in a more parsimonious model. Such an approach may be useful in strongly age-structured ungulate populations, with young and very old individuals being particularly prone to mortality factors during adverse conditions (resulting in a population structure that differs before and after extreme climatic events). A simulation study demonstrates that our approach is able to properly detect the ecological effects of such extreme climate events.