Limit cycles in a chemostat model for a single species with age structure

We model an age-structured population feeding on an abiotic resource by combining the Gurtin-MacCamy [Math. Biosci. 43 (1979) 199] approach with a standard chemostat model. Limit cycles arise by Hopf bifurcations at low values of the chemostat dilution rate, even for simple maternity functions for which the original Gurtin-MacCamy model has no oscillatory solutions. We find the exact location in parameter space of the Hopf bifurcations for special cases of our model. The onset of cycling is largely independent of both the form of the resource uptake function and the shape of the maternity function.     

Dynamics of a biochemical system with multiple oscillatory domains as a clue for multiple modes of neuronal oscillations

We analyze the behavior of a two-variable biochemical model in conditions where it admits multiple oscillatory domains in parameter space. The model represents an autocatalytic enzyme reaction with input of substrate both from a constant source and from non-linear recycling of product into substrate. This system was previously studied for birhythmicity, i.e. the coexistence between two stable periodic regimes (Moran and Goldbeter 1984), and for multithreshold excitability (Moran and Goldbeter 1985). When two distinct oscillatory domains obtain as a function of the substrate injection rate, the system is capable of exhibiting two markedly different modes of oscillations for slightly different values of this control parameter. Phase plane analysis shows how the multiplicity of oscillatory domains depends on the parameters that govern the underlying biochemical mechanism of product recycling. We analyze the response of the model to various kinds of transient perturbations and to periodic changes in the substrate input that bring the system through the two ranges of oscillatory behavior. The results provide a qualitative explanation for experimental observations (Jahnsen and Llinas 1984b) related to the occurrence of two different modes of oscillations in thalamic neurones.     

Joint modelling of paired sparse functional data using principal components

We propose a modelling framework to study the relationship betweentwo paired longitudinally observed variables. The data for eachvariable are viewed as smooth curves measured at discrete time-pointsplus random errors. While the curves for each variable are summarizedusing a few important principal components, the associationof the two longitudinal variables is modelled through the associationof the principal component scores. We use penalized splinesto model the mean curves and the principal component curves,and cast the proposed model into a mixed-effects model frameworkfor model fitting, prediction and inference. The proposed methodcan be applied in the difficult case in which the measurementtimes are irregular and sparse and may differ widely acrossindividuals. Use of functional principal components enhancesmodel interpretation and improves statistical and numericalstability of the parameter estimates.     

Sensitivity of Resistance to Net Blotch in Barley

The aim of this study was to demonstrate various methods of analysing terminal net blotch, Pyrenophora teres Drechs. f. teres Smedeg., severity data from 15 spring barleys, Hordeum vulgare L., grown in Finnish official variety trials in five environments. The analyses have been developed and used principally by plant breeders for assessing crop yield, but lend themselves to use by plant pathologists. Pyrenophora teres is the major barley phytopathogen in Finland and improved resistance to it is sought. Joint regression analysis (JRA) and an additive main effects and multiplicative interaction (AMMI) model were used to investigate the data. Statistically significant genotype by environment (GE) interaction for resistance was indicated, and this included qualitative (crossover) interactions among genotypes over environments. A stable, non-sensitive, response to net blotch over environments, combined with a low mean score for terminal severity of the disease characterized the six-row barley 'Thule' which showed statistically significant crossover interaction only with 'Tyra'. 'Kustaa' exhibited the lowest mean terminal net blotch severity, but was relatively sensitive to net blotch. 'Arve' exhibited severe terminal net blotch in all environments, was relatively sensitive to environment and exhibited no crossover interaction with other genotypes. AMMI analysis appeared to represent a useful method for analysing these disease severity data, facilitating the selection of useful sources of resistance. Plots of AMMI-adjusted mean net blotch severities against first principal component axis (PCA) scores were informative for differentiating genotype response over environments, and are therefore potentially useful to plant pathologists and barley breeders seeking to gauge and subsequently improve the resistance status of barley to net blotch.     

Competing species model with behavioral adaptation

This paper studies the properties of a modified Lotka-Volterra model for two competing species, in which the coefficients of the interaction terms are time-dependent averages of the level of interaction over the entire past. For this model, it is shown that (1) competitive exclusion does not occur, (2) there are two possible stable equilibrium points, and (3) in a certain region of parameter space numerical simulations suggest the existence of interesting oscillatory solutions.     

Oscillatory isozymes as the simplest model for coupled biochemical oscillators

We analyze a simple model for two autocatalytic reactions catalyzed by two distinct isozymes transforming, with different kinetic properties, a given substrate into the same product. This two-variable system can be viewed as the simplest model of chemically coupled biochemical oscillators. Phase-plane analysis indicates how the kinetic differences between the two enzymes give rise to complex oscillatory phenomena such as the coexistence of a stable steady state and a stable limit cycle, or the co-existence of two simultaneously stable oscillatory regimes (birhythmicity). The model allows one to verify a previously proposed conjecture for the origin of birhythmicity. In other conditions, the system admits multiple oscillatory domains as a function of a control parameter whose variation gives rise to markedly different types of oscillations. The latter behavior provides an explanation for the occurrence of multiple modes of oscillations in thalamic neurons.     

Simulation of circadian rhythm generation in the suprachiasmatic nucleus with locally coupled self-sustained oscillators

In mammals, circadian rhythms are driven by a pacemaker located in the suprachiasmatic nuclei (SCN) of the anterior hypothalamus. The firing rate of neurons within the SCN exhibits a circadian rhythm. There is evidence that individual neurons within the SCN act as circadian oscillators. Rhythm generation in the SCN was therefore modeled by a system of self-sustained oscillators. The model is composed of up to 10000 oscillatory elements arranged in a square array. Each oscillator has its own (randomly determined) intrinsic period reflecting the widely dispersed periods observed in the SCN. The model behavior was investigated mainly in the absence of synchronizing zeitgebers. Due to local coupling the oscillators synchronized and an overall rhythm emerged. This indicates that a locally coupled system is capable of integrating the output of individual clock cells with widely dispersed periods. The period of the global output (average of all oscillators) corresponded to the average of the intrinsic periods and was stable even for small amplitudes and during transients. Noise, reflecting biological fluctuations at the cellular level, distorted the global rhythm in small arrays. The period of the rhythm could be stabilized by increasing the array size, which thus increased the robustness against noise. Since different regions of the SCN have separate output pathways, the array of oscillators was subdivided into four quadrants. Sudden deviations of periodicity sometimes appeared in one quadrant, while the periods of the other quadrants were largely unaffected. This result could represent a model for splitting, which has been observed in animal experiments. In summary, the multi-oscillator model of the SCN showed a broad repertoire of dynamic patterns, revealed a stable period (even during transients) with robustness against noise, and was able to account for such a complex physiological behavior as splitting.     

Modeling homeorhetic trajectories of milk component yields,body composition and dry-matter intake in dairy cows: Influence of parity,milk production potential and breed

The control of nutrient partitioning is complex and affected by many factors, among them physiological state and production potential. Therefore, the current model aims to provide for dairy cows a dynamic framework to predict a consistent set of reference performance patterns (milk component yields, body composition change, dry-matter intake) sensitive to physiological status across a range of milk production potentials (within and between breeds). Flows and partition of net energy toward maintenance, growth, gestation, body reserves and milk components are described in the model. The structure of the model is characterized by two sub-models, a regulating sub-model of homeorhetic control which sets dynamic partitioning rules along the lactation, and an operating sub-model that translates this into animal performance. The regulating sub-model describes lactation as the result of three driving forces: (1) use of previously acquired resources through mobilization, (2) acquisition of new resources with a priority of partition towards milk and (3) subsequent use of resources towards body reserves gain. The dynamics of these three driving forces were adjusted separately for fat (milk and body), protein (milk and body) and lactose (milk). Milk yield is predicted from lactose and protein yields with an empirical equation developed from literature data. The model predicts desired dry-matter intake as an outcome of net energy requirements for a given dietary net energy content. The parameters controlling milk component yields and body composition changes were calibrated using two data sets in which the diet was the same for all animals. Weekly data from Holstein dairy cows was used to calibrate the model within-breed across milk production potentials. A second data set was used to evaluate the model and to calibrate it for breed differences (Holstein, Danish Red and Jersey) on the mobilization/reconstitution of body composition and on the yield of individual milk components. These calibrations showed that the model framework was able to adequately simulate milk yield, milk component yields, body composition changes and dry-matter intake throughout lactation for primiparous and multiparous cows differing in their production level.     

Modeling the olfactory bulb and its neural oscillatory processings

The olfactory bulb of mammals aids in the discrimination of odors. A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations of the highly non-linear model produce a 35–60 Hz modulated activity which is coherent across the bulb. The decision states (for the odor information) in this system can be thought of as stable cycles, rather than point stable states typical of simpler neuro-computing models. Analysis shows that a group of coupled non-linear oscillators are responsible for the oscillatory activities. The output oscillation pattern of the bulb is determined by the odor input. The model provides a framework in which to understand the transform between odor input and the bulbar output to olfactory cortex. There is significant correspondence between the model behavior and observed electrophysiology.     

Oscillatory glucose flux in INS 1 pancreatic β cells: a self-referencing microbiosensor study

Signaling and insulin secretion in β cells have been reported to demonstrate oscillatory modes, with abnormal oscillations associated with type 2 diabetes. We investigated cellular glucose influx in β cells with a self-referencing (SR) microbiosensor based on nanomaterials with enhanced performance. Dose–response analyses with glucose and metabolic inhibition studies were used to study oscillatory patterns and transporter kinetics. For the first time, we report a stable and regular oscillatory uptake of glucose (averaged period 2.9 ± 0.6 min), which corresponds well with an oscillator model. This oscillatory behavior is part of the feedback control pathway involving oxygen, cytosolic Ca²⁺/ATP, and insulin secretion (periodicity approximately 3 min). Glucose stimulation experiments show that the net Michaelis–Menten constant (6.1 ± 1.5 mM) is in between GLUT2 and GLUT9. Phloretin inhibition experiments show an EC₅₀ value of 28 ± 1.6 μM phloretin for class I GLUT proteins and a concentration of 40 ± 0.6 μM phloretin caused maximum inhibition with residual nonoscillating flux, suggesting that the transporters not inhibited by phloretin are likely responsible for the remaining nonoscillatory uptake, and that impaired uptake via GLUT2 may be the cause of the oscillation loss in type 2 diabetes. Transporter studies using the SR microbiosensor will contribute to diabetes research and therapy development by exploring the nature of oscillatory transport mechanisms.     

An extended first approximation model for the amygdaloid kindling phenomenon

A first approximation model, which accounts for the strongest phenomena defining kindling is suggested. It is based on an excitatory-inhibitory coupling of neural aggregates, to which a self-stimulation element for the excitatory aggregate was added. The functional linking hypothesis views the representation of kindling as a process of gradual transition through structural changes from a stable system to a system showing stability for small perturbations and an oscillatory orbit for larger perturbations, to a purely oscillatory system. The anatomical linking hypothesis views the excitatory aggregate as representing the hypothalamus, the inhibitory aggregate as representing the hippocampal-septal-preoptic complex, and the selfstimulating element of the excitatory aggregate as representing the amygdaloid-pyriform complex. The model was realized on a digital computer with graphic capabilities and showed good qualitative agreement with the experimental data related to kindling. In addition, the use of the model for generating new experiments is discussed.     

中国薹草属黑穗薹草组的数量分类研究

对中国薹草属黑穗薹草组Sect.Racemosae及外类群冻原薹草组Sect.Frigidae共20种3变种采用38个形态特征进行了数量分类研究。聚类分析结果表明,黑穗薹草组应是一个自然分类群;支持了《中国植物志》将两对相似种：乌拉草（Carer meyeriana）与红原薹草（Carer hongyuanensis）、膨囊薹草（Carex lehmanii）与五台山薹草（Carex montis-wutaii）分别处理为种的观点。主成分分析结果表明,本组的分类特征较为稳定与集中,本组主成分分析散点图与聚类分析的分类结果大致吻合,并表明有关小坚果、果囊、鳞片、主茎叶和苞片的性状在本组的分类中起到了主要作用。     

A macroscopic approach to demography

A canonical/lognormal model for human demography is established, specifying the net maternity function and the age distribution for mothers of new-borns using a single macroscopic parameter vector of dimension five. The age distribution of mothers is canonical, while the net maternity function normalizes to a lognormal density. Comparison of an actual population with the model serves to identify anomalies in the population which may be indicative of phase transitions or influences from levels outside the demographic. Tracking the time development of the parameter vector may be used to predict the future state of a population, or to interpolate for data missing from the record. In accordance with classical theoretical considerations of Backman, Prigogine, et al., it emerges that the logarithm of a mothers age is the most fundamental time variable for demographic purposes.     

Oscillations in plant membrane transport: model predictions, experimental validation, and physiological implications

Although oscillations in membrane-transport activity are ubiquitous in plants, the ionic mechanisms of ultradian oscillations in plant cells remain largely unknown, despite much phenomenological data. The physiological role of such oscillations is also the subject of much speculation. Over the last decade, much experimental evidence showing oscillations in net ion fluxes across the plasma membrane of plant cells has been accumulated using the non-invasive MIFE technique. In this study, a recently proposed feedback-controlled oscillatory model was used. The model adequately describes the observed ion flux oscillations within the minute range of periods and predicts: (i) strong dependence of the period of oscillations on the rate constants for the H+ pump; (ii) a substantial phase shift between oscillations in net H+ and K+ fluxes; (iii) cessation of oscillations when H+ pump activity is suppressed; (iv) the existence of some 'window' of external temperatures and ionic concentrations, where non-damped oscillations are observed: outside this range, even small changes in external parameters lead to progressive damping and aperiodic behaviour; (v) frequency encoding of environmental information by oscillatory patterns; and (vi) strong dependence of oscillatory characteristics on cell size. All these predictions were successfully confirmed by direct experimental observations, when net ion fluxes were measured from root and leaf tissues of various plant species, or from single cells. Because oscillatory behaviour is inherent in feedback control systems having phase shifts, it is argued from this model that suitable conditions will allow oscillations in any cell or tissue. The possible physiological role of such oscillations is discussed in the context of plant adaptive responses to salinity, temperature, osmotic, hypoxia, and pH stresses.     

A Mathematical Model of Uterine Dynamics and its Application to Human Parturition

We have developed a simple mathematical model with three physiologically significant states to describe the changes in intrauterine pressure associated with a contraction during human parturition. The myometrium is modelled as a set of smooth muscle cells, each of which is in one of three states (quiescent, contracted, refractory) at a given time. These states are occupied according to a cycle governed by three temporal parameters. The solutions of the equations describing the model show an oscillatory behavior for particular values of these parameters, which is very similar to the time dependant development of intrauterine pressure during labor. Due to its non-linear terms, our model could lead to chaotic oscillations (in the mathematical sense), whose clinical counterpart may occur in cases of dystocia. Despite its simplicity, this model appears to be a useful guide to further investigations of the oscillatory behavior of the myometrium, or other smooth muscles, in normal and pathological situations.     

Study of Spectral Response Characteristics of Oilseed Rape (<i>Brassica napus</i>) to Particulate Matters Based on Hyper-Spectral Technique

Haze is mainly caused by the suspended particulate matters in the air, of which the particulate matters pollution harms leaf vegetables. In this paper, oilseed rapes at four different growing periods were investigated in a simulated particulate pollution environment. In combination of hyper-spectral technology and micro examination, the response of hyper-spectral characteristics of the leaf to particulate matters was investigated in-depth. The hyperspectral, chlorophyll content, net photosynthetic rate and stomatal conductance of leaf were obtained. The deposition and adsorption of particulate matters on the leaf were observed by Environmental Scanning Electron Microscope (ESEM). Normalized difference vegetation index (NDVI), modified red edge normalized (mNDVI705) and modified red edge simple ratio index (mSR705) were selected as characteristic parameters and the range of 510 nm~620 nm as the sensitive band. 16 methods were used to establish the physiological information inversion model. The main results were as follows: Under the influence of particulate matters, the spectral reflectance decreased as a whole. With the increase of leaf age, the phenomenon of blue shift aggravated. The amplitude of yellow and blue edge decreased with overall decreasing vegetation indices. The furrows and irregular band protrusions in leaves were favorable for keeping particulate matters. With longer affecting time and more deposition of particle matters on the leaf, the stomatal opening became smaller. After comparing, principal component regression (PCR) + multiple scatter correction (MSC) + second derivative (SD) + Savitzky-Golay smooth (SG), and partial least square (PLS) + multiple scatter correction (MSC) + first derivative (FD) + Savitzky-Golay smooth (SG) were determined the best method to establish the inversion model of chlorophyll content and net photosynthetic rate respectively. This study may bring novel ideas for the diagnosis and analysis of the physiological response of leaf vegetables under particulate matters pollution using hyper-spectral technology.     

Spiking neural network model for memorizing sequences with forward and backward recall

We present an oscillatory network of conductance based spiking neurons of Hodgkin–Huxley type as a model of memory storage and retrieval of sequences of events (or objects). The model is inspired by psychological and neurobiological evidence on sequential memories. The building block of the model is an oscillatory module which contains excitatory and inhibitory neurons with all-to-all connections. The connection architecture comprises two layers. A lower layer represents consecutive events during their storage and recall. This layer is composed of oscillatory modules. Plastic excitatory connections between the modules are implemented using an STDP type learning rule for sequential storage. Excitatory neurons in the upper layer project star-like modifiable connections toward the excitatory lower layer neurons. These neurons in the upper layer are used to tag sequences of events represented in the lower layer. Computer simulations demonstrate good performance of the model including difficult cases when different sequences contain overlapping events. We show that the model with STDP type or anti-STDP type learning rules can be applied for the simulation of forward and backward replay of neural spikes respectively.     

Behavioural responses in a net restraint test predict interrenal reactivity in Arctic charr Salvelinus alpinus

In this study, a 1 min net restraint test was evaluated as a method to predict stress‐coping style in Arctic charr Salvelinus alpinus, by investigating the relationship between behaviour during the test and levels of plasma cortisol sampled after 30 min confinement. In two separate groups of S. alpinus, general linearized model revealed significant correlations between cortisol levels and principal component scores extracted from principal component analysis, combining measures of activity in the tests. With the use of glmulti, the model selection ruled out any effects of size, sex and order of capture on interrenal reactivity. In general, S. alpinus that were more active in the net restraint test also had low levels of circulating cortisol, suggesting a proactive coping style. The results from two repeated runs were not correlated, but both runs, performed eight days apart, show a negative correlation between post‐stress cortisol level and activity in the net. The lack of consistency could be explained by different treatments before each run and individual differences in behavioural plasticity. The net restraint test is thus predictive of stress‐coping style in S. alpinus, and has the benefit of being less time‐consuming than the commonly used confinement stress test.     

Parameterization and prediction of community interaction models using stable-state assumptions and computational techniques: an example from the high rocky intertidal

Many ecological communities exist in a stable state where, if undisturbed, no net change will occur in the populations or in the interactions between the component parts of the system. In this paper we present computational methods (evolutionary algorithms and random searches) to parameterize mathematical models that describe communities in stable states. The initial parameterization of the model requires only "best guess" estimates for parameters and can therefore be used in data-poor situations. The technique locates the stable state that occurs with minimum deviation from these parameters. Alternative stable states in which the community may exist after a disturbance event can also be assessed using this technique, even though the number of alternative states may be large. Using available but incomplete data from an intertidal grazer/biofilm community, we created a prediction of the dynamics of both a pre- and post-disturbance community. Using limited data, we then predicted the most likely post-disturbance community, which proved to be a good match to experimental data, indicating the usefulness of this technique as a predictive tool.     

Relationship of net chloride flow across the human erythrocyte membrane to the anion exchange mechanism

The parallel effects of the anion transport inhibitor DIDS (4,4'- diisothiocyanostilbene-2,2'-disulfonate) on net chloride flow and on chloride exchange suggest that a major portion of net chloride flow takes place through the anion exchange system. The "slippage" model postulates that the rate of net anion flow is determined by the movement of the unloaded anion transport site across the membrane. Both the halide selectivity of net anion flow and the dependence of net chloride flux on chloride concentration over the range of 75 to 300 mM are inconsistent with the slippage model. Models in which the divalent form of the anion exchange carrier or water pores mediate net anion flow are also inconsistent with the data. The observations that net chloride flux increases with chloride concentration and that the DIDS- sensitive component tends to saturate suggest a model in which net anion flow involves "transit" of anions through the diffusion barriers in series with the transport site, without any change in transport site conformation such as normally occurs during the anion exchange process. This model is successful in predicting that the anion exchange inhibitor NAP-taurine, which binds to the modifier site and inhibits the conformational change, has less effect on net chloride flow than on chloride exchange.