Stability patterns and trophic structure in a Delaware Bay plankton community.

Using qualitative loop analysis we have extended our examination of a Delaware Bay plankton community to include an investigation of the roles played by the various entities (population, guild or nutrient) in the community. In an entity removal exercise, we used stability relationships as a probe into community structure. Six types of stability change are possible as a result of entity removal from the system: stable to stable (s-->s); stable to unstable (s-->u); stable to disconnected (s-->d); unstable to stable (u-->s); unstable to unstable (u-->u); unstable to disconnected (u-->d). Using these changes as an investigative tool, we found that in order to account for the stability-instability patterns, it was necessary to construct a refined trophic structure model. The observed connections between the entities in the larger model could be grouped into two different types of stability substructures: a simple pattern and a more complex branching pattern. These patterns map easily onto the refined trophic structure model. Using stability analysis it is also possible to model community structure in ways other than the traditional trophic approach. Patterns of system necessity and relative contribution to stability are observed. These patterns match the refined trophic structure model derived previously. The roles that the various entities play in the overall community were followed over an annual cycle. Entities were seen to change their roles as a function of time and status within a subgroup. These results show that stability determinations have the potential to be used as a valuable tool in community analysis.     

Ligand binding with continuous modification of binding sites

Simultaneous formulation binding and structure modification of the binding site leads to binding process that can be analyzed within the framework of the non-linear theory of dynamic systems. Such an approach allows us to obtain several properties of the binding center: plurality of stationary (stable and unstable) states at binding, recognition of bistable and hysteretic binding modes. It is also shown that adsorption centre deformation leads to a S-shaped adsorption curve.     

A mathematical model for the population of giant pandas and bamboo in Yele Nature Reserve of Xiangling Mountains

We describe an improved mathematical model for the relationship between the population of giant pandas (Ailuropoda melanoleuca) and bamboo (Bashania spanostachya) developed by Smith (1979) and Yuan et al. (1989), by adding a correction term which takes into account the effect of a sudden collapse of bamboo as a food source. The values for the co-efficients were based on field data collected in 1994 and 1995 in Yele Nature Reserve (Mianning county, Sichuan Province). The model reflects the dynamic relationship between giant pandas and bamboo in Xiangling Mountains. It is more realistic than earlier models. The density dependent co-efficient for bamboo in the model, Parameter a, decides whether the positive equilibrium point B is a stable or an unstable focus as a changes. The branching value a₀ exists in a very narrow interval. The fundamental structure of the phase graph of the model changes significantly and one stable limit cycle is obtained.     

相岭山系冕宁冶勒自然保护区大熊猫-竹子种群数学模型的研究

本文对袁重桂、张洪德(1990)提出的大熊猫-竹子种群的数学模型做了较大的改进,加入了修正项(m-x2)y2/km得到新模型x=rx-ix-αx2-cy,y=by-dy-ey2-(m-x)y2/km其中的生命系数是作者在冕宁县冶勒自然保护区作实际资料收集统计得来的;并将α作为参数,当改变参数α时,正平衡点B是稳定的焦点或是不稳定的焦点;分支值α0存在于一个很小的区间,模型的相图的基本结构发生了较大的变化,出现了一个稳定的极限环。     

Hydrodynamics of arterial branching--the effect of arterial branching on distal blood supply

A study was conducted to investigate the hydrodynamics of branching flow in relation to the blood supply to the basal part of the brain. A series of measurements of the branching loss-coefficients under laminar steady flow were conducted using model branches with various geometries, and the effect of branching on blood supply to distal areas was described using a lumped-parameter model of the vascular structure. It was revealed that in the blood circulation, branching loss is important where a small artery divides off with a large branching angle from a large trunk. It was also indicated that the effect of such branching on the distal blood supply might become more significant when the peripheral resistance is reduced, thereby increasing the blood velocity in the trunk.     

Prey dispersal and predator persistence

To understand how patchiness influences population dynamics of a tri-trophic interaction, a tractable model is formulated in terms of differential equations. Motivated by the structure of systems such as plants, phytophagous mites and predatory mites, the model takes dispersal into account at the middle trophic level. The effect of dispersal for the middle level in a tri-trophic system could be either stabilising or destabilising since the middle level acts both as prey and as predator. First a simple model with logistic growth for the lowest level is formulated. A model with logistic growth for the lowest level and instantaneous dispersal has a globally stable three-species equilibrium, if this equilibrium exists. Addition of a middle level dispersal phase of non-negligible duration influences equilibrium stability. In the absence of the top trophic level a limit cycle can occur, caused by the delay that exists in the reaction of the middle level to the changes in the lowest level. With low predator efficiency, it is also possible to have an unstable three-species equilibrium. So addition of a middle level dispersal phase of non-negligible duration can work destabilising. Next the persistence of the third trophic level is studied. Even when the three-species equilibrium exists, the third trophic level need not be persistent. A two-species limit cycle can keep its stability when a three-species equilibrium exists; the system is then bistable. It is argued that such a bistability can offer an alternative explanation for pesticide-induced outbreaks of spider mites and failure of predator introduction.     

Electrical Bistability of the Motoneuronal Dendritic Membrane Determined by Non-inactivating Inward Currents: a Model Study

We investigated features of the spatial pattern of electrical bistable states of dendrites using a computer model of an abducens motoneuron with the dendritic branching reconstructed in detail. The dendritic membrane has an N-shaped current-voltage relation (I-V curve) determined mainly by the presence of L-type calcium channels. Such channels, according to indirect experimental data, are present in the dendrites of these cells together with glutamatergic NMDA-type channels also capable of determining electrical bistability of the membrane and the corresponding specific patterns of electrical activity generated by such neurons. For our model, we obtained steady-state local I-V curves and transferred spatial distribution maps of the membrane potential difference (surface density of transmembrane currents), as well as increments of the axial dendritic current, to three-dimensional images of the reconstructed branching dendrites. The latter increments determine the contribution of a dendritic site in general axial current delivering the charge to the trigger zone of a neuron. The simulation results showed that incorporation of non-inactivating calcium channels into dendritic membrane leads to the origination of a pattern of spatial distribution of bistable electrical states in the dendrites, which were not described earlier. Such features are most important under conditions of a stable state of high depolarization of the relevant parts of the dendrites. In this case, the respective feature was the existence of a zone of maximum density of the inward transmembrane current, which covers areas of first-order branching of all dendrites. Since the greatest relative contribution to the total current belongs to the inward calcium current, the above zone of first branchings can be considered a “hot spot” zone characterized by increased entry of Ca²⁺. This may have important functional consequences for local intracellular calcium signaling.     

Multiple stable recurrent outbreaks and predictability in seasonally forced nonlinear epidemic models

A seasonally forced nonlinear SEIR epidemic model is used to simulate small and large amplitude periodic outbreaks. The model is shown to exhibit bistable behavior for a fixed set of parameters. Basins of attraction for each recurrent outbreak are computed, and it is shown that the basins of two coexisting stable outbreaks are intertwined in a complicated manner. The effect of such a basin structure is shown to result in an obstruction in predicting asymptotically the type of outbreak given an uncertainty in the initial population of susceptibles and infectives.     

Bistable nerve conduction

It has been demonstrated experimentally that slow and fast conduction waves with distinct conduction velocities can occur in the same nerve system depending on the strength or the form of the stimulus, which give rise to two modes of nerve functions. However, the mechanisms remain to be elucidated. In this study, we use computer simulations of the cable equation with modified Hodgkin-Huxley kinetics and analytical solutions of a simplified model to show that stimulus-dependent slow and fast waves recapitulating the experimental observations can occur in the cable, which are the two stable conduction states of a bistable conduction behavior. The bistable conduction is caused by a positive feedback loop of the wavefront upstroke speed, mediated by the sodium channel inactivation properties. Although the occurrence of bistable conduction only requires the presence of the sodium current, adding a calcium current to the model further promotes bistable conduction by potentiating the slow wave. We also show that the bistable conduction is robust, occurring for sodium and calcium activation thresholds well within the experimentally determined ones of the known sodium and calcium channel families. Since bistable conduction can occur in the cable equation of Hodgkin-Huxley kinetics with a single inward current, i.e., the sodium current, it can be a generic mechanism applicable to stimulus-dependent fast and slow conduction not only in the nerve systems but also in other electrically excitable systems, such as cardiac muscles.     

Genetic and Enzymatic Experiments Relating to the Tertiary Structure of β-Galactosidase

Fifty-six amber mutations of the β-galactosidase gene of Escherichia coli were suppressed by crossing into a stock containing the supD suppressor gene. The resultant enzymes, differing only in the position of the inserted serine, were tested for stability at 57 C. Most of the suppressed enzymes were either as stable to heat as the normal enzyme or very unstable. Tests of enzymes produced by the action of other suppressors showed that the degree of stability was characteristic of a particular position in the polypeptide chain of the amino acid substitution and independent of the amino acid inserted. The mutations were placed in linear order in the gene by deletion mapping and three-point linkage tests. The consequent order of the serine substitutions disclosed an alternating pattern of stable and unstable regions over the amino-terminal two-thirds of the enzyme; the carboxy-terminal third of the enzyme was generally unstable. Considerations of coding relations and enzyme structure suggested that serine and glutamine suppression usually result in a change in the hydrophilic nature of the side chains on the outside of the enzyme molecule. It was shown that the potentially unstable regions of the enzyme are probably not indicative of stretches of α-helix or of sites of association. The apparent position of the substrate binding sites was correlated with the location of some of the potentially unstable regions, which may mark the parts of the polypeptide chain in proximity with the substrate.     

Similarities and gradients in growth unit branching patterns during ontogeny in "Fuji" apple trees: a stochastic approach

This study aims to explore and model the changes in growth unit (GU) branching patterns during tree ontogeny. The question was addressed in apple trees cv. "Fuji", by analysing the relative impact of GU length and within-tree position. The development of two 6-year-old trees was recorded over 6 years. The fate of axillary buds along each GU was represented as a sequence of symbols corresponding to five types of lateral growth: latent buds, short, medium, long, and floral lateral GUs. Based on an exploratory analysis of data and a priori hypotheses, a hidden semi-Markov chain was estimated from all of these GU sequences. This model was composed of six transient states representing successive branching zones along the GUs. The accuracy of this global model was a posteriori assessed by fitting the characteristic distributions computed from model parameters to the corresponding empirical characteristic distributions extracted from the observed sequences. The observed sequences were then grouped hierarchically according to the GU length, year of growth, and branching order. Comparing model parameters between these sub-groups revealed similarities between GUs. These similarities were based on particular branching zones whose composition and relative position within the GUs remained invariant across the subgroups: the latent zones, floral zone, and short-lateral zone. The probability of occurrence of the floral zone varied with the year, showing the alternate fruiting of "Fuji". It is shown that, during tree ontogeny, as GU length decreases, branching patterns tend to progressively simplify due to the disappearance of the most central zones and a progressive reduction in the length of the floral zone.     

Prediction of N-linked glycan branching patterns using artificial neural networks

A model was developed for novel prediction of N-linked glycan branching pattern classification for CHO-derived N-linked glycoproteins. The model consists of 30 independent recurrent neural networks and uses predicted quantities of secondary structure elements and residue solvent accessibility as an input vector. The model was designed to predict the major component of a heterogeneous mixture of CHO-derived glycoforms of a recombinant protein under normal growth conditions. Resulting glycosylation prediction is classified as either complex-type or high mannose. The incorporation of predicted quantities in the input vector allowed for theoretical mutant N-linked glycan branching predictions without initial experimental analysis of protein structures. Primary amino acid sequence data were effectively eliminated from the input vector space based on neural network prediction analyses. This provided further evidence that localized protein secondary structure elements and conformational structure may play more important roles in determining glycan branching patterns than does the primary sequence of a polypeptide. A confidence interval parameter was incorporated into the model to enable identification of false predictions. The model was further tested using published experimental results for mutants of the tissue-type plasminogen activator protein [J. Wilhelm, S.G. Lee, N.K. Kalyan, S.M. Cheng, F. Wiener, W. Pierzchala, P.P. Hung, Alterations in the domain structure of tissue-type plasminogen activator change the nature of asparagine glycosylation. Biotechnology (N.Y.) 8 (1990) 321-325].     

Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed.     

A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree

A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree extending Rall's equivalent cylinder model is presented. It is obtained from a combination of cable theory with the continuum approach. Replacing the fine structure of the branching dendrites by an equivalent, conductive medium characterized by averaged electrical parameters, the one-dimensional cable equations with spatially varying parameters are derived. While these equations can be solved in general only numerically, we were able to formulate a general branching condition (comprising Rall's 3/2 power relationship as a special case) under which analytical solutions can be deduced from those of the equivalent cylinder model. This model allows dendritic trees with a greater variety of branching patterns than before to be analytically treated.     

An application of a general branching process in the study of the genetics of aging.

A general branching process model is developed to analyse familial dependence in longevity data. A general formula for the survival function of a randomly chosen sibling of an individual of a specified age is derived. The branching process model takes into account that siblings' ages may be censored. This is applied to a data set consisting of lifelengths of siblings of centenarians. Age distributions used in the branching process model are estimated from US Census data from the relevant period. It is demonstrated that there is a marked difference in the survival function according to the formula assuming no familial effect and the empirical survival function estimated from the data; thus, indicating a strong familial component.     

Branching enzyme assay: selective quantitation of the alpha 1,6-linked glucosyl residues involved in the branching points

Methods previously described for glycogen or amylopectin branching enzymatic activity are insufficiently sensitive and not quantitative. A new, more sensitive, specific, and quantitative one was developed. It is based upon the quantitation of the glucose residues joined by alpha 1,6 bonds introduced by varying amounts of branching enzyme. The procedure involved the synthesis of a polysaccharide from Glc-1-P and phosphorylase in the presence of the sample to be tested. The branched polysaccharide was then purified and the glucoses involved in the branching points were quantitated after degradation with phosphorylase and debranching enzymes. This method appeared to be useful, not only in enzymatic activity determinations but also in the study of the structure of alpha-D-glucans when combined with those of total polysaccharide quantitation, such as iodine and phenol-sulfuric acid.     

Consequences of root growth kinetics and vascular structure on the distribution of lateral roots

It has been proposed that the acropetal initiation of lateral roots is a built‐in process specified as part of the general process of cell division and differentiation in the parent root tip. Conversely, it is commonly reported that root branching is essentially a variable feature. In the present study, the interlateral distance along the parent root has been investigated using three banana varieties (Musa spp.) grown in two substrates. The pattern of lateral root initiation was obscured by variations of root growth patterns and vascular structure among roots, genotypes and substrates. A framework model is formulated showing the influence of growth pattern and vascular structure on branching density. The model raises a distinction between growth components which should not affect the branching density (i.e. rate of cell division) and which may affect it (i.e. size of mature cells and number of transverse divisions performed by cells executing their trajectory in the meristem). It appears also that lateral root density and root growth rate might be independently modulated by appropriate changes of root growth patterns, in banana and presumably many other taxa.     

Unstable chromosome sites and evolutionary rearrangements in akodont rodents (Cricetidae)

Evolutionary rearrangements producing changes in chromosome 1 of Akodon molinae were traced by comparing the G banding patterns of the karyotypes from six species of akodont rodents. It was possible to subdivide chromosome 1 of A. molinae into unstable and stable regions. Most of the spontaneous rearrangements of chromosome 1 appearing in passages 116-128 of a continuous line of A. molinae cells (AKm line) occurred in the unstable regions which comprise repetitive DNA sequences favouring the setting up of heteroduplexes leading to rearrangements. When AKm cells were irradiated with UV light it was observed that unstable regions of chromosome 1 showed higher rates of unscheduled DNA synthesis (UD) than stable areas. A differential degree of condensation making certain regions of the chromatin fibril more accessible to repair enzymes or a better target for damage, is probably the cause of the variable response to UV light, and perhaps to most clastogenic agents (including those responsible for spontaneous rearrangements). Thus, the distribution of repetitive DNA sequences, the structure of the chromatin fibril and the efficiency of the DNA repair machinery may be important factors in the origin of spontaneous chromosomal rearrangements.     

Spatial patterns in benthic invertebrate community structure: products of habitat stability or are they habitat specific?

1. The effects of habitat stability on benthic invertebrate community structure were examined at eleven sites (ten streams and a wind-swept lake shore) with similar physicochemical characteristics but differing stability. 2. Habitat characteristics were assessed to place the study sites within the framework of the disturbance-productivity-diversity model, the intermediate disturbance hypothesis and a variant of the habitat templet model to examine their predictions with respect to community structure. 3. Many of the most common invertebrate species were present at all the study site, although their relative abundance and density differed markedly between sites. Thus, while stability did not appear to affect colonization of the study sites by these taxa, it did affect their relative success. 4. Communities at unstable sites were very similar and shared a number of taxa such as Deleatidium, Austrosimulium and several species of chironomid, presumably well-adapted to surviving and recolonizing after flood events. 5. Communities at the stable sites differed markedly, both from each other and the group of unstable sites. The characteristic fauna at each of the stable sites seemed to be a result of the site's intrinsic character and possibly biotic interactions. 6. Although stability was a pervading influence on community structure, acting as a bottleneck to the development of a site-specific suite of taxa, none of the above models could adequately explain the observed patterns.     

Comparative Analysis of Ultradian and Circadian Behavioural Rhythms for Diagnosis of Biorhythmic State of Animals

A chronobiological procedure has been developed for evaluation of living conditions, behaviour and internal state of free-ranging animals. It is based on continuous recordings of activity and feeding with subsequent comparison of levels, daily patterns as well as daily and ultradian rhythms. Telemetric observations were carried out on alpaca, sheep, Przewalski horse, roe deer, red deer and mouflon under various conditions. The time patterns of the different species were analysed macroscopically and by autocorrelation function and power spectral analysis. A stable ultradian structure of behaviour was obvious especially for ruminants. A more unstable, adaptive time pattern was found in Przewalski horses. Activity as a multi-purpose behaviour was generally more variable than feeding which in most cases was of clearly rhythmic and harmonic structure. Degrees of Functional Couplings (DFCs) were used for comparison of rhythmic structure. DFCs express the percentage of the circadian component and harmonic ultradian components in relation to all rhythmic components of a spectrum. They were found to be high in well adapted, healthy and undisturbed individuals but were lowered during periods of adaptation, sickness or social interactions.