Modeling of glycolytic wave propagation in an open spatial reactor with inhomogeneous substrate influx

The spatio-temporal dynamics of traveling waves in glycolysis as it occurs in yeast extract have been studied, both theoretically and experimentally. We describe this phenomenon with the distributed Selkov model that accounts for the reactions of phosphofructokinase, which is a key enzyme of the glycolytic reaction cascade. To describe the experimentally observed phase waves in an open spatial reactor we introduce a non-homogeneous flux of substrate in the model. The experimental observation that waves can change their direction of propagation during the experiment is considered in the model. The mechanism for such a change in wave direction is discussed.     

Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

Ecological correlates of population density and behavior in the circumtropical black triggerfish Melichthys niger (Balistidae)

The remarkable swarming of black triggerfish Melichthys niger (Balistidae) on oceanic islands led us to undertake a comparative ecological study of high-density and low-density populations of this unusual circumtropical species. Abundance, distribution, and aggressive encounters were recorded in the field from the high-density Johnston Atoll (JA) population, the low-density Belize (BE) population, and a local high-density aggregation from Puerto Rico (PR). JA and PR populations of M. niger occurred at significantly higher densities and were more aggregated than in BE. Intraspecific aggression (chases/min/fish) was an order of magnitude higher in BE than in JA, while interspecific aggression was similar among sites. Size frequency, growth rate, diet composition, body condition (liver-somatic index LSI) were assessed from collected specimens. JA grew more slowly than BE as determined by back-calculations from dorsal spine rings, suggesting density-dependent growth limitation. Size frequency analysis reflected this difference with significantly more large fish in the BE sample. Maximum age of triggerfish in both populations was estimated at 11 years, and 35–40% of growth occurred in the first year. Diet composition was similar in all three locations and indicated broad omnivory. Percent organic composition of gut contents (food quality measure) and LSI (body condition assay) were both significantly higher in the PR population, but no difference was detected between JA and BE. An increase in consumption of algae on the degraded PR reef may explain this pattern.     

Disease transmission models with density-dependent demographics

The models considered for the spread of an infectious disease in a population are of SIRS or SIS type with a standard incidence expression. The varying population size is described by a modification of the logistic differential equation which includes a term for disease-related deaths. The models have density-dependent restricted growth due to a decreasing birth rate and an increasing death rate as the population size increases towards its carrying capacity. Thresholds, equilibria and stability are determined for the systems of ordinary differential equations for each model. The persistence of the infectious disease and disease-related deaths can lead to a new equilibrium population size below the carrying capacity and can even cause the population to become extinct.Research supported in part by Centers for Disease Control contract 200-87-0515     

Differential survival of Venus gallina and Scapharca inaequivalvis during anoxic stress: Covalent modification of phosphofructokinase and glycogen phosphorylase during anoxia

Summary Biochemical mechanisms underlying anaerobiosis were assessed in two Mediterranean bivalve species, Scapharca inaequivalvis and Venus gallina, with widely differing tolerances for oxygen lack. These species displayed LT₅₀ values for anoxic survival at 17–18°C of 17 and 4 d, respectively. Succinate and alanine were the major products of 24 h anaerobic metabolism in both species but only S. inaequivalvis further metabolized succinate to propionate. Both species reduced metabolic rate while anoxic but metabolic arrest was more pronounced in S. inaequivalvis. Calculated ATP turnover rate (MATP) during exposure to N₂-bubbled seawater was only 4.51% of the aerobic rate in S. inaequivalvis but was 12.68% in V. gallina. To counteract a greater load of acid end products, V. gallina foot showed a significantly greater buffering capacity, 23.38±0.20 slykes, compared to 19.6±0.79 slykes in S. inaequivalvis. The two species also differed distinctly in the enzymatic regulation of anaerobiosis. In V. gallina anoxia exposure caused only a small change in PFK kinetic parameters (a decrease in K_a AMP) and had no effect on glycogen phosphorylase. By contrast, S. inaequivalvis foot showed a strong modification of enzyme properties in anoxia. The percentage of glycogen phosphorylase in the a form dropped significantly only in S. inaequivalvis. Other changes included alterations in the properties of PFK leading to a less active enzyme form in anoxia. Compared to the aerobic enzyme form, PFK from anoxic foot showed a reduced affinity for fructose-6-P (K_m increased 2.4-fold), greater inhibition by ATP (I₅₀ decreased 6.8-fold), and an increase in sensitivity to AMP activation (K_a decreased by 50%). These enzyme changes appear to be key to a glycolytic rate depression during anaerobiosis in S. inaequivalvis foot muscle.Abbreviations EDTA ethylenediaminetetraacetic acid - EGTA ethyleneglycol-bis-(2-aminoethyl)-tetraacetic acid - Fructose-2,6-P ₂ fructose-2,6-bisphosphate - Fructose-6-P fructose-6-phosphate - K _a AMP Activation constant (concentration of AMP required to increase the reaction to twice the rate it shows in the absence of AMP) - MATP ATP turnover rate - P _i inorganic phosphate - PCA Perchloric acid - PFK 6-phosphofructo-1-kinase - TCA Trichloroacetic acid     

Allelopathy as a competitive strategy in persistent thickets of Lantana camara L. in three Australian forest communities

Field experiments were established to assess possible allelopathic suppression by Lantana camara L. of two indigenous tree species. The design allowed comparison of allelopathic effects with density-dependent resource competition effects. Fire and its role in competitive interactions was included as an experimental treatment. Allelopathic responses were measured in L. camara thickets by germinating and growing Alectryon subcinereus (A. Gray) Radlk. in dry rainforest ecotones (Macleay River) or Cryptocarya rigida (Meissner) in warm temperate rainforest and wet sclerophyll forest (Lake Macquarie) at 10, 20 and 30 seedlings m^-2, where L. camara was either physically removed (LR), burnt (LB), or cut and left in place (LT). Germination for both species increased significantly by completely removing L. camara (LR) whereas burning (LB) was significant only for C. rigida. Seedling growth for both species was negatively related to increasing density when all L. camara was removed (LR) but was positively related in the other two treatments (LB and LT). C. rigida seedling biomass increased 47.4% (1.75%2.58 g) and 68.6% (1.98%2.95 g) with increasing seedling density for LT and LB respectively and decreased 23.2% (2.93–2.25 g) for LR. A. subcinereus seedling biomass increased 29.7% (1.95–2.53 g) and 34.7% (2.25–3.03 g) with increasing seedling density for LT and LB respectively and decreased 27.9% (3.30–2.38 g) for LR. Phytotoxin dilution effects were inferred in LT and LB rather than density-dependent intraspecific competition, whereas the reverse was true for LR. Seedling biomass for C. rigida resulting from potential phytotoxin dilution at high seedling density was not significantly different from the response of LR at low seedling density but, for A. subcinereus, the phytotoxin dilution response was significantly less than LR at low seedling density. Moderately intense fire (LB) was not significantly different from the LT treatment at both locations, emphasising that moderate to low intensity fires should not be used to control existing invasions of L. camara. Competitive strategies for invasive populations are identified that may modify succession following disturbance, thereby allowing thicket formation and long-term persistence to affect community dynamics. Such strategies need to be recognised in managing natural communities, particularly for biodiversity conservation.Nomenclature: Harden (1990).     

Population size dependent incidence in models for diseases without immunity

Epidemiological models of SIS type are analyzed to determine the thresholds, equilibria, and stability. The incidence term in these models has a contact rate which depends on the total population size. The demographic structures considered are recruitment-death, generalized logistic, decay and growth. The persistence of the disease combined with disease-related deaths and reduced reproduction of infectives can greatly affect the population dynamics. For example, it can cause the population size to decrease to zero or to a new size below its carrying capacity or it can decrease the exponential growth rate constant of the population.     

Feeding by larvae of Hypoatherina tropicalis (Pisces: Atherinidae) and its relation to prey availability in One Tree Lagoon,Great Barrier Reef,Australia

Synopsis Feeding of and food availability for larvae of Hypoatherina tropicalis were investigated in One Tree Lagoon, Great Barrier Reef, Australia, during November 1981 and January 1982. These surface-dwelling larvae and their microzooplankton prey were sampled as near to simultaneously as possible on 12 occasions during the daytime. Larvae of all sizes (5–17 mm SL) fed successfully over the observed range of mean prey densities (12–235 per liter), and the overall feeding incidence was 98.9%. Larger larvae consumed greater numbers and more categories of prey than did smaller larvae. Larvae selected copepods of all sizes, and nauplii, gastropods, bivalves, and foraminiferans that were greater than 75 ¢s mm in width. Tintinnids (mostly 37–74 µm in width) were generally avoided by larvae, but were occasionally important in the diets when they constituted more than 60% of the total available prey, regardless of the density of the selected prey categories. Larvae less than 14 mm SL ingested meroplankton (gastropods, bivalves, foraminiferans, and polychaetes) in direct relation to the densities available, and without regard to the densities of copepods available. However, the largest larvae (14–17 mm SL) ingested meroplankton in inverse relation to the density of copepods available, indicating that larvae consumed more meroplankton when the concentration of copepods was low. Such flexibility and opportunism in feeding behavior may increase the larvae's chances of obtaining adequate nutrition during periods of suboptimal feeding conditions.     

Metabolic changes during carcinogenesis: potential impact on invasiveness

Successful adaptation to varying microenvironmental constraints plays a crucial role during carcinogenesis. We develop a hybrid cellular automation approach to investigate the cell-microenvironmental interactions that mediate somatic evolution of cancer cells. This allows investigation of the hypothesis that regions of premalignant lesions develop a substrate-limited environment as proliferation carries cells away from blood vessels which remain separated by the intact basement membrane. We find that selective forces in tumoural regions furthest from the blood supply act to favour cells whose metabolism is best suited to respond to local changes in oxygen, glucose and pH levels. The model predicts three phases of somatic evolution. Initially, cell survival and proliferation is limited due to diminished oxygen levels. This promotes adaptation to a second phase of growth dominated by cells with constitutively up-regulated glycolysis, less reliant on oxygen for ATP production. Increased glycolysis induces acidification of the local environment, limiting proliferation and inducing cell death through necrosis and apoptosis. This promotes a third phase of cellular evolution, with emergence of phenotypes resistant to acid-induced toxicity. This emergent cellular phenotype has a significant proliferative advantage because it will consistently acidify the local environment in a way that is toxic to its competitors but harmless to itself. The model's results suggest this sequence is essential in the transition from self-limited premalignant growth to invasive cancer, and, therefore, that this transition may be delayed or prevented through novel strategies directed towards interrupting the hypoxia-glycolysis-acidosis cycle.     

Density-dependent size regulation and negative growth in the sea urchin Diadema antillarum Philippi

Summary This study documents size- and density-dependent growth (positive and negative), in the sea urchin Diadema antillarum. In the summer of 1983, an inverse relationship was found between Diadema test diameter and population density at seven sites in Lameshur Bay, St. John, United States Virgin Islands. The regression of this relationship improved when test diameter was plotted against density per unit grazing area. A field experiment demonstrated that 1) Diadema has the ability to reduce skeletal body size, and 2) direction (growth or shrinkage) and rate of growth can be predicted accurately based on the urchin's body size and population density. The ability to adjust body size as density fluctuates may allow Diadema to persist when density increases, by shrinking and reducing metabolic costs, and to take advantage of decreases in density, by increasing in size and fecundity.     

The role of phosphofructokinase in glycolytic control in the facultative anaerobe Sipunculus nudus

Summary The involvement of phosphofructokinase (PFK) in glycolytic control was investigated in the marine peanut worm Sipunculus nudus. Different glycolytic rates prevailed at rest and during functional and environmental anaerobiosis: in active animals glycogen depletion was enhanced by a factor of 120; during hypoxic exposure the glycolytic flux increased only slightly. Determination of the mass action ratio (MAR) revealed PFK as a non-equilibrium enzyme in all three physiological situations. Duirng muscular activity the PFK reaction was shifted towards equilibrium; this might account for the observed increase in glycolytic rate under these conditions. PFK was purified from the body wall muscle of S. nudus. The enzyme was inhibited by physiological ATP concentrations and an acidic pH; adenosine monophosphate (AMP), inorganic phosphate (P_i), and fructose-2,6-bisphosphate (F-2,6-P₂) served as activators. PFK activity, determined under simulated cellular conditions of rest and muscular work, agreed well with the glycolytic flux in the respective situations. However, under hypoxia PFK activity surpassed the glycolytic rate, indicating that PFK may not be rate-limiting under these conditions. The results suggest that glycolytic rate in S. nudus is mainly regulated by PFK during rest and activity. Under hypoxic conditions the regulatory function of PFK is less pronounced.Abbreviations ATP, ADP, AMP adenosine tri-, di-, monophosphate - DTT dithiothreitol - EDTA ethylene diaminetetra-acetic acid - F-6-P fructose-6-phosphate - F-1,6-P₂ fructose-1,6-bisphosphate - F-2,6-P₂ fructose-2,6-bisphosphate; bwm, body wall muscle; fresh mass, total body weight - G-6-P glucose-6-phosphate - H enthalpy change - K _a activation constant - K _eq equilibrium constant - K _i inhibition constant - K _m Michaelis constant - MAR mass action ratio - NMR nuclear magnetic resonance - PFK phosphofructokinase - P_i inorganic phosphate - PLA phospho-l-arginine - SD standard deviation - TRIS, TRIS (hydroxymethyl) aminomethane - TRA triethanolamine hydrochloride - V _max maximal velocity     

Modeling pollen tube growth: Feeling the pressure to deliver testifiable predictions

The frequency and amplitude of oscillatory pollen tube growth can be altered by changing the osmotic value of the surrounding medium. This has motivated the proposition that the periodic change in growth velocity is caused by changes in turgor pressure. Using mathematical modeling we recently demonstrated that the oscillatory pollen tube growth does not require turgor to change but that this behavior can be explained with a mechanism that relies on changes in the mechanical properties of the cell wall which in turn are caused by temporal variations in the secretion of cell wall precursors. The model also explains why turgor and growth rate are correlated for oscillatory growth with long growth cycles while they seem uncorrelated for oscillatory growth with short growth cycles. The predictions made by the model are testifiable by experimental data and therefore represent an important step towards understanding the dynamics of the growth behavior in walled cells.     

To be or not to be a locust? A comparative analysis of behavioral phase change in nymphs of Schistocerca americana and S. gregaria

Phenotypic plasticity in behavior induced by high rearing density is often part of a migratory syndrome in insects called phase polyphenism. Among locust species, swarming and the expression of phase polyphenism are highly correlated. The american grasshopper, Schistocerca americana, rarely swarms even though it is closely related to the swarming Old World desert locust, S. gregaria, as well as two swarming New World locusts. Anecdotal field observations of locust-like behavior in S. americana indicate that it may express behavioral phase polyphenism, but empirical investigations are lacking. In this study, I tested the hypothesis that S. americana expresses locust-like density-dependent changes in behavior during both the first and final nymphal instars. I then compared the expression of behavioral phase change between S. americana and S. gregaria. First instar S. americana exhibited significant geographic variation in behavior with grasshoppers from a North Carolina population expressing more pronounced density-dependent changes relative to grasshoppers from a Texas population. The behavior of final instar S. americana was only slightly affected by rearing density and there was no evidence for a difference between populations. Comparison with S. gregaria revealed that the magnitude of density-dependent behavioral change, particularly among final instar nymphs, was much reduced in S. americana.     

Phosphocreatine production coupled to the glycolytic reactions in the cytosol of cardiac cells

Phosphocreatine production catalyzed by a cytosolic fraction from cardiac muscle containing all glycolytic enzymes and creatine kinase in a soluble form has been studied in the presence of creatine, adenine nucleotides and different glycolytic intermediates as substrates. Glycolytic depletion of glucose, fructose 1,6-bis(phosphate) and phosphoenolpyruvate to lactate was coupled to efficient phosphocreatine production. The molar ratio of phosphocreatine to lactate produced was close to 2.0 when fructose 1,6-bis(phosphate) was used as substrate and 1.0 with phosphoenolpyruvate. In these processes the creatine kinase reaction was not the rate-limiting step: the mass action ratio of the creatine kinase reaction was very close to its equilibrium value and the maximal rate of the forward creatine kinase reaction exceeded that of glycolytic flux by about 6-fold when fructose 1,6-bis(phosphate) was used as a substrate. Therefore, the creatine kinase raction was continuously in the state of quasiequilibrium and the efficient synthesis of phosphocreatine observed is a result of constant removal of ADP by the glycolytic system at an almost unchanged level of ATP ([ATP] ? [ADP]), this leading to a continuous shift of the creatine kinase equilibrium position.When phosphocreatine was added initially at concentrations of 5–15 mM the rate of the coupled creatine kinase and glycolytic reactions was very significantly inhibited due to a sharp decrease in the steady-state concentration of ADP. Therefore, under conditions of effective phosphocreatine production in heart mitochondria, which maintain a high phosphocreatine: creatine ratio in the myoplasm in vivo, the glycolytic flux may be suppressed due to limited availability of ADP restricted by the creatine kinase system. The possible physiological role of the control of the glycolytic flux by the creatine kinase system is discussed.     

Continuous photoautotrophic cultures of the eukaryotic alga Chlorella vulgaris can exhibit stable oscillatory dynamics

Sustained oscillations in cell concentration, average per cell DNA content, and average cell size were found in continuous photoautotrophic cultures of Chlorella vulgaris at low dilution rates (0.1/day). The period of oscillation was approximately 10 days. DNA histograms determined by flow cytometry exhibited reproducible pattern through consecutive oscillations. At the maximum cell concentration during an oscillation, the DNA histograms showed that the majority of the cells were not replicating their chromosomes, and most of the culture was comprised of single cells in G0/G1 phase. The cells then initiated DNA replication; however, because of the long generation time, the cell concentration decreased to a minimum, and at the same time the average per cell DNA content reached its maximum value. At this point the cells began to divide, and the cell concentration increased until it reached its maximum value at the beginning of the next oscillation. Calculations based on the supplied nutrients and comparison to biomass generation showed that the oscillatory behavior in continuous photoautotrophic cultures of C. vulgaris was not due to nutrient limitation, but most likely was due to the secretion of compounds that alter cell cycle kinetics. The oscillatory behavior disappeared when the dilution rate was increased to 0.3/day and the culture reached a stable steady state.     

Mathematical modelling of tumour acidity

Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as the existence of the benign steady state, or predicted incorrectly the size of the inter-tissue gap. Here we show that taking proper account of quiescence ameliorates these drawbacks as well as revealing novel behaviour. The simplicity of the model allows us to fully identify the key parameters controlling different aspects of behaviour.