Multiple Limit Cycles in a Gause Type Predator–Prey Model with Holling Type III Functional Response and Allee Effect on Prey

This work aims to examine the global behavior of a Gause type predator–prey model considering two aspects: (i) the functional response is Holling type III and, (ii) the prey growth is affected by the Allee effect. We prove the origin of the system is an attractor equilibrium point for all parameter values. It has also been shown that it is the ω-limit of a wide set of trajectories of the system, due to the existence of a separatrix curve determined by the stable manifold of the equilibrium point (m,0), which is associated to the Allee effect on prey. When a weak Allee effect on the prey is assumed, an important result is obtained, involving the existence of two limit cycles surrounding a unique positive equilibrium point: the innermost cycle is unstable and the outermost stable. This property, not yet reported in models considering a sigmoid functional response, is an important aspect for ecologists to acknowledge as regards the kind of tristability shown here: (1) the origin; (2) an interior equilibrium; and (3) a limit cycle of large amplitude. These models have undoubtedly been rather sensitive to disturbances and require careful management in applied conservation and renewable resource contexts.     

Trophic functioning of the Tiahura reef sector, Moorea Island, French Polynesia

 Energy-balanced steady-state models of the fringing and barrier reefs of Tiahura, Moorea Island, French Polynesia, are presented. A total of 43 and 46 trophic groups were identified on the two reef habitats respectively. The models’ outputs indicate that most of the substantial primary productivity is processed and recycled (59–69% of NPP) in the web through detritus based, microbially mediated food webs, with a substantial but secondary flux through grazer-based webs. This mechanism produces long pathways with low trophic efficiencies at the higher trophic levels. The trophic structure of both reef habitats efficiently conserves energy and materials within the reef ecosystem through two forms of internal recycling: a relatively large cycle produced through detritus and a microbial food web, and a relatively short one directly produced through predation. The models outputs suggest that bottom-up and top-down control are each ecologically important in both reef habitats. Accepted: 14 April 1997     

Local and global bifurcations at infinity in models of glycolytic oscillations

 We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models concerning parameter values for which the system does not admit any physical (bounded) behavior. Analytic results on the scaling of amplitude and period close to the bifurcations are obtained and confirmed by numerical computations. Finally, we consider more realistic modified models where all solutions are bounded and show that some of the features stemming from the bifurcations at infinity are still present. Received 4 September 1995; received in revised form 18 September 1996     

A mathematical model of the sleep/wake cycle

We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous “flip–flop” conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip–flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip–flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip–flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics.     

Nonlinear EEG analysis based on a neural mass model

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics. Received: 11 August 1997 / Accepted in revised form: 20 April 1999     

Operation of light-dark cycles within simple ecosystem models of primary production and the consequences of using phytoplankton models with different abilities to assimilate N in darkness

We compare the output of a nitrogen–phytoplankton–zooplankton(NPZ) model and of a hypothetical diatom–flagellate competitionscenario operating in continuous light or in a diurnal light–darkcycle of equal daily photon dose. Within these models, phytoplanktonwere configured with contrasting abilities to assimilate nitrogenin darkness. If only a single phytoplankton group is being consideredthen it appears unnecessary to describe the diurnal light cycle.However, given the minimal additional processing time requiredto include the light cycle when running complex biological models,inclusion is recommended where model output is used to providean insight into the behaviour of the organisms and food webs.This is particularly so for considering temporal variationsin the use of ammonium and nitrate (pertaining to the f ratiofor new production) by different phytoplankton groups and hencethe interaction between these organisms and their zooplanktonpredators that regenerate ammonium. In that instance it is importantto endow the phytoplankton model with a capacity for dark Nassimilation commensurate with the type of organism (namelydiatom or non-diatom) being considered. Such different capabilitieslikely affect competition and succession of these groups innature and do affect these interactions in simulations.     

Structure of the bank vole (<Emphasis Type="Italic">Myodes glareolus</Emphasis>) population cycles in the core and periphery of its species area

The results of long-term studies of two bank vole (Myodes glareolus) populations in stationary sites in the central part and periphery of its species area are described. Four phases of a multiannual population cycle and two of its structural parts have been detected for both populations. The first part of the cycle is “determined,” with the “peak” phase passing into a “depression” (population collapse). This transition is mainly determined by intrapopulation processes and is weakly dependent on the external conditions of each individual year. The second part is “stochastic,” starting from a stable point in the cycle in the depression phase. The duration of the second part is determined by the state of the population and its ability to increase its size, as well as by the weather and food factors, predation pressure, and location of the population within the species area. The transition from the peak phase to the depression phase (the determined part) for both populations takes place during one fall-winter-spring season and has no effect on the cycle duration. The duration of the stochastic part in the core of the species area (the period from depression phase to peak phase) is 1–3 years and in the periphery, 2–4 years.     

Serum LH,progesterone and estradiol-17β levels throughout the ovarian cycle,during the early stage of pregnancy and after the parturition and the abortion in the common marmoset,Callithrix jacchus

In the ovarian cycle of common marmosets, serum progesterone began to increase at two to three days after estradiol-17β or LH surge, attained a peak of 25–70 ng/ml and then declined to a level of under 2 ng/ml before the ensuing rise in estradiol-17β and LH. Serum estradiol-17β increased to 700–5,500 pg/ml during the luteal phase, synchronizing with progesterone. It is suggested that the corpus luteum secreted estradiol-17β as well as progesterone. The cycle length as determined from the interval between successive LH surges was approximately 28 days. During the luteal phase, the levels of progesterone and estradiol-17β were higher than in Old World monkeys and women, but marmosets were not accompanied by any clinical symptoms due to excessive progesterone and estradiol-17β. This suggests that such unresponsiveness to progesterone and estradiol-17β in marmosets reflects the small amount of estradiol-17β receptor and presumably also the lower function of the post receptor system. Recovery of the post-partum ovarian cycle in two marmosets differed from that observed in Old World monkeys and women. The first LH surge was found on the ninth and tenth day after parturition and the first ovulation led to the next pregnancy. This suggests that the suckling stimulus of newborns in the common marmoset does not cause any delay in recovery of the ovarian cycle. In three cases of abortion, the recovery of the ovarian cycle was almost the same as that in the case of normal parturition: the first LH surge appeared on the 10th, 14th, and 34th day after abortion.     

Mechanisms for lateral turns in lamprey in response to descending unilateral commands: a modeling study

 Straight locomotion in the lamprey is, at the segmental level, characterized by alternating bursts of motor activity with equal duration and spike frequency on the left and the right sides of the body. Lateral turns are characterized by three main changes in this pattern: (1) in the turn cycle, the spike frequency, burst duration, and burst proportion (burst duration/cycle duration) increase on the turning side; (2) the cycle duration increases in both the turn cycle and the succeeding cycle; and (3) in the cycle succeeding the turn cycle, the burst duration increases on the non-turning side (rebound). We investigated mechanisms for the generation of turns in single-segment models of the lamprey locomotor spinal network. Activation of crossing inhibitory neurons proved a sufficient mechanism to explain all three changes in the locomotor rhythm during a fictive turn. Increased activation of these cells inhibits the activity of the opposite side during the prolonged burst of the turn cycle, and slows down the locomotor rhythm. Secondly, this activation of the crossing inhibitory neurons is accompanied by an increased calcium influx into the cells. This gives a suppressed activity on the turning side and a contralateral rebound after the turn, through activation of calcium-dependent potassium channels. Received: 28 June 2000 / Accepted for publication: 10 May 2001     

Life cycle assessment of commercial furniture: a case study of Formway LIFE chair

Background, aims and scope  The environmental aspects of companies and their products are becoming more significant in delivering competitive advantage. Formway Furniture, a designer and manufacturer of office furniture products, is a New Zealand-based company that is committed to sustainable development. It manufactures two models of the light, intuitive, flexible and environmental (LIFE) office chair: one with an aluminium base and one with a glass-filled nylon (GFN) base. It was decided to undertake a life cycle assessment (LCA) study of these two models in order to: (1) determine environmental hotspots in the life cycle of the two chairs (goal 1); (2) compare the life cycle impacts of the two chairs (goal 2); and (3) compare alternative potential waste-management scenarios (goal 3). The study also included sensitivity analysis with respect to recycled content of aluminium in the product. Materials and methods  The LIFE chair models consist of a mix of metal and plastic components manufactured by selected Formway suppliers according to design criteria. Hence, the research methodology included determining the specific material composition of the two chair models and acquisition of manufacturing data from individual suppliers. These data were compiled and used in conjunction with pre-existing data, specifically from the ecoinvent database purchased in conjunction with the SimaPro7 LCA software, to develop the life cycle inventory of the two chair models. The life cycle stages included in the study extended from raw-material extraction through to waste management. Impact assessment was carried out using CML 2 baseline 2000, the methodology developed by Leiden University’s Institute for Environmental Sciences. Results  This paper presents results for global warming potential (GWP100). The study showed a significant impact contribution from the raw-material extraction/refinement stage for both chair models; aluminium extraction and refining made the greatest contribution to GWP100. The comparison of the two LIFE chair models showed that the model with the aluminium base had a higher GWP100 impact than the model with the GFN base. The waste-management scenario compared the GWP100 result when (1) both chair models were sent to landfill and (2) steel and aluminium components were recycled with the remainder of the chair sent to landfill. The results showed that the recycling scenario contributed to a reduced GWP100 result. Since production and processing of aluminium was found to be significant, a sensitivity analysis was carried out to determine the impact of using aluminium with different recycled contents (0%, 34% and 100%) in both waste-management scenarios; this showed that increased use of recycled aluminium was beneficial. The recycling at end-of-life scenarios was modelled using two different end-of-life allocation approaches, i.e. consequential and attributional, in order to illustrate the variation in results caused by choice of allocation approach. The results using the consequential approach showed that recycling at end-of-life was beneficial, while use of the attributional method led to a similar GWP100 as that seen for the landfill scenario. Discussion  The results show that the main hotspot in the life cycle is the raw-material extraction/refinement stage. This can be attributed to the extraction and processing of aluminium, a material that is energy intensive. The LIFE chair model with the aluminium base has a higher GWP100 as it contains more aluminium. Sensitivity analysis pertaining to the recycled content of aluminium showed that use of aluminium with high recycled content was beneficial; this is because production of recycled aluminium is less energy intensive than production of primary aluminium. The waste-management scenario showed that recycling at end-of-life resulted in a significantly lower GWP100 than landfilling at end-of-life. However, this result is dependent upon the modelling approach used for recycling. Conclusions  With respect to goal 1, the study found that the raw-material extraction/refinement stage of the life cycle was a significant factor for both LIFE chair models. This was largely due to the use of aluminium in the product. For goal 2, it was found that the LIFE chair model with the aluminium base had a higher GWP100 than the GFN model, again due to the material content of the two models. Results for goal 3 illustrated that recycling at end-of-life is beneficial when using a system expansion (consequential) approach to model recycling; if an attributional ‘cut-off’ approach is used to model recycling at end-of-life, there is virtually no difference in the results between landfilling and recycling. Sensitivity analysis pertaining to the recycled content of aluminium showed that use of higher recycled contents leads to a lower GWP100 impact. Recommendation and perspectives  Most of the GWP100 impact was contributed during the raw-material extraction/refinement stage of the life cycle; thus, the overall impact of both LIFE chair models may be reduced through engaging in material choice and supply chain environmental management with respect to environmental requirements. The study identified aluminium components as a major contributor to GWP100 for both LIFE chair models and also highlighted the sensitivity of the results to its recycled content. Thus, it is recommended that the use of aluminium in future product designs be limited unless it is possible to use aluminium with a high recycled content. With respect to waste management, it was found that a substantial reduction in the GWP100 impact would occur if the chairs are recycled rather than landfilled, assuming an expanding market for aluminium. Thus, recycling the two LIFE chair models at end-of-life is highly recommended.     

Mass-Balance Analyses of Boreal Forest Population Cycles: Merging Demographic and Ecosystem Approaches

UsingEcopath, a trophic mass-balance modeling framework, we developed six models of a Canadian boreal forest food web centered around snowshoe hares, which have conspicuous 10-year population cycles. Detailed models of four phases of the cycle were parameterized with long-term population data for 12 vertebrate taxa. We also developed five other models that, instead of observed data, used parameter values derived from standard assumptions. Specifically, in the basic model, production was assumed to equal adult mortality, feeding rates were assumed to be allometric, and biomass was assumed to be constant. In the actual production, functional response, and biomass change models, each of these assumed values from the basic model was replaced individually by field data. Finally, constant biomass models included actual production by all species and functional responses of mammalian predators and revealed the proportion of herbivore production used by species at higher trophic levels. By comparing these models, we show that detailed information on densities and demographics was crucial to constructing models that captured dynamic aspects of the food web. These detailed models reinforced an emerging picture of the causes and consequences of the snowshoe hare cycle. The snowshoe hare decline and low phases were coincident with times when per capita production was relatively low and predation pressure high. At these times, ecotrophic efficiencies (EE) suggest there was little production that remained unconsumed by predators. The importance of both production and consumption implies that bottom–up and top–down factors interacted to cause the cycle. EEs of other herbivores (ground squirrels, red squirrels, small mammals, small birds, grouse) were generally low, suggesting weak top–down effects. Predation rates on these “alternative” prey, except ground squirrels, were highest when predators were abundant, not when hares were rare; consequently, any top–down effects reflected predator biomass and were not a function of diet composition or functional responses. Finally, several predators (lynx, coyotes, great-horned owls) showed clear bottom–up regulation, reproducing only when prey exceeded threshold densities. Taken altogether, these results demonstrate that ecosystem models parameterized by population data can describe the dynamics of nonequilibrial systems, but only when detailed information is available for the species modeled. Received 30 November 2000; Accepted 6 September 2001.     

Biennial cycling caused by demographic delays in a fire-adapted annual plant

We explored models explaining population cycling in the annual Warea carteri. We modeled the life cycle of W. carteri and compared projected trajectories to independently observed trajectories (up to 16 years) of plants in 74 patches in three populations. We built matrix models with an annual time step for two populations, including four stages, (recently produced seeds, seeds in the seed bank, seedlings, and adults) and five vital rates, summarized in seven transitions. Fluctuations of both observed and modeled populations were evaluated using power spectra, autocorrelation, amplitude, and damping. Observed populations had two point cycling. Observed amplitude was higher in frequently burned populations, reached its maximum 1 year after fire, and then dampened. Asymptotic transition and vital rate elasticities showed that seedling survival was the most important factor for long-term population growth, but transient elasticities showed that recruitment from the seed bank was important during the first years post-fire. Deterministic modeling and elasticity analyses indicated that delayed germination (for 1 year) may explain biennial population cycling. Stochastic models created similar cycling with slower damping than deterministic models, but still had lower amplitudes (especially 1–3 years post-fire) than observed populations. The biennial cycle in W. carteri is likely caused by the delay in seed germination, which creates two overlapping cohorts of plants, much like a strict biennial. Fire initiates the cycle by killing aboveground individuals and promoting seedling recruitment in the first post-fire year.     

Reassessment of Models of Facilitated Transport and Cotransport

Most membrane transport models are determinate, requiring the transported ligand(s) to bind initially to a vacant site, which undergoes translation and releases ligand to the alternate side. The carrier reverts to its initial position to complete the net transport cycle. Ligand affinity may change during translation, but this must be compensated by an equivalent energy change(s) within the transport cycle. However, any asymmetric cyclic equilibrium deduced on this basis is thermodynamically fallacious. Determinate cotransport models imply lossless stoichiometric relationships between the complexed cotransported ligands. Independent ligand leakage apart from the mobile cotransport complex must occur outside the canonical cotransport pathway. In contrast, stochastic transport models assume independent ligand diffusion through a variably occluded channel(s) containing binding sites where ligands may undergo bimolecular exchanges. Energy dissipation is intrinsic to all stochastic transport models and occurs within the primary transport pathway. Frictional interactions within a shared path generate flow coupling between ligands. The primary driving forces causing transmembrane ligand flows are their electrochemical potential differences between the external solutions. Demonstrations that ligand exchanges in CLC and neurotransmitter transporters can be multimodal, encompassing both “channel”-like high and “transporter”-like lower conductance states and have independently regulated import and export exchange fluxes are major challenges to determinate models but are explicable by transient widening of a close-encounter region within the channel, leading to decreased coupling and enhanced efflux.     

A modeling approach of the in vitro conversion of oil palm (Elaeis guineensis) somatic embryos

A mathematical model for the growth and conversion of somatic embryos was developed with the aim of monitoring the large scale production of oil palm microplants. The predicted biomass of somatic embryos obtained and subcultured (B _n ), together with the number of harvested shoots (Sh _n ) – two key parameters for production forecasts – have been modeled for seven different shoot harvesting procedures. For the four different clonal lines studied, observed differences between experimental B _n values at the end of each culture cycle and their theoretical counterpart generated by mathematical models were found to range between −30% to +14% at the end of the first 6-weeks culture cycle, then from −50% to +70% after the 6th subculturing operation (36 weeks). Concerning the predicted number of shoots harvested after conversion of somatic embryos (Sh _n ), average variations between experimental and theoretical values ranged between −45% and +41%. Predicted values for biomass (B _n ) between two culture cycles were found to vary slightly (+6% to +10%) indicating that the production of embryo biomass, as predicted by the model, was rather stable, for a given clonal line, from one 6-week cycle to another. The established model could thus be regarded as valid and the variations observed for B _n and Sh _n were found to be acceptable when compared to the those described by other models. Taken as a whole, predicted values for the two studied production parameters were in agreement with the corresponding experimental data (correlation=0.98).     

Evaluation of Multitype Mathematical Models for CFSE-Labeling Experiment Data

Carboxy-fluorescein diacetate succinimidyl ester (CFSE) labeling is an important experimental tool for measuring cell responses to extracellular signals in biomedical research. However, changes of the cell cycle (e.g., time to division) corresponding to different stimulations cannot be directly characterized from data collected in CFSE-labeling experiments. A number of independent studies have developed mathematical models as well as parameter estimation methods to better understand cell cycle kinetics based on CFSE data. However, when applying different models to the same data set, notable discrepancies in parameter estimates based on different models has become an issue of great concern. It is therefore important to compare existing models and make recommendations for practical use. For this purpose, we derived the analytic form of an age-dependent multitype branching process model. We then compared the performance of different models, namely branching process, cyton, Smith–Martin, and a linear birth–death ordinary differential equation (ODE) model via simulation studies. For fairness of model comparison, simulated data sets were generated using an agent-based simulation tool which is independent of the four models that are compared. The simulation study results suggest that the branching process model significantly outperforms the other three models over a wide range of parameter values. This model was then employed to understand the proliferation pattern of CD4+ and CD8+ T cells under polyclonal stimulation.     

Karyokinesis in growing and reverting protoplasts ofSchizosaccharomyces pombe

Division of nuclei without cytokinesis proceeds in growing protoplasts ofSchizosaccharomyces pombe. Prior to regeneration of the complete cell wall and reversion the protoplasts contain 1–7 nuclei, protoplasts with 1–2 nuclei are most frequent. When regeneration of the wall is postponed by adding snail enzymes to the growth medium, protoplasts with a higher number of nuclei (2–4) occur. Multinuclear protoplasts can revert to cells. During the first cytokinesis the protoplast with the regenerated cell wall is divided into two cells by a septum, distribution of nuclei between the two cells being probably incidental. More than only a single nucleus can pass to the revertants even during the second cytokinesis. Septation of protoplasts occurs also during a partial blockage of the wall formation by the snail enzyme preparation, however, reversion to cells can never be observed here (it occurs only after transfer of protoplasts to the medium without the enzyme preparation). The growing and reverting protoplasts represent a very good model system for studying relations among individual processes of the cell cycle, primarily growth of the cell, nuclear cycle and cytokinesis. Yeast protoplasts are often utilized as models for studying morphogenic processes, relations among regeneration of the cell wall, including division of the nucleus (karyokinesis) and cytokinesis.     

Generalist and specialist predators that mediate permanence in ecological communities

 General dynamic models of systems with two prey and one or two predators are considered. After rescaling the equations so that both prey have the same intrinsic rate of growth, it is shown that there exists a generalist predator that can mediate permanence if and only if there is a population density of a prey at which its per-capita growth rate is positive yet less than its competitor’s invasion rate. In particular, this result implies that if the outcome of competition between the prey is independent of initial conditions, then there exists a generalist predator that mediates permanence. On the other hand, if the outcome of competition is contingent upon initial conditions (i.e., the prey are bistable), then there may not exist a suitable generalist predator. For example, bistable prey modeled by the Ayala–Gilpin (θ-Logistic) equations can be stabilized if and only if θ<1 for one of the prey. It is also shown that two specialist predators always can mediate permanence between bistable prey by creating a repelling heteroclinic cycle consisting of fixed points and limit cycles. Received 10 August 1996; received in revised form 21 March 1997     

Numerical simulations of stochastic circulatory models

Properties of two of the stochastic circulatory models theoretically introduced by Smith et al., 1997, Bull. Math. Biol. 59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov-Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.     

The α-glycerophosphate cycle inDrosophila melanogaster. I. Biochemical and developmental aspects

The two α-glycerophosphate dehydrogenases ofDrosophila melanogaster (mitochondrial αGPO and soluble αGPDH) have been biochemically characterized in a preliminary investigation of the α-glycerophosphate cycle inDrosophila. The soluble enzyme is NAD linked and can be distinguished from the mitochondrial oxidase in terms of locational specificity,pH optimum, salt precipitation, and electrophoretic behavior. The mitochondrial enzyme is NAD independent and exhibits behavior typical of a lipoprotein. Extraction procedures are described for αGPO with nonionic detergents. Isoelectric focusing of αGPO on polyacrylamide gels resolved two molecular forms of αGPO which differ in isoelectric point, ease of extraction, and developmental and spatial distribution. Developmental profiles of both αGPO and αGPDH are presented. The occurrence of multiple forms of both the soluble (Wright and Shaw, 1969) and the mitochondrial forms of the enzymes is discussed in light of a multifunctional role of the α-glycerophosphate cycle inDrosophila. This project was supported by a Genetics Training Grant T1 GM 1035 from the National Institute of General Medical Sciences.     

Modelling and analysis of time-lags in some basic patterns of cell proliferation

 In this paper, we present a systematic approach for obtaining qualitatively and quantitatively correct mathematical models of some biological phenomena with time-lags. Features of our approach are the development of a hierarchy of related models and the estimation of parameter values, along with their non-linear biases and standard deviations, for sets of experimental data. We demonstrate our method of solving parameter estimation problems for neutral delay differential equations by analyzing some models of cell growth that incorporate a time-lag in the cell division phase. We show that these models are more consistent with certain reported data than the classic exponential growth model. Although the exponential growth model provides estimates of some of the growth characteristics, such as the population-doubling time, the time-lag growth models can additionally provide estimates of: (i) the fraction of cells that are dividing, (ii) the rate of commitment of cells to cell division, (iii) the initial distribution of cells in the cell cycle, and (iv) the degree of synchronization of cells in the (initial) cell population. Received: 15 September 1997/Revised version: 1 April 1998