Progression age enhanced backward bifurcation in an epidemic model with super-infection

 We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one. Received: 11 October 2001 / Revised version: 17 September 2002 / Published online: 17 January 2003 Present address: Department of Biological Statistics and Computational Biology, 434 Warren Hall, Cornell University, Ithaca, NY 14853-7801 This author was visiting Arizona State University when most of the research was done. Research partially supported by NSF grant DMS-0137687. This author's research was partially supported by NSF grant DMS-9706787. Key words or phrases: Backward bifurcation – Multiple endemic equilibria – Alternating stability – Break-point density – Super-infection – Dose-dependent latent period – Progressive and quiescent latent stages – Progression age structure – Threshold type disease activation – Operator semigroups – Hille-Yosida operators – Dynamical systems – Persistence – Global compact attractor     

Xylem transfer cells in the rosette plant Hieracium floribundum

Summary Xylem transfer cells in the rhizome of Hieracium floribundum are described for the first time and several methods used in visualizing these cells are discussed. The most marked wall ingrowths occur in transfer cells associated with the xylem of foliar traces.This research was supported by an NRC of Canada grant to Dr. R. L. Peterson.Undergraduate student and Associate Professor, resp.     

Nocodazole does not synchronize cells: implications for cell-cycle control and whole-culture synchronization

It has been predicted that nocodazole-inhibited cells are not synchronized because nocodazole-arrested cells with a G2-phase amount of DNA would not have a narrow cell-size range reflecting the cell size of some specific, presumably G2-phase, cell-cycle age. Size measurements of nocodazole-inhibited cells now fully confirm this prediction. Further, release from nocodazole inhibition does not produce cells that move through the cell cycle mimicking the passage of normal unperturbed cells through the cell cycle. Nocodazole, an archetypal whole-culture synchronization method, can inhibit growth to produce cells with a G2-phase amount of DNA, but such cells are not synchronized. Cells produced by a selective (i.e., non-whole-culture) method not only have a specific DNA content, but also have a narrow size distribution. The current view of cell-cycle control that is based on methods that are not suitable for cell-cycle analysis must therefore be reconsidered when results are based on whole-culture synchronization.This work was supported by the National Science Foundation (grant MCB–0323346) and (in part) by the National Institutes of Health (University of Michigan’s Cancer Center, support grant 5 P30 CA46592). G.I., M.T., and P. B. are associated with the Undergraduate Research Opportunity Program of the University of Michigan, which also supported this research.     

Analysis of an autonomous phase model for neuronal parabolic bursting

An understanding of the nonlinear dynamics of bursting is fundamental in unraveling structure-function relations in nerve and secretory tissue. Bursting is characterized by alternations between phases of rapid spiking and slowly varying potential. A simple phase model is developed to study endogenous parabolic bursting, a class of burst activity observed experimentally in excitable membrane. The phase model is motivated by Rinzel and Lee's dissection of a model for neuronal parabolic bursting (J. Math. Biol. 25, 653–675 (1987)). Rapid spiking is represented canonically by a one-variable phase equation that is coupled bi-directionally to a two-variable slow system. The model is analyzed in the slow-variable phase plane, using quasi steady-state assumptions and formal averaging. We derive a reduced system to explore where the full model exhibits bursting, steady-states, continuous and modulated spiking. The relative speed of activation and inactivation of the slow variables strongly influences the burst pattern as well as other dynamics. We find conditions of the bistability of solutions between continuous spiking and bursting. Although the phase model is simple, we demonstrate that it captures many dynamical features of more complex biophysical models.This research was partially supported by NSF-JOINT RESEARCH grant 8803573, grant from CONCYT and DGAPA(UNAM) Mexico for H. Carrillo, and for the S. M. Baer NSF DMS-9107538     

A new RNA synthesis mutant of E. coli

A temperature-sensitive mutant of E. coli is described. At the nonpermissive temperature, the capacity for RNA and protein synthesis decreases logarithmically in the mutant. The mutant is unable to support the growth of f2 or T7 virus, even at the permissive temperature. The temperature-sensitive mutation maps approximately 1 away from rif ^r in E. coli and therefore affects a gene previously undescribed. The temperature sensitivity is suppressed by sublethal concentrations of rifampicin. Moreover, in rif ^r T^s double mutants, the T ^s mutation suppresses rif ^r and vice versa. The partially purified RNA polymerases from mutant and wild-type cells have different temperature and salt optima.This research was supported by Public Health Service grant GM-14368 from the National Institute of General Medical Sciences and by grant IN-29 from the American Cancer Society. One of us (D.P.) is a predoctoral trainee, supported by a National Science Foundation Graduate Traineeship Program and by a National Institutes of Health Predoctoral Research Fellowship. S. Marshall is supported by LASBAU.     

Dynamical synaptic plasticity: a model and connection to some experiments

 Using a modified version of a phenomenological model for the dynamics of synaptic plasticity, we examine some recent experiments of Wu et al. [(2001) J Physiol 533:745–755]. We show that the model is quantitatively consistent with their experimental protocols producing long-term potentiation (LTP) and long-term depression (LTD) in slice preparations of rat hippocampus. We also predict the outcome of similar experiments using different frequencies and depolarization levels than reported in their results. Received: 3 September 2002 / Accepted in revised form: 22 October 2002 / Published online: 24 February 2003 Correspondence to: H.D.I. Abarbanel (e-mail: hdia@jacobi.ucsd.edu) Acknowledgements. We are very grateful to A. Selverston and D. Feldman for conversations about this work. This work was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Engineering and Geosciences, under grants No. DE-FG03-90ER14138 and No. DE-FG03-96ER14592, by a grant from the National Science Foundation, NSF PHY0097134, by a grant from the Army Research Office, DAAD19-01-1-0026, by a grant from the Office of Naval Research, N00014-00-1-0181, and by a grant from the National Institutes of Health, NIH R01 NS40110-01A2. This work was also partially supported by M. Ciencia y Tecnologa BFI2000-0157 (R.H.).     

Trace feature map: a model of episodic associative memory

An approach to episodic associative memory is presented, which has several desirable properties as a human memory model. The design is based on topological feature map representation of data. An ordinary feature map is a classifier, mapping an input vector onto a topologically meaningful location on the map. A trace feature map, in addition, creates a memory trace on that location. The traces can be stored episodically in a single presentation, and retrieved with a partial cue. Nearby traces overlap, which results in plausible memory interference behavior. Performance degrades gracefully as the memory is overloaded. More recent traces are easier to recall as are traces that are unique in the memory.This research was supported in part by an ITA Foundation grant and by fellowships from the Academy of Finland, the Emil Aaltonen Foundation and the Foundation for the Advancement of Technology (Finland) when the author was at UCLA     

Mathematical model of memory trace and forgetfulness

A mathematical model of a memory trace and forgetfulness is proposed here based on an improved version of our previous work (Harth et al., 1970; Anninos et al., 1970). Thus it was shown that the trace of a stimulus pattern presented to a subject decays with time due to the interference theory which assumes that competition among different associations leads to losses of retention. Such interference theory has been tested in this model by assuming that the retention of a first learned item followed by the learning of other successive tasks, depends on the inhibitory effect induced by them on the first item.This research has been supported by NIH grants NS-8012 and NS-8498, and NSP grant GB-30498. Computation assistance was provided by the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources grant RR-3.     

Intranuclear annulate lamellae in oocytes of the tunicate,Styela partita

Summary Intranuclear annulate lamellae have been observed with the electron microscope in oocytes of the tunicate, Styela partita. Morphological evidence suggests that the annulate lamellae may arise by a specialized fusion process of individual vesicles. Intranuclear vesicles appear to be formed, in time, before differentiated annulate lamellae. It is also suggested that the position and structure of an annulus is in large part determined by the fusion of the vesicles. An annulus may be present as soon as two vesicles have completed their fusion process. Finally, it is again suggested on the basis of morphological evidence that the intranuclear vesicles are derived by the blebbing activity of the inner layer of the nuclear envelope.This investigation was supported by grants (RG-9229, 9230) from the National Institutes of Health, Public Health Service. The electron microscope facilities used were also supported by a grant (GM-05479) from the National Institutes of Health to Professor H. W. Beams.     

Multiple limit cycles in the standard model of three species competition for three essential resources

We consider the dynamics of the standard model of 3 species competing for 3 essential (non-substitutable) resources in a chemostat using Liebig's law of the minimum functional response. A subset of these systems which possess cyclic symmetry such that its three single-population equilibria are part of a heteroclinic cycle bounding the two-dimensional carrying simplex is examined. We show that a subcritical Hopf bifurcation from the coexistence equilibrium together with a repelling heteroclinic cycle leads to the existence of at least two limit cycles enclosing the coexistence equilibrium on the carrying simplex- the ``inside' one is an unstable separatrix and the ``outside' one is at least semi-stable relative to the carrying simplex. Numerical simulations suggest that there are exactly two limit cycles and that almost every positive solution approaches either the stable limit cycle or the stable coexistence equilibrium, depending on initial conditions. Bifurcation diagrams confirm this picture and show additional features. In an alternative scenario, we show that the subcritical Hopf together with an attracting heteroclinic cycle leads to an unstable periodic orbit separatrix. This research was partially supported by NSF grant DMS 0211614. KY 40292, USA. This author's research was supported in part by NSF grant DMS 0107160     

Multiple pulse interactions and averaging in systems of coupled neural oscillators

Oscillators coupled strongly are capable of complicated behavior which may be pathological for biological control systems. Nevertheless, strong coupling may be needed to prevent asynchrony. We discuss how some neural networks may be designed to achieve only simple locking behavior when the coupling is strong. The design is based on the fact that the method of averaging produces equations that are capable only of locking or drift, not pathological complexity. Furthermore, it is shown that oscillators that interact by means of multiple pulses per cycle, dispersed around the cycle, behave like averaged equations, even if the number of pulses is small. We discuss the biological intuition behind this scheme, and show numerically that it works when the oscillators are taken to be composites, each unit of which is governed by a well-known model of a neural oscillator. Finally, we describe numerical methods for computing from equations for coupled limit cycle oscillators the averaged coupling functions of our theory.Research partially supported by the National Science Foundation under grants DMS 8796235 and DMS 8701405 and the Air Force Office of Scientific Research under University Research Contract F 49620-C-0131 to Northeastern University     

Global dynamics of microbial competition for two resources with internal storage

We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model. B. Li’s research was partially supported by NSF grants DMS 0211614 and DMS 0616445. H. L. Smith’s research was supported in part by NSF grant DMS 0414270.     

Community action on water pollution

Actions to improve local water or air quality are likely to combine collective benefits with specific costs. This suggests that the variations among communities in their actions to improve water quality will involve opposition from industries bearing the specific costs. The use of Environmental Protection Agency (EPA)-funded matching grants for sewerage construction by large U.S. cities varies inversely with the imputed opposition from polluting industries. Use also increases with assessed need and with the extent of certain resources, including the credit rating. Matching grants funded by the Department of Housing and Urban Development (HUD) are not likely to have such specific costs, and imputed opposition does not affect their distribution. When location and the growth rate are controlled, use of restrictions and surcharges on industrial wastes increases with imputed opposition. It is possible that industries influence the specific regulations. Alternative explanations of the statistical relationship between opposition and EPA grant use are discussed.This research was partially supported by Department of Commerce Grants 2-35227 and 04-3-158-45 to the University of Southern California Sea Grant Program.     

Neural network model of selective visual attention using Hodgkin–Huxley equation

We propose a mathematical model of selective visual attention using a two-layered neural network with neurons described by the Hodgkin–Huxley equation in order to investigate part of the assumption proposed by Desimone and Duncan. The neural network consists of a layer of hippocampal formation and of visual cortex. A frequency of firing and a firing time for each neuron and also a correlation of the firing times between neurons are calculated numerically to clarify an attention state, a nonattention state, and an attention shift. We find that synchronous phenomena occur not only for the frequency but also for the firing time between the neurons in the hippocampal formation and those in a part of the visual cortex in our model. It also turns out that the attention shift is performed quickly in our model.Acknowledgements We are grateful to T. Omori for his valuable discussions and comments. K. K. was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. This work was partially supported by Grant-In-Aid for Scientific Research No. 13680383 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.     

A general procedure for protoplast recovery,callus and plant regeneration in plants

A portion of this work was supported by NSF grant DCB 8718314 and by the Missouri Agricultural Experiment Station. This research is a joint contribution from the Missouri Agricultural Experiment Station, Journal Series No. 10,789 and from the Massachusetts Agricultural Experiment Station, Amherst, MA 01003; Journal Paper No. MAES 2959. Ousama Zaghmout was supported by the Food for the 21st Century Program, College of Agriculture, University of Missouri, Columbia, MO.     

Slow Noise in the Period of a Biological Oscillator Underlies Gradual Trends and Abrupt Transitions in Phasic Relationships in Hybrid Neural Networks

In order to study the ability of coupled neural oscillators to synchronize in the presence of intrinsic as opposed to synaptic noise, we constructed hybrid circuits consisting of one biological and one computational model neuron with reciprocal synaptic inhibition using the dynamic clamp. Uncoupled, both neurons fired periodic trains of action potentials. Most coupled circuits exhibited qualitative changes between one-to-one phase-locking with fairly constant phasic relationships and phase slipping with a constant progression in the phasic relationships across cycles. The phase resetting curve (PRC) and intrinsic periods were measured for both neurons, and used to construct a map of the firing intervals for both the coupled and externally forced (PRC measurement) conditions. For the coupled network, a stable fixed point of the map predicted phase locking, and its absence produced phase slipping. Repetitive application of the map was used to calibrate different noise models to simultaneously fit the noise level in the measurement of the PRC and the dynamics of the hybrid circuit experiments. Only a noise model that added history-dependent variability to the intrinsic period could fit both data sets with the same parameter values, as well as capture bifurcations in the fixed points of the map that cause switching between slipping and locking. We conclude that the biological neurons in our study have slowly-fluctuating stochastic dynamics that confer history dependence on the period. Theoretical results to date on the behavior of ensembles of noisy biological oscillators may require re-evaluation to account for transitions induced by slow noise dynamics.     

Is human conversation more efficient than chimpanzee grooming?

Clique sizes for chimpanzee (Pan troglodytes) grooming and for human conversation are compared in order to test Robin Dunbar’s hypothesis that human language is almost three times as efficient a bonding mechanism as primate grooming. Recalculation of the data provided by Dunbar et al. (1995) reveals that the average clique size for human conversation is 2.72 whereas that of chimpanzee grooming is shown to be 2.18. The efficiency of human conversation and actual chimpanzee grooming over Dunbar’s primate grooming model (always one-to-one and a one-way interaction) is 1.27 and 1.25, respectively, when we take role alternation into account. Chimpanzees can obtain about the same efficiency as humans in terms of quantity of social interactions because their grooming is often mutual and polyadic. The fieldwork was supported by a grant from the International Scientific Research Program (07041138 to T. Nishida) of the Monbusho (Japanese Ministry of Education, Science, Sports, and Culture). Michio Nakamura is a research fellow at Japan Monkey Centre. He received his Master of Science degree from Kyoto University in 1996. He is carrying out research on the grooming behavior of chimpanzees at Mahale, Tanzania, for his doctorate.     

An analysis of the mammalian ventricular action potential

Summary A Hodgkin-Huxley model for ventricular excitation is abstracted from electrophysiological data. A singular perturbation analysis of the 8-dimensional phase portrait of the model characterizes the role of calcium during the plateau phase of the ventricular action potential and demonstrates how the calcium refractory period prevents tetanization. Supported in part by the Undergraduate Research Opportunities Program, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA     

Nutritional studies of histoplasma capsulatum

Summary A chemically defined medium, composed of inorganic salts, glucose, asparagine, cystine, and a vitamin supplement, has been devised for growth of the yeast phase ofHistoplasma capsulatum. Growth in this medium was abundant and compared favorably with that in media containing complex natural material. Conversion of each of the 20 strains examined was accomplished by one or more passages on agar slants of the medium and incubation of the cultures at 37° C. Yeast phase cultures on this medium have been stored for 6 months or more at approximately 4° C without conversion or loss of viability. Of the 20 strains examined for vitamin requirements of the yeast phase, all were partially deficient for thiamine; nine for inositol; five, either partially or completely deficient for niacin; and one, completely deficient for biotin.No specific amino acid was required for growth of the yeast phase, but an organic source of sulfur and one of nitrogen were essential. Cystine and cysteine were equally effective for growth of the yeast phase when supplied on an equivalent sulfur basis and very little difference in growth occurred in media which contained equal amounts of nitrogen in any one of the following compounds: asparagine, glutamic acid, aspartic acid, and proline,Of the 20 strains, all but one, which requires biotin, were capable of continued growth in the mycelial phase when subcultured on an agar medium containing only inorganic salts and dextrose, but growth was improved significantly by asparagine or casein hydrolysate.This investigation was supported in part by a PHS research grant (AI-03524) from the National Institute of Allergy and Infectious Diseases, Public Health Service.     

Deterministic extinction effect of parasites on host populations

 Experimental studies have shown that parasites can reduce host density and even drive host population to extinction. Conventional mathematical models for parasite-host interactions, while can address the host density reduction scenario, fail to explain such deterministic extinction phenomena. In order to understand the parasite induced host extinction, Ebert et al. (2000) formulated a plausible but ad hoc epidemiological microparasite model and its stochastic variation. The deterministic model, resembles a simple SI type model, predicts the existence of a globally attractive positive steady state. Their simulation of the stochastic model indicates that extinction of host is a likely outcome in some parameter regions. A careful examination of their ad hoc model suggests an alternative and plausible model assumption. With this modification, we show that the revised parasite-host model can exhibit the observed parasite induced host extinction. This finding strengthens and complements that of Ebert et al. (2000), since all continuous models are likely break down when all population densities are small. This extinction dynamics resembles that of ratio-dependent predator-prey models. We report here a complete global study of the revised parasite-host model. Biological implications and limitations of our findings are also presented. Received: 30 October 2001 / Revised version: 11 February 2002 / Published online: 17 October 2002 Work is partially supported by NSF grant DMS-0077790 Mathematics Subject Classification (2000): 34C25, 34C35, 92D25. Keywords or phrases: Microparasite model – Ratio-dependent predator-prey model – Host extinction – Global stability – Biological control