Homoclinic chaos in a model of natural selection

 We modify a simple mathematical model for natural selection originally formulated by Robert M. May in 1983 by permitting one homozygote to have a larger selective advantage when rare than the other, and show that the new model exhibits dynamical chaos. We determine an open region of parameter space associated with homoclinic points, and prove that there are infinite sequences of period-doubling bifurcations along selected paths through parameter space. We also discuss the possibility of chaos arising from imbalance in the homozygote fitnesses in more realistic biological situations, beyond the constraints of the model. Received 3 February 1995; received in revised form 1 November 1995     

Effects of plant hybridization on herbivore-parasitoid interactions

We studied the effects of host plant hybridization on the survival and mortality of the leaf-mining moth Phyllonorycter salicifoliella on hybrid and parental willow plants in the field and in a common garden experiment. P. salicifoliella survival differed significantly among three willow taxa in the field in 1994 but not in the field in 1995 or in the common garden. Parasitism by eulophid wasps differed significantly among taxa in 1994 and appeared to account for the variation in their survival. In the field in 1995, host feeding predation varied significant among taxa. The theory of tritrophic interactions predicts that plant genotype can affect natural enemy impact, and this study supports this prediction. Significant variation in survival and eulophid parasitism was also found among genotypes within taxa in the field in both years and in the common garden experiment. The common garden results show that genetic differences in plants affect the herbivore-parasitoid interaction. Variation among years in the patterns of survival and causes of mortality among field plants suggest that genotype by environment interactions may be important. Received: 1 March 1996 / Accepted: 4 November 1996     

Heart and T-Lymphocyte Cell Surfaces Both Exhibit Positive Cooperativity in Binding a Membrane-Lytic Toxin

Cobra venom cytotoxins (CTX) have been shown to disrupt cells as different as immunocytes, skeletal myocytes, erythrocytes and tumor cells. Nevertheless, even subpopulations of tumor cells are differentially susceptible to CTX by an order of magnitude. In the present study, our objective was to compare CTX-specific binding with cytolytic potency for two disparate cell types in vitro. We investigated the lytic activity of cytotoxin-III from Naja naja atra (NNA, fraction D) using heart cells and human leukemic T-cells (CEM cells). For both cell types, 50% cytolysis, assessed by tetrazolium dye conversion, occurred with μm concentrations of toxin (EC₅₀= 2.2 μm). We examined the binding of radiolabeled CTX III to both heart cells and CEM cells and found the apparent dissociation constant (K _Dapp) to be 0.69 μm and 0.75 μm, for CEM and heart cells respectively. The B _max for the CEM cells was 1.0 fmoles/cell and that for heart cells was 5.2 fmoles/cell, both exhibiting positive cooperativity between the sites (Hill coefficients 1.4, T-cells; 1.6, heart). Relatively modest dissociation constants plus high numbers of binding sites per cell are consistent with a model of CTX binding to plasma membranes by interaction with phospholipids in the bilayer. Our results suggest that the lytic activity of this cytotoxin follows its binding to a population of sites on the cells in a cooperative fashion. Received: 8 May 1995/Revised: 17 November 1995     

A Mathematical Model of the Pancreatic Ductal Epithelium

A mathematical model of the HCO⁻ ₃-secreting pancreatic ductal epithelium was developed using network thermodynamics. With a minimal set of assumptions, the model accurately reproduced the experimentally measured membrane potentials, voltage divider ratio, transepithelial resistance and short-circuit current of nonstimulated ducts that were microperfused and bathed with a CO₂/HCO⁻ ₃-free, HEPES-buffered solution, and also the intracellular pH of duct cells bathed in a CO₂/HCO⁻ ₃-buffered solution. The model also accurately simulated: (i) the effect of step changes in basolateral K⁺ concentration, and the effect of K⁺ channel blockers on basolateral membrane potential; (ii) the intracellular acidification caused by a Na⁺-free extracellular solution and the effect of amiloride on this acidification; and (iii) the intracellular alkalinization caused by a Cl⁻-free extracellular solution and the effect of DIDS on this alkalinization. In addition, the model predicted that the luminal Cl⁻ conductance plays a key role in controlling both the HCO⁻ ₃ secretory rate and intracellular pH during HCO⁻ ₃ secretion. We believe that the model will be helpful in the analysis of experimental data and improve our understanding of HCO⁻ ₃-transporting mechanisms in pancreatic duct cells. Received: 18 October 1995/Revised: 5 July 1996     

Earthworm secondary production and N flux in agroecosystems: a comparison of two approaches

Production was estimated for Aporrectodea spp. and Lumbricus spp. populations in corn agroecosystems with a 5-year history of manure or inorganic fertilizer applications during 1994–1995 and 1995–1996. Earthworm biomass and production were greater in manure than inorganic fertilizer plots, although biomass and production declined by about 50% between 1994–1995 and 1995–1996 due to unfavorable climatic conditions. Production was highest during the spring and autumn when soil temperatures were between 4 and 22°C. Production was higher in Lumbricus spp. than Aporrectodea spp. populations due to greater Lumbricus spp. biomass. Aporrectodea spp. production was 3.47–16.14 g ash-free dry weight (AFDW) m^–2 year^–1, while Lumbricus spp. production was 6.09–18.11 g AFDW m^–2 year^–1, depending on the fertilizer treatment and the method used to estimate production. However, production estimates from the instantaneous growth rate method were within 27% of the values calculated using the size-frequency method. Nitrogen flux through earthworms was used to estimate efficiency quotients. Net production efficiency (P/A) ranged from 0.64 to 0.76, assimilation efficiency (A/C) ranged from 0.1 to 0.3, and gross production efficiency (P/C) ranged from 0.06 to 0.22. Annual N flux through earthworm populations was higher in manure than inorganic fertilizer plots, and ranged from 2.95 to 5.47 g N m^–2 year^–1 in 1994–1995 and 1.76 to 2.92 g N m^–2 year^–1 in 1995–1996. The N flux through earthworms represented an amount equivalent to 16–30% of crop N uptake during 1994–1995 and 11–18% of crop N uptake during 1995–1996. We concluded that the effects of earthworms on N cycling in corn agroecosystems were substantial, and that N flux through earthworms was influenced significantly by fertilizer amendments. Received: 20 September 1999 / Accepted: 24 March 2000     

Multiparametric bifurcations for a model in epidemiology

 In the present paper we make a bifurcation analysis of an SIRS epidemiological model depending on all parameters. In particular we are interested in codimension-2 bifurcations. Received 8 April 1994; received in revised form 29 June 1995     

A Turing model with correlated random walk

 If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and different speeds. Furthermore, a Hopf bifurcation can be found if the reproduction rate of the activator is greater than its rate of change of direction, and oscillating patterns are possible. Received 24 February 1995; received in revised form 6 September 1995     

Identification of Isoforms of G Proteins and PKC that Colocalize with Tight Junctions

Recent evidence suggests that the formation and permeability of tight junctions are actively regulated by second-messenger-generating systems involving G proteins and protein kinase C (PKC). A possible specific target for these regulatory proteins is the tight junction protein ZO-1. An extensive immunocytochemical study was performed in cultured epithelial monolayers of MDCK and Caco-2 cells to identify which isoforms of G proteins and PKC are present at or near the zonula occludens complex. Antibodies against α-subunits of each one of the four major subfamilies were used for the localization of the G proteins. For the PKC localization, antibodies against eight different isoforms were used. In confluent monolayers, Gα₁₂ and PKC ζ, were the only isoforms of these proteins present at the cell borders. In subconfluent monolayers, Gα₁₂ and PKC ζ were found at the plasma membrane only along the areas of lateral cell-cell contact. These isoforms formed a pattern of distribution very similar to the ZO-1 protein. The present findings indicate that Gα₁₂ and PKC ζ may be part of the zonula occludens complex and may locally regulate formation and permeability of tight junctions. Received: 29 July 1995/Revised: 13 October 1995     

A model including photoperiod in degree days for estimating Hevea bud growth

 The aim of this study was to verify the applicability of a heat-sum model and an alternative model that included photoperiod to describe Hevea bud growth. Considering 19° C as the base temperature, approx. 172 degree days were required for bud growth up to leaf blade expansion. The applicability of the heat-sum model for Hevea bud growth was confirmed. The inclusion of day length as an exponential term in accumulated degree days resulted in the model fitting much better for the spring than for the winter conditions. Received: 21 May 1995 / Revised: 28 October 1996 / Accepted: 27 January 1997     

On periodic cohort solutions of a size-structured population model

 We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable ‘substrate’. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter β. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n≧2) with small size differences will tend to a periodic one-cohort solution as t→∞. Received 16 March 1995; received in revised form 7 January 1997     

Effect of Antipeptide Antibodies Directed against Three Domains of Connexin43 on the Gap Junctional Permeability of Cultured Heart Cells

Cell-to-cell communication can be blocked by intracellular injections of antibodies raised against gap junction proteins, but the mechanism of channel obstruction is unknown. Binding to connexins could lead to a conformational change, interfere with regulatory domains or cause a steric hindrance. To address these questions, the effects on cell-to-cell communication of affinity purified polyclonal antibodies raised against peptides reproducing the intracellular sequences 5–17, 314–322 and 363–382 of rat connexin43 were investigated in cultured rat ventricular cells. The antibodies against sequence 363–382 were characterized by immunoblotting and immunocytochemistry. Characterization of antibodies 5–17 and 314–322 has been previously reported. In a first series of experiments, the effect on gap junctional communication was assessed by injecting a junction-permeant fluorescent dye into cells adjacent to one cell previously microinjected with antibodies. In a second series, junctional permeability was quantitatively determined on records of fluorescence recovery after the photobleaching of 6-carboxyfluorescein-loaded cells. Antibodies 5–17 marked a 43 kDa band on immunoblots, but did not immunolabel gap junctions and had no functional effect. Antibodies 314–322 recognized the 43 kDa protein and labeled the intercalated disks, but failed to interfere with junctional permeability. Antibodies to the nearby sequence 363–382, for which all immunospecific tests had been positive, caused a delayed diffusional uncoupling in 50% of the microinjected cells. It is suggested that the blocking of junctional communication by antibodies results from interference with a regulatory domain of the connexin. Received: 25 July 1995/Revised: 21 December 1995     

A Novel,Volume-correlated Cl− Conductance in Marginal Cells Dissociated from the Stria Vascularis of Gerbils

Using the whole-cell patch-clamp technique, we examined Cl⁻-selective currents manifested by strial marginal cells isolated from the inner ear of gerbils. A large Cl⁻-selective conductance of ∼18 nS/pF was found from nonswollen cells in isotonic buffer containing 150 mm Cl⁻. Under a quasi-symmetrical Cl⁻ condition, the `instantaneous' current-voltage relation was close to linear, while the current-voltage relation obtained at the end of command pulses of duration 400 msec showed weak outward rectification. The permeability sequence for anionic currents was as SCN⁻ > Br⁻≅ Cl⁻ > F⁻ > NO⁻ ₃≅ I⁻ > gluconate⁻, corresponding to Eisenmann's sequence V. When whole-cell voltage clamped in isotonic bathing solutions, the cells exhibited volume changes that were accounted for by the Cl⁻ currents driven by the imposed electrochemical potential gradients. The volume change was elicited by lowered extracellular Cl⁻ concentration, anion substitution and altered holding potentials. The Cl⁻ conductance varied in parallel with cell volume when challenged by bath anisotonicity. The whole-cell Cl⁻ current was only partially blocked by both 5-nitro-2-(3-phenylpropylamino) benzoic acid (NPPB, 0.5 mm) and diphenylamine-2-carboxylic acid (DPC, 1.0 mm), but 4-acetamido-4′-isothiocyanato-stilbene-2,2′-disulfonic acid (SITS, 0.5 mm) was without effect. The properties of the present whole-cell Cl⁻ current resembled those of the single Cl⁻ channel previously found in the basolateral membrane of the marginal cell (Takeuchi et al., Hearing Res. 83:89–100, 1995), suggesting that the volume-correlated Cl⁻ conductance could be ascribed predominantly to the basolateral membrane. This Cl⁻ conductance may function not only in cell volume regulation but also for the transport of Cl⁻ and the setting of membrane potential in marginal cells under physiological conditions. Received: 15 August 1995/Revised: 3 November 1995     

Estimation of 131I thyroid doses for the evacuees from Pripjat

  The thyroid doses of 49 360 inhabitants of Pripjat evacuated after the accident at Chernobyl were reconstructed. During their evacuation most of the evacuees passed through highly contaminated territories. The evaluation of a large-scale public survey showed that only about 50% of the evacuees had left the contaminated areas within 5 days and that 30% of them stayed there for more than 30 days. As a first step, the model of dose estimations was improved, and thyroid doses were assessed for the group of evacuees for whom the ¹³¹I activity in the thyroids was measured. The ¹³¹I incorporation during the first 5 days after the accident was described by a single-intake model (inhalation); later incorporations were assumed to be proportional to the radioiodine activity in milk. As a second step, the correlation between the calculated doses and individual parameters (place of residence in Pripjat, intake of stable iodine, and age at the time of the accident) was described by an empirical equation. This equation was applied to all evacuees who completed the questionnaires of the public survey. Previous dose assessments were found to overestimate the thyroid doses especially for the younger evacuees. On the basis of these estimations, collective doses and the resulting radiation risks for thyroid cancer were assessed for different age groups. Received: 28 November 1995 / Accepted in revised form: 6 March 1996     

Global stability in consumer-resource cascades

 Models of population growth in consumer-resource cascades (serially arranged containers with a dynamic consumer population, v, receiving a flow of resource, u, from the previous container) with a functional response of the form h(u/v ^b ) are investigated. For b∈[0, 1], it is shown that these models have a globally stable equilibrium. As a result, two conclusions can be drawn: (1) Consumer density dependence in the functional or in the per-capita numerical response can result in persistence of the consumer population in all containers. (2) In the absence of consumer density dependence, the consumer goes extinct in all containers except possibly the first. Several variations of this model are discussed including replacing discrete containers by a spatial continuum and introducing a dynamic resource. Received 25 February 1995 / received in revised form 27 July 1995     

Competitive exclusion and persistence in models of resource and sexual competition

 We study a combined mathematical model of resource and sexual competition. The population dynamics in this model is analyzed through a coupled system of reaction-diffusion equations. It is shown that strong sexual competition and low birth rate lead to competitive exclusion of the biological species. If sexual competition is weak, then the persistence of the species is possible, depending on the initial density functions and the growth rates of the species. When sexual competition affects both species, persistence and competitive exclusion results are also obtained in terms of the ecological data in the model. Received 1 November 1995; received in revised form 13 January 1996     

A mathematical model for drug administration by using the phagocytosis of red blood cells

 A mathematical model for the delivery of drug directly to the macrophages by using the phagocytosis of senescent red blood cells is proposed. The model is based on the following assumption: At time t=0 a preassigned red blood cell population n(0, a)=φ(a), a>0, loaded by the drug, is injected in the blood circulation. Among the cells of that population only those with an age a≧ā (ā=120 days) will be phagocytosed by macrophages. Of course, the lifetime of the drug must be higher than ā. Within the red blood cells it cannot be metabolized, neither can it diffuse through their membranes. The emphasis of the paper is on the mathematical properties and on the formulation of the control problem. Received 15 December 1994; received in revised form 20 July 1995     

Optimization models for the force and energy in competitive running

 In [2] the author has developed an optimization model for the force and energy in competitive running. In this paper the energy processes in the muscle were described by a three-compartment hydraulic model. Here this is reviewed briefly and applied to the current world records in order to determine the key parameters, maximal force, energy reserves and oxygen uptake. These values agree well with those given in the literature and those obtained by other means. The velocity profiles for 100 m sprints are described equally well. The model is then applied to older world records to deduce a relation between the force and energy by linear regression. Finally the fully parameterized model is used to compute the effects of adverse wind and altitude. Inasmuch as there are data available, there is a good agreement. Received 19 July 1995; received in revised form 27 February 1996     

Peripheral natural killer cell activity and intraperitoneal soluble p55 tumor necrosis factor receptor in patients with malignant ascites: two possible indicators for response to intraperitoneal combined tumor necrosis factor α and interferon γ treatment

 Tumor necrosis factor α (TNFα) and interferon γ (IFNγ) are important immunomodulators. They are capable of acting in a synergistic manner on tumor cells in vitro and in vivo. In a clinical phase I study 13 patients with malignant ascites due to abdominal spread of different primary tumors received intraperitoneally (i. p.) TNFα and IFNγ once weekly over 3 – 8 weeks in order to evaluate the effect of locoregionally administered TNFα/IFNγ on ascites formation. Therefore some peripheral and local immunological functional parameters of peripheral blood and malignant ascites were investigated. Mononuclear lymphocytes and natural killer (NK) cell activity of peripheral blood and ascites, TNF-inhibitory activity, soluble p55 and p75 TNF receptors, and prostaglandin E₂ values in ascites were measured immediately before and 24 h after each TNFα/IFNγ infusion. Peripheral mononuclear lymphocytes and NK activity decreased significantly 24 h after i. p. TNFα/IFNγ application. However, over the entire treatment schedule, peripheral NK activity in all responders showed a continuous increase, when compared to pre TNFα/IFNγ treatment levels. In contrast, NK activity in non-responders constantly decreased. In contrast to non-responders, TNF-inhibitory activity and soluble p55 TNF receptor levels, determined in ascites, decreased in responders. Taken together, our findings suggest, that successful locoregional i. p. TNFα/IFNγ therapy induces systemic immunological reactions possibly after saturation of soluble p55 TNF receptors in ascites, which leads to an increase of peripheral NK activity. Received: 28 September 1995 / Accepted: 16 November 1995     

Index of unidentified ectomycorrhizae

 This latest instalment of the index of unidentified ectomycorrhizae lists binomials and reference specimen characterizations of ectomycorrhizae first described in 1995–1997. Accepted: 14 May 1998     

An indicator quantitatively comparing two treatment effect sizes on responder and non-responder groups – exponential of estimated interaction parameter

 Sometimes a specific treatment is effective in one subgroup but not in another. An indicator allowing quantitative comparison of treatment effect in two subgroups would be useful in clinical medicine. We have developed such an indicator. It is obtained by calculations using Cox’s proportional hazard or logistic model with therapy, subgroup, and confounding explanatory variables. The parameter of the interaction between therapy and subgroup can be estimated and tested statistically. The exponential value of the interaction parameter is what we tentatively call the “hazard ratio ratio”, meaning the ratio between the treatment effects in two subgroups. The 95% confidence interval of the indicator can also be calculated. As a numerical example, the hazard ratio between the survival times of postoperative gastric cancer patients treated by adjuvant immunochemotherapy and patients without adjuvant immunochemotherapy in a subgroup with high serum glycosidically bound sialic acid (SA) level was lower than that in a low-SA subgroup using an estimate for hazard ratio ratio of less than 0.5 with statistical significance. We propose this indicator be used as a “responder/non-responder ratio” of therapy effect. Received: 11 April 1995 / Accepted: 5 September 1995