Effective drift velocities and effective diffusivities of swimming microorganisms in external flows

 In this note we calculate the effective drift velocities and the effective diffusivities of swimming microorganisms in an external flow field. It is shown that if the ambient velocity field is incompressible then the effects of reorientation of the cells can under certain circumstances enhance the effective drift velocity along the preferred direction. Received: 4 January 1999     

Aggregation and collapse in a mechanical model of fungal tip growth

 Interconnected hyphal tubes form the mycelia of a fungal colony. The growth of the colony results from the elongation and branching of these single hyphae. The material being incorporated into the extending hyphal wall is supplied by vesicles which are formed further back in the hyphal tip. Such wall-destined vesicles appear conspicuously concentrated in the interior of the hypha, just before the hyphal apex, in the form of an apical body or Spitzenk?rper. The cytoskeleton of the hyphal tube has been implicated in the organisation of the Spitzenk?rper and the transport of vesicles, but as yet there is no postulated mechanism for this. We propose a mechanism by which forces generated by the cytoskeleton are responsible for biasing the movement of vesicles. A mathematical model is derived where the cytoskeleton is described as a viscoelastic fluid. Viscoelastic forces are coupled to the conservation equation governing the vesicle dynamics, by weighting the diffusion of vesicles via the strain tensor. The model displays collapse and aggregation patterns in one and two dimensions. These are interpreted in terms of the formation of the Spitzenk?rper and the initiation of apical branching. Received: 16 September 1996 / Revised version: 20 July 1998     

Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows

 Analytic approximations are obtained to solutions of the steady Fokker-Planck equation describing the probability density functions for the orientation of dipolar particles in a steady, low-Reynolds-number shear flow and a uniform external field. Exact computer algebra is used to solve the equation in terms of a truncated spherical harmonic expansion. It is demonstrated that very low orders of approximation are required for spheres but that spheroids introduce resolution problems in certain flow regimes. Moments of the orientation probability density function are derived and applications to swimming cells in bioconvection are discussed. A separate asymptotic expansion is performed for the case in which spherical particles are in a flow with high vorticity, and the results are compared with the truncated spherical harmonic expansion. Agreement between the two methods is excellent. Received 10 February 1997; received in revised form 26 May 1997     

Respiratory gas exchange,nitrogenous waste excretion,and fuel usage during aerobic swimming in juvenile rainbow trout

 The types of fuel burned by juvenile rainbow trout (17 g) during a 58-h period of aerobic sustained exercise were studied by respirometry. Attempts to measure fuel usage by depletion (the compositional approach) in these same fish were unsuccessful due to lack of detectable changes in proximate body composition. O₂ consumption, CO₂ excretion, and nitrogenous waste excretion (ammonia-N plus urea-N) were measured in individual fish swum continuously at 55% and 80% of maximum sustainable swimming speed and in non-swimming controls. O₂ consumption and CO₂ excretion increased with swimming speed, and decreased over time. Absolute rates of N excretion were independent of swimming speed and time. Instantaneous aerobic fuel use, as calculated from the respiratory quotients and nitrogen quotients, was approximately 47% lipid, 30% protein, and 23% carbohydrate in non-swimmers at the start of the experiment. With increased swimming speed there was no change in absolute rates of protein oxidation, while lipid and carbohydrate oxidation both increased. Therefore, the relative protein contribution decreased with increasing speed but increased with swimming duration as the oxidation of other fuels declined over time. However, lipid oxidation predominated at all speeds and at all times. The relative contribution of carbohydrate increased with swimming speed and decreased over time. These results suggest that swimming becomes more efficient over time and help resolve uncertainties in the literature. We conclude that lipid is the main fuel of aerobic exercise, that protein catabolism is kept at minimum levels necessary for maintenance, and that carbohydrate oxidation becomes more important with increased white muscle recruitment at higher speed. Accepted: 3 July 1996     

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak

 The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak (‘fade-out’). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations. Received 20 July 1995; received in revised form 6 May 1996     

Polymorphism, distribution, and segregation of AFLP markers in a doubled haploid rice population

We exploited the newly developed amplified fragment length polymorphism (AFLP) technique to study the polymorphism, distribution and inheritance of AFLP markers with a doubled haploid rice population derived from ‘IR64’/‘Azucena’. Using only 20 pairs of primer combinations, we detected 945 AFLP bands of which 208 were polymorphic. All 208 AFLP markers were mapped and distributed over all 12 chromosomes. When these were compared with RFLP markers already mapped in the population, we found the AFLP markers to be highly polymorphic in rice and to follow Mendelian segregation. As linkage map of rice can be generated rapidly with AFLP markers they will be very useful for marker-assisted backcrossing. Received: 11 April 1996 / Accepted: 14 June 1996     

Analysis of an SEIRS epidemic model with two delays

 A disease transmission model of SEIRS type with exponential demographic structure is formulated. All newborns are assumed susceptible, there is a natural death rate constant, and an excess death rate constant for infective individuals. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional to I(t)/N(t) where N(t) is the total (variable) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stability of the disease free proportion equilibrium, and existence, uniqueness, and stability of an endemic proportion equilibrium, are investigated. The stability results are stated in terms of a key threshold parameter. More detailed analyses are given for two cases, the SEIS model (with no immune period), and the SIRS model (with no latent period). Several threshold parameters quantify the two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero. Received 8 May 1995; received in revised form 7 November 1995     

Copper-mediated oxidative burst in Nicotiana tabacum L. cv. Bright Yellow 2 cell suspension cultures

Summary.  In cell suspension cultures of Nicotiana tabacum L. cv. Bright Yellow 2 (BY-2) a rapid and concentration-dependent accumulation of H₂O₂ is induced by excess concentrations of copper (up to 100 μM). This specific and early response towards copper stress was shown to be extracellular. Addition of 300 U of catalase per ml decreased the level of H₂O₂. Superoxide dismutase (5 U/ml) induced an increase in H₂O₂ production by 22.2%. This indicates that at least part of the H₂O₂ is produced by dismutation of superoxide. Pretreatment of the cell cultures with the NAD(P)H oxidase inhibitors diphenylene iodonium (2 and 10 μM) and quinacrine (1 and 5 mM) prevented the generation of H₂O₂ under copper stress for 90%. The influence of the pH on the H₂O₂ production revealed the possible involvement of cell-wall-dependent peroxidases in the generation of reactive oxygen species after copper stress. Received May 20, 2002; accepted July 26, 2002; published online May 21, 2003 RID="*" ID="*" Correspondence and reprints: Plant Physiology, Department of Biology, University of Antwerp (RUCA), Groenenborgerlaan 171, 2020 Antwerp, Belgium.     

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     

Comparative environmental tolerances of threatened delta smelt (Hypomesus transpacificus) and introduced wakasagi (H. nipponensis) in an altered California estuary

In California’s Sacramento-San Joaquin estuary, environmental protection and habitat restoration efforts directed at a threatened native osmerid, the delta smelt (Hypomesus transpacificus), are complicated by the presence of a morphologically similar non-native congener, the wakasagi (H. nipponensis), transported to the estuary from upstream reservoirs. In order to better define delta smelt critical habitat and to evaluate the potential for habitat overlap by these two species, we compared the tolerances of the two species to temperature, salinity, and water velocity, environmental factors that vary spatially and temporally within the estuary. For fishes acclimated to 17°C and fresh water (0 ppt), we measured critical thermal maxima and minima, chronic upper salinity tolerance limits, and critical swimming velocities. Wakasagi had higher critical thermal maxima (29.1°C vs. 25.4°C for delta smelt), lower critical thermal minima (2.3°C vs. 7.5°C for delta smelt), higher upper salinity tolerances (26.8 ppt vs. 19.1 ppt for delta smelt), and swam faster (for 6–6.9 cm SL fish, 43.3 cm s^–1 vs. 28.2 cm s^–1 for delta smelt) than delta smelt. This suggests that the wide seasonal and year-to-year fluctuations in temperature, salinity, and flow typical in the estuary would not exclude wakasagi, although their eggs and larvae may be less tolerant. With respect to these factors, the native delta smelt may be at a physiological disadvantage, particularly in habitats with suboptimal environmental conditions, and may be excluded from shallow-water habitat restoration sites, which are characterized by poor circulation, low flows, and more environmentally extreme conditions. The low abundance of wakasagi in the estuary recorded to date may indicate that factors other than temperature, salinity, and flow determine wakasagi distribution. Received: 25 August 1999 / Accepted: 22 November 1999     

Meteorological forcing of plankton dynamics in a large and deep continental European lake

The timing of various plankton successional events in Lake Constance was tightly coupled to a large-scale meteorological phenomenon, the North Atlantic Oscillation (NAO). A causal chain of meteorological, hydrological, and ecological processes connected the NAO as well as winter and early spring meteorological conditions to planktonic events in summer leading to a remarkable memory of climatic effects lasting over almost half a year. The response of Daphnia to meteorological forcing was most probably a direct effect of altered water temperatures on daphnid growth and was not mediated by changes in phytoplankton concentrations. High spring water temperatures during ”high-NAO years” enabled high population growth rates, resulting in a high daphnid biomass as early as May. Hence, a critical Daphnia biomass to suppress phytoplankton was reached earlier in high-NAO years yielding an early and longer-lasting clear-water phase. Finally, an earlier summer decline of Daphnia produced in a negative relationship between Daphnia biomass in July and the NAO. Meteorological forcing of the seasonal plankton dynamics in Lake Constance included simple temporal shifts of processes and successional events, but also complex changes in the relative importance of different mechanisms. Since Daphnia plays an important role in plankton succession, a thorough understanding of the regulation of its population dynamics provides the key for predictions of the response of freshwater planktonic food webs to global climate change. Received: 15 February 1999 / Accepted: 23 August 1999     

Identifiability of a stochastic model for cell debris in flow cytometry

 One of the most important problems in recovering DNA distribution from flow cytometric DNA measurements is the presence of background noise. In this paper, we analyse a probabilistic model recently proposed for background debris distribution and based on a specific probabilistic mechanism for the DNA fragmentation process of the cell nucleus. In particular, we carry out some sufficient conditions to uniquely identify the original DNA distribution from the flow cytometric data. Received: 15 June 1997 / Revised version: 18 November 1997     

The number of segregating sites in a sample of DNA sequences from a geographically structured population

 The distribution of the number of segregating sites among randomly sampled DNA sequences from a geographically structured population is studied. We assume the infinitely-many-sites model of neutral genes and no recombination. Employing the genealogical process, we derive an equation for the generating function of the distribution of the number of segregating sites. First we study the strong-migration limit and prove that the distribution converges to that for a panmictic population. We also study the case of two sampled DNA sequences in the d-dimensional torus model with homogeneous migration. Received 13 July 1995; received in revised form 21 April 1997     

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

 We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons with synaptic coupling. This provides a simple model of excitable neural tissue. We first derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-propagation depends on various parameters that characterize neuronal interactions such as synaptic and axonal delays, and the passive membrane properties of dendritic cables. We also establish that excitable networks support the propagation of solitary pulses in the long-wavelength limit. We then derive a general condition for the (local) asymptotic stability of traveling waves in terms of the characteristic equation of the linearized firing time map, which takes the form of an integro-difference equation of infinite order. We use this to analyze the stability of solitary pulses in the long-wavelength limit. Solitary wave solutions are shown to come in pairs with the faster (slower) solution stable (unstable) in the case of zero axonal delays; for non-zero delays and fast synapses the stable wave can itself destabilize via a Hopf bifurcation. Received: 27 October 1998     

Identification of a signal peptide for oryzacystatin-I

 A previously unidentified extension of an open reading frame from the genomic DNA of Japonica rice (Oryza sativa L.) encoding oryzacystatin-I (OC-I; access. M29259, protein ID AAA33912.1) has been identified as a 5′ gene segment coding for the OC-I signal peptide. The signal peptide appears to direct a pre-protein (SPOC-I; Accession No. AF164378) to the endoplasmic reticulum, where it is processed into the mature form of OC-I. The start codon of SPOC-I begins 114 bp upstream from that previously published for OC-I. A putative proteolytic site, which may yield a mature OC-I approximately 12 residues larger than previously described, has been identified within SPOC-I between Ala-26 and Glu-27. The signal peptide sequence was amplified by polymerase chain reaction using genomic DNA from O. sativa seedlings and ligated to the 5′ end of the truncated OC-I gene at the endogenous SalI site. Partially purified protein extracts from Escherichia coli expressing SPOC-I reacted with polyclonal antibodies raised against OC-I and revealed a protein of the expected molecular weight (15,355 Da). In-vitro translation of SPOC-I in the presence of microsomal membranes yielded a processed product approximately 2.7 kDa smaller than the pre-protein. Nicotiana tabacum L. cv. Xanthi plants independently transformed with the SPOC-I gene processed SPOC-I and accumulated the mature form of OC-I (approximately 12.6 kDa), which co-migrated with natural, mature OC-I extracted from rice seed when separated by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Received: 29 July 1999 / Accepted: 25 August 1999     

Travelling waves and pattern formation in a model for fungal development

 Under a variety of conditions, the hyphal density within the expanding outer edge of growing fungal mycelia can be spatially heterogeneous or nearly uniform. We conduct an analysis of a system of reaction-diffusion equations used to model the growth of fungal mycelia and the subsequent development of macroscopic patterns produced by differing hyphal and hence biomass densities. Both local and global results are obtained using analytical and numerical techniques. The emphasis is on qualitative results, including the effects of changes in parameter values on the structure of the solution set. Received 22 November 1995; received in revised form 17 May 1996     

Mapping of two genes for resistance to clubroot (Plasmodiophora brassicae) in a population of doubled haploid lines of Brassica oleracea by means of RFLP and AFLP markers

A genetic map covering 615 cM in 12 linkage groups was assembled based on 92 RFLP and AFLP markers segregating in a population of 107 doubled haploid lines (DH lines) of Brassica oleracea. The DH-line population was obtained through microspore culture from the of two homozygous parents: DH-line Bi derived from the cabbage landrace Bindsachsener, and DH-line Gr from broccoli cv ‘Greenia’. Sixty-five percent of the loci, and in some cases complete linkage groups, displayed distorted segregation ratios, a frequency much higher than that observed in populations of the same species. DH-line Bi was resistant to clubroot, which is caused by a Dutch field isolate of Plasmodiophora brassicae. Resistance in the DH-line population was determined in two ways: by assigning symptom grades to each plant, and by measuring the fresh weights of the healthy and affected parts of the root system of each plant. Using a multiple QTL mapping approach to analyze the fresh weight data, we found two loci for clubroot resistance; these were designated pb-3 and pb-4. The additive effects of these loci were responsible for 68% of the difference between the parents and for 60% of the genetic variance among DH-line means. Also, indications for the presence of two additional, minor QTLs were found. Analysis of symptom grades revealed the two QTLs pb-3 and pb-4, as well as one of the two minor QTLs indicated by analysis of the fresh weight data. Received: 29 April 1996 / Accepted: 10 May 1996     

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     

Methylation reactions and the phytoalexin response in alfalfa suspension cultures

 In order to determine why the activated methyl cycle is up-regulated in plants undergoing defence responses to fungal pathogens we have monitored the utilisation of methyl groups derived from methionine in cell-suspension cultures of alfalfa (Medicago sativa L.) treated for various times with fungal elicitor, by carrying out a parallel labelling study with [³⁵S]methionine and [methyl-³H]methionine. The distribution of the two radiolabels among the medium, soluble cellular components and cell wall was then determined. In the absence of elicitor the utilisation of the two radiolabels was similar. However, in the presence of the elicitor the total incorporation of radioactivity from [methyl-³H]methionine into metabolites was far greater than from [³⁵S]methionine, indicating that the methyl label had been utilised in methylation reactions. Elicitor treatment resulted in up to a sixfold increase in the use of ³H-methyl groups in the methylation of hydrophobic metabolites. In the period 0–24 h after elicitor treatment, increased methylation was directed largely into the synthesis of the isoflavonoid phytoalexin medicarpin and related metabolites. Newly synthesized phytoalexins were exported into the medium, while a significant proportion of the medicarpin accumulating in the cell in the early stages of elicitation was derived from the hydrolysis of its respective conjugate. Elicitor treatment also modified the incorporation of ³H-methyl groups into the cell wall. Between 0 and 24 h after elicitor treatment the methylation of pectin in the cell wall declined. After 24 h, pectin methylation recovered and was associated with an increase in the methylation of other wall-bound polysaccharide components. Since no other major metabolic sink for the increased methylation was determined we conclude that the increased activity of the activated methyl cycle during defence interactions in alfalfa is required to support phytoalexin synthesis and cell wall modifications. Received: 1 August 1996 / Accepted: 24 October 1996     

Gain-induced oscillations in blood pressure

 “Mayer waves” are long-period (6 to 12 seconds) oscillations in arterial blood pressure, which have been observed and studied for more than 100 years in the cardiovascular system of humans and other mammals. A mathematical model of the human cardiovascular system is presented, incorporating parameters relevant to the onset of Mayer waves. The model is analyzed using methods of Liapunov stability and Hopf bifurcation theory. The analysis shows that increase in the gain of the baroreflex feedback loop controlling venous volume may lead to the onset of oscillations, while changes in the other parameters considered do not affect stability of the equilibrium state. The results agree with clinical observations of Mayer waves in human subjects, both in the period of the oscillations and in the observed age-dependence of Mayer waves. This leads to a proposed explanation of their occurrence, namely that Mayer waves are a gain-induced oscillation. Received: 15 September 1997/Revised version: 15 March 1998