Computational model of the cockroach escape behavior: winner and losers in a population code

 I present a comprehensive biologically oriented computational model to account for the escape response of the cockroach on the ground. This model is an expansion of previous work that accounted only for discriminating left from right wind directions [Ezrachi et al. (1999) Biol Cybern 81: 89–99]. The model is composed of computational elements describing the biological processes taking place in the various neurons and includes input which emulates empirical data. With this model it is possible to obtain escape behavior that resembles natural behavior. The model is used to address an ongoing debate as to whether the cockroach's turn direction is determined by computations carried out by the entire neuronal population (PC) or rather by a “winner-take-all” (WTA) mechanism. I suggest that the computation mechanism that underlies the cockroach escape response is composed of both PC and WTA principles. Based on the properties of the suggested new mechanism I denote it a “Darwinian population code.” Received: 26 March 2002 / Accepted in revised form: 24 June 2002 Acknowledgements. I thank H. Parnas for her advice and assistance, J. M. Camhi for helpful comments, and D. Lipson for developing the simulation tools. Correspondence to: E. A. Ezrachi (e-mail: erez@piano.ls.huji.ac.il, Tel.: +972-2-6585818, Fax: +972-2-6585569)     

Temperature controls a latitudinal gradient in the proportion of watershed nitrogen exported to coastal ecosystems

Increased export of biologically available nitrogen (N) to the coastal zone is strongly linked to eutrophication, which is a major problem in coastal marine ecosystems (NRC (2000) Clean Coastal Waters: Understanding and Reducing the Effects of Nutrient Pollution. National Academy Press, Washington, DC; Bricker et al. (1999) National Estuarine Eutrophication Assessment. Effects of nutrient enrichment in the nation’s estuaries. NOAA-NOS Special Projects Office, Silver Spring, MD). However, not all of the nitrogen input to a watershed is exported to the coast (Howarth et al. (1996) Biogeochemistry 35:75–139; Jordan and Weller (1996) Bioscience 46:655–664). Global estimates of nitrogen export to coasts have been taken to be 25% of watershed input, based largely on northeastern U.S. observations (Galloway et al. (2004) Biogeochemistry 70:153–226; Boyer et al. (2006) Global Biogeochem Cycle 20:Art. No. GB1S91). We applied the N budgeting methodology developed for the International SCOPE Nitrogen project (Howarth et al. (1996) Biogeochemistry 35:75–139; Boyer et al. (2002) Biogeochemistry 57:137–169) to 12 watersheds in the southeastern U.S., and compared them with estimates of N export for 16 watersheds in the northeastern U.S. (Boyer et al. (2002) Biogeochemistry 57:137–169). In southeastern watersheds, average N export was only 9% of input, suggesting the need for downward revision of global estimates. The difference between northern and southern watersheds is not a function of the absolute value of N inputs, which spanned a comparable range and were positively related to export in both cases. Rather, the proportion of N exported was significantly related to average watershed temperature (% N export = 58.41 e^{−0.11 * temperature}; R ² = 0.76), with lower proportionate nitrogen export in warmer watersheds. In addition, we identified a threshold in proportionate N export at 38°N latitude that corresponds to a reported breakpoint in the rate of denitrification at 10–12°C. We hypothesize that temperature, by regulating denitrification, results in increased proportionate N export at higher latitudes. Regardless of the mechanism, these observations suggest that temperature increases associated with future climate change may well reduce the amount of nitrogen that reaches estuaries, which will have implications for coastal eutrophication.     

Use of an immobilized cell bioreactor for the continuous inoculation of milk in fresh cheese manufacturing

A system was developed to continuously acidify and inoculate skim milk for the production of fresh cheese. Four strains of mesophilic lactic acid bacteria were entrapped separately in κ -carrageenan/locust bean gum gel beads and used in a stirred bioreactor operated at 26°C with a 25% (v/v) gel load. The pH in the reactor was controlled at 6.0 by adding fresh milk using proportional integrated derived regulation. The bioreactor was operated during 8-h daily cycles for up to 7 weeks with different milks (heat treatment, dry matter content) and differing starting procedures. The heat treatment of the milk was an important factor for process performance: a dilution rate increase of 57% and an inoculation level decrease of 63% were observed with sterilized UHT skim milk (142°C – 7.5 s) compared with pasteurized skim milk (72°C – 15 s). The dry matter content of the milk (8–13% w/w) had no detectable effect on these parameters. A convenient starting procedure of the system was tested; steady-state was reached in less than 40 min following an interruption period of 16–60 h. These results combined with our published data on process performance show the feasibility of using an integrated immobilized cell bioreactor for milk prefermentation in cheese manufacture. Received 10 June 1996/ Accepted in revised form 15 October 1996     

Exact sampling formulas for multi-type Galton-Watson processes

 Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution. It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions. Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction. Received: 10 June 2001 / Revised version: 21 November 2001 / Published online: 23 August 2002 Mathematics Subject Classification (2000): Primary 60J80, Secondary 92D10, 92D25 Key words or phrases: Multi-type Galton-Watson process – sampling formula – PCR – mitochondrial DNA     

Early development and quorum sensing in bacterial biofilms

 We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm. The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum wave speed, determined by linearisation, is realised for a wide class of initial conditions. Received: 10 February 2002 / Revised version: 29 October 2002 / Published online: 19 March 2003 Key words or phrases: Bacterial biofilm – Quorum sensing – Mathematical modelling – Numerical solution – Asymptotic analysis – Travelling wave analysis     

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     

ROS-Mediated ABA Signaling

In plants, reactive oxygen species (ROS) are short-lived molecules produced through various cellular mechanisms in response to biotic and abiotic stimuli. ROS function as second messengers for hormone signaling, development, oxygen deprivation, programmed cell death, and plant–pathogen interactions. Recent research on ROS-mediated responses has produced stimulating findings such as the specific sources of ROS production, molecular elements that work in ROS-mediated signaling and homeostasis, and a ROS-regulated gene network (Neill et al., Curr Opin Plant Biol 5:388–395, 2002a; Apel and Hirt, Annu Rev Plant Biol 55:373–399, 2004; Mittler et al., Trends Plant Sci 9:490–498, 2004; Mori and Schroeder, Plant Physiol 135:702–708, 2004; Kwak et al., Plant Physiol 141:323–329, 2006; Torres et al., Plant Physiol 141:373–378, 2006; Miller et al., Physiol Plant 133:481–489, 2008). In this review, we highlight new discoveries in ROS-mediated abscisic acid (ABA) signaling. Drs. Daeshik Cho and June M. Kwak are the corresponding authors for this paper.     

Stomatal control of transpiration in the canopy of a clonal Eucalyptus grandis plantation

 Predawn leaf water potential, stomatal conductance and microclimatic variables were measured on 13 sampling days from November 1995 through August 1996 to determine how environmental and physiological factors affect water use at the canopy scale in a plantation of mature clonal Eucalyptus grandis Hill ex-Maiden hybrids in the State of Espirito Santo, Brazil. The simple ”big leaf” Penman-Monteith model was used to estimate canopy transpiration. During the study period the predawn leaf water potential varied from –0.4 to –1.3 MPa, with the minimum values observed in the winter months (June and August 1996), while the average estimated values for canopy conductance and canopy transpiration fell from 17.3 to 5.8 mm s^–1 and from 0.54 to 0.18 mm h^–1, respectively. On the basis of all measurements, the average value of the decoupling coefficient was 0.25. During continuous soil water shortage a proportional reduction was observed in predawn leaf water potential and in daily maximum values of stomatal conductance, canopy transpiration and decoupling coefficient. The results showed that water vapour exchange in this canopy is strongly dominated by the regional vapour pressure deficit and that canopy transpiration is controlled mainly by stomatal conductance. On a seasonal basis, stomatal conductance and canopy transpiration were mainly related to predawn leaf water potential and, thus, to soil moisture and rainfall. Good results were obtained with a multiplicative empirical model that uses values of photosynthetically active radiation, vapour pressure deficit and predawn leaf water potential to estimate stomatal conductance. Received: 10 June 1998 / Accepted: 20 July 1998     

A numerical method for renal models that represent tubules with abrupt changes in membrane properties

 The urine concentrating mechanism of mammals and birds depends on a counterflow configuration of thousands of nearly parallel tubules in the medulla of the kidney. Along the course of a renal tubule, cell type may change abruptly, resulting in abrupt changes in the physical characteristics and transmural transport properties of the tubule. A mathematical model that faithfully represents these abrupt changes will have jump discontinuities in model parameters. Without proper treatment, such discontinuities may cause unrealistic transmural fluxes and introduce suboptimal spatial convergence in the numerical solution to the model equations. In this study, we show how to treat discontinuous parameters in the context of a previously developed numerical method that is based on the semi-Lagrangian semi-implicit method and Newton's method. The numerical solutions have physically plausible fluxes at the discontinuities and the solutions converge at second order, as is appropriate for the method. Received: 13 November 2001 / Revised version: 28 June 2002 / Published online: 26 September 2002 This work was supported in part by the National Institutes of Health (National Institute of Diabetes and Digestive and Kidney Diseases, grant DK-42091.) Mathematics Subject Classification (2000): 65-04, 65M12, 65M25, 92-04, 92C35, 35-04, 35L45 Keywords or phrases: Mathematical models – Differential equations – Mathematical biology – Kidney – Renal medulla – Semi-Lagrangian semi-implicit     

Year class coexistence or competitive exclusion for strict biennials?

 We consider a discrete time model of semelparous biennial population dynamics. Interactions between individuals are modelled with the aid of an ``environmental' variable I. The impact on and the sensitivity to the environmental condition is age specific. The main result is that competitive exclusion between the year classes is possible as is their coexistence. For moderate values of the basic reproduction ratio R ₀ there is a strict dichotomy: depending on the other parameters we either find competitive exclusion or coexistence. We characterize rather precisely the patterns of age specific impact and sensitivity that lead to either of these outcomes. Received: 13 July 2001 / Revised version: 26 June 2002 / Published online: 19 November 2002 Key words or phrases: Competitive exclusion – Semelparous species – Periodical insects     

A genetic map of bovine Chromosome 7 with an interspecific hybrid backcross panel

A genetic linkage map of bovine Chromosome (Chr) 7 was generated with a Bos taurus×Bos gaurus interspecific hybrid backcross panel. This study included six previously mapped microsatellites and five unmapped expressed genes that were identified by PCR-based restriction fragment length variants (RFLVs). The gene order (from centromere to telomere) and the map distances (in centimorgans) are as follows: cen–BM2607–11.2–LDLR–3.6–AMH,CSF2–11.2–BP41–19–BM6117–19–SPARC–14.4–FGFA–15.5–BM1853–11.2–RASA–18.8–ILSTS006. Previous comparative synteny mapping demonstrated that bovine Chr 7 shares homologous regions with both HSA5q and HSA19p. A break or fusion between AMH and CSF2 in an ancestral chromosome is suggested to account for the current arrangement of these homologous segments in the human and bovine genomes. In this study, we demonstrate that a short proximal portion of BTA7 is homologous with HSA19p, while a larger distal portion of BTA7 is homologous with human Chr 5q. The orientation of these conserved human segments on BTA7 is also demonstrated. Our data show that the linear order of genes has not been conserved within the homologous region of HSA5 and BTA7, and one chromosomal translocation or inversion is proposed to account for this difference. Received: 11 June 1996 / Accepted: 9 November 1996     

On the dynamics of discrete food chains: low- and high-frequency behavior and optimality of chaos

 In this paper we derive and analyze a discrete version of Rosenzweig's (Am. Nat. 1973) food-chain model. We provide substantial analytical and numerical evidence for the general dynamical patterns of food chains predicted by De Feo and Rinaldi (Am. Nat. 1997) remaining largely unaffected by this discretization. Our theoretical analysis gives rise to a classification of the parameter space into various regions describing distinct governing dynamical behaviors. Predator abundance has a local optimum at the edge of chaos. Received: 13 August 1999 / Revised version: 12 March 2002 / Published online: 17 October 2002 Mathematics Subject Classification (1991): 92D40 Keywords or phrases: Discrete food-chain – Discrete Hopf (Neimark-Sacker) bifurcation – Pulsewise birth processes – Mean yield maximization – Nicholson-Bailey model     

Early ontogeny of a South Pacific gonostomatid fish <Emphasis Type="Italic">Sigmops longipinnis</Emphasis>

 During the R/V Hakuho-maru Cruise KH-95-2, Ocean Research Institute, University of Tokyo, from Tokyo, Japan to the South Pacific east of Australia (22° N–30° S; 126° E–176° E) from June to September, 1995, 77 unidentified gonostomatid larvae (5.5–20.0 mm SL) were collected south of 20° S with an IKMT net. They subsequently were identified as Sigmops longipinnis (Mukhacheva), and its ontogeny during the latter part of the larval stage (body form and proportions, photophores, pigmentation, and meristics) is described here. The larvae develop a species-specific row of melanophores along the midlateral line anterior to the caudal peduncle and another along the middorsal line from before the dorsal fin to just before the caudal fin. Received: June 24, 2002 / Revised: November 2, 2002 / Accepted: January 31, 2003     

Genome-wide meta-analysis for rheumatoid arthritis

Meta-analysis is being increasingly used as a tool for integrating data from different studies of complex phenotypes, because the power of any one study to identify causal loci is limited. We applied a novel meta-analytical approach (Loesgen et al. in Genet Epidemiol 21(Suppl 1):S142–S147, 2001) in compiling results from four studies of rheumatoid arthritis in Caucasians including two studies from NARAC (Jawaheer et al. in Am J Hum Genet 68:927–936, 2001; Jawaheer et al. in Arthritis Rheum 48:906–916, 2003), one study from the UK (MacKay et al. in Arthritis Rheum 46:632–639, 2001) and one from France (Cornelis et al. in Proc Natl Acad Sci USA 95:10746–10750, 1998). For each study, we obtained NPL scores by performing interval mapping (2 cM intervals) using GeneHunter2 (Kruglyak et al. in Am J Hum Genet 58:1347–1363, 1996; Markianos et al. in Am J Hum Genet 68:963–977, 2001). The marker maps differed among the three consortium groups, therefore, the marker maps were aligned after the interval mapping was completed and the NPL scores that were within 1 cM of each other were combined using the method of Loesgen et al. (Genet Epidemiol 21(Suppl 1):S142–S147, 2001) by calculating the weighted average of the NPL score. This approach avoids some problems in analysis encountered by using GeneHunter2 when some markers in the sample are not genotyped. This procedure provided marginal evidence (P<0.05) of linkage on chromosome 1, 2, 5 and 18, strong evidence (P<0.01) on chromosomes 8 and 16, and overwhelming evidence in the HLA region of chromosome 6.     

Dynamics of annual influenza A epidemics with immuno-selection

 The persistence of Influenza A in the human population relies on continual changes in the viral surface antigens allowing the virus to reinfect the same hosts every few years. The epidemiology of such a drifting virus is modeled by a discrete season-to-season map. During the epidemic season only one strain is present and its transmission dynamics follows a standard epidemic model. After the season, cross-immunity to next year's virus is determined from the proportion of hosts that were infected during the season. A partial analysis of this map shows the existence of oscillations where epidemics occur at regular or irregular intervals. Received: 16 February 2001 / Revised version: 11 June 2002 / Published online: 28 February 2003 Key words or phrases: Infectious disease – Influenza drift – Cross-immunity – Seasonal epidemics – Iterated map     

A discrete,size-structured model of phytoplankton growth in the chemostat: introduction of inhomogeneous cell division size

 We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. Then we run numerical simulations of the system, and compare the predictions of the model to data related to phytoplankton growth, whose obtention we discuss. We end with the identification of several parameters of the system. Received: 9 February 2000 / Revised version: 10 October 2001 / Published online: 23 August 2002 RID="*" ID="*" Present address: Department of Mathematics and Statistics, University of Victoria, B.C., Canada. e-mail: jarino@math.uvic.ca Key words or phrases: Chemostat – Structured population models – Discrete model – Inhomogeneous division size