A periodicity result for a nonlinear functional integral equation

In this paper, we study the effect of introducing a delay in a model of cell proliferation considered originally by O. Arino and M. Kimmel (J. Math. Biol. 27, 341–354 (1989)). We prove that slow oscillations take place and periodic oscillations appear for appropriate values of a parameter.     

Daphnia revisited: local stability and bifurcation theory for physiologically structured population models explained by way of an example

We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differential equation for the resource concentration). As many results for such systems are available (Diekmann et al. in SIAM J Math Anal 39:1023–1069, 2007), we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman–Metz Daphnia model (Kooijman and Metz in Ecotox Env Saf 8:254–274, 1984; de Roos et al. in J Math Biol 28:609–643, 1990) and a model introduced by Gurney–Nisbet (Theor Popul Biol 28:150–180, 1985) and Jones et al. (J Math Anal Appl 135:354–368, 1988), and next obtain various ecological insights by analytical or numerical studies of special cases.     

Molecular mobility in the gap regions of type 1 collagen fibrils

Recent studies of the structure of Type I collagen fibrils (Piez and Trus,Biosci. Rep. 1:801–810, 1981; Fraser, MacRae, Miller and Suzuki,J. Mol. Biol. 167:497–521, 1983) suggest that the segments of the collagen molecule which comprise the gap region are more mobile than those which comprise the overlap region. We have analyzed the distribution of amino acid residues and triplet types between the two regions, and find significantly non-uniform distributions for Ala, Gln, His, Hyp, Leu, Phe, and Tyr, and for triplets containing two imino acid residues. Taken together with the lower packing density in the gap region these observations provide a basis for understanding the greater mobility of the molecular segments in the gap region. In addition, we have examined the linear distribution of residue types in the two regions and also the hydropathy profile (Kyte and Doolittle,J. Mol. Biol. 157: 105–113, 1982). These reveal a segment of the gap region comprising helical residues 165–173, 399–407, 633–641 and 867–975 which has the highest hydropathy index, is devoid of charged residues, and contains very high proportions of Ala, Hyp and Phe.     

Galactosyltransferase activity is not localized to the brush border membrane of human small intestine

A recent report [Rothet al. (1985)J. Cell Biol. 100: 118–125], using immunocytochemical techniques, calimed that human duodenal galactosyltransferase is located predominantly on the external aspect of enterocyte brush border membranes. Analytical subcellular fractionation by sucrose density gradient centrifugation of human jejunum biopsy homogenates demonstrated that galactosyltransferase activity is localized to the Golgi fraction (equilibrium density of 1.14 g cm^–3) and is not found in significant amounts in the brush border membrane (equilibrium density of 1.22 g cm^–3).     

Existence of traveling wave solutions in a diffusive predator-prey model

 We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R ⁴ and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R ⁴ . The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem. Received: 25 May 2001 / Revised version: 5 August 2002 / Published online: 19 November 2002 RID="*" ID="*" Research was supported by the National Natural Science Foundations (NNSF) of China. RID="*" ID="*" Research was partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. On leave from the Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada. Mathematics Subject Classification (2000): 34C35, 35K57 Key words or phrases: Traveling wave solution – Wazewski set – Shooting argument – Hopf bifurcation Acknowledgements. We would like to thank the two referees for their careful reading and helpful comments.     

The biennial life strategy in a random environment

In a previous paper (J. Math. Biol. 26, 199–215 (1988)) we calculated the mean and variance of the long-run geometric growth rate of a discrete-time population model with two age classes in a random environment. The formula which was used in that paper as the starting point for the computation of the variance represents only the contribution of the one-period variances. Here we supplement these results by a calculation of the exact variance. All qualitative conclusions reached before are unaffected.     

Preparation of biologically active recombinant human progastrin(1-80)

The bacterial expression of human progastrin_6–80 has been reported previously [Baldwin, G.S. et al. (2001) J. Biol. Chem. 276: 7791-7796]. The aims of the present study were to prepare full-length recombinant human progastrin_1–80 and to compare its biological activity with that of progastrin_6–80 in vitro, to determine whether or not the N-terminal five amino acids contributed to activity. A fusion protein of glutathione-S-transferase and human progastrin_1–80 was expressed in Escherichia coli, collected on glutathione-agarose beads, and cleaved with enterokinase. Progastrin_1–80 was purified by reversed-phase and anion exchange HPLC and characterized by radioimmunoassay, amino acid sequencing, and mass spectrometry. No differences were detected in the extent of stimulation by progastrin_1–80 and progastrin_6–80 in proliferation and migration assays with the mouse gastric cell line IMGE-5. We conclude that residues 1–5 of progastrin_1–80 are not essential for biological activity.     

Persistence and global stability in a predator-prey model consisting of three prey genotypes with fertility differences

A model of a predator-prey interaction, where the prey population consists of three genotypes with random mating and continuous, nonlinear birth and death processes with fertility differences, is proposed. Sufficiency conditions giving the existence of a globally stable equilibrium on one of the coordinate planes are given. This extends results of Freedman and Waltman [J. Math. Biol. 6, 367–374 (1978) andRocky Mountain J. Math. 12, 779–784 (1982)]. In addition, conditions are derived which guarantee the persistence of all components of the populations. Research in part is from a Ph.D. thesis submitted to the Faculty of Graduate Studies and Research of the University of Alberta. Research partially supported by the Natural Sciences and Engineering Research Council of Canada, grant no. NSERC A4813.     

Statistics of canonical RNA pseudoknot structures

In this paper we study canonical RNA pseudoknot structures. We prove central limit theorems for the distributions of the arc-numbers of k-noncrossing RNA structures with given minimum stack-size τ over n nucleotides. Furthermore we compare the space of all canonical structures with canonical minimum free energy pseudoknot structures. Our results generalize the analysis of Schuster et al. obtained for RNA secondary structures [Hofacker, I.L., Schuster, P., Stadler, P.F., 1998. Combinatorics of RNA secondary structures. Discrete Appl. Math. 88, 207–237; Jin, E.Y., Reidys, C.M., 2007b. Central and local limit theorems for RNA structures. J. Theor. Biol. 250 (2008), 547–559; 2007a. Asymptotic enumeration of RNA structures with pseudoknots. Bull. Math. Biol., 70 (4), 951–970] to k-noncrossing RNA structures. Here k2 and τ are arbitrary natural numbers. We compare canonical pseudoknot structures to arbitrary structures and show that canonical pseudoknot structures exhibit significantly smaller exponential growth rates. We then compute the asymptotic distribution of their arc-numbers. Finally, we analyze how the minimum stack-size and crossing number factor into the distributions.     

Explaining how and explaining why: developmental and evolutionary explanations of dominance

There have been two different schools of thought on the evolution of dominance. On the one hand, followers of Wright [Wright S. 1929. Am. Nat. 63: 274–279, Evolution: Selected Papers by Sewall Wright, University of Chicago Press, Chicago; 1934. Am. Nat. 68: 25–53, Evolution: Selected Papers by Sewall Wright, University of Chicago Press, Chicago; Haldane J.B.S. 1930. Am. Nat. 64: 87–90; 1939. J. Genet. 37: 365–374; Kacser H. and Burns J.A. 1981. Genetics 97: 639–666] have defended the view that dominance is a product of non-linearities in gene expression. On the other hand, followers of Fisher [Fisher R.A. 1928a. Am. Nat. 62: 15–126; 1928b. Am. Nat. 62: 571–574; Bürger R. 1983a. Math. Biosci. 67: 125–143; 1983b. J. Math. Biol. 16: 269–280; Wagner G. and Burger R. 1985. J. Theor. Biol. 113: 475–500; Mayo O. and Reinhard B. 1997. Biol. Rev. 72: 97–110] have argued that dominance evolved via selection on modifier genes. Some have called these “physiological” versus “selectionist,” or more recently [Falk R. 2001. Biol. Philos. 16: 285–323], “functional,” versus “structural” explanations of dominance. This paper argues, however, that one need not treat these explanations as exclusive. While one can disagree about the most likely evolutionary explanation of dominance, as Wright and Fisher did, offering a “physiological” or developmental explanation of dominance does not render dominance “epiphenomenal,” nor show that evolutionary considerations are irrelevant to the maintenance of dominance, as some [Kacser H. and Burns J.A. 1981. Genetics 97: 639–666] have argued. Recent work [Gilchrist M.A. and Nijhout H.F. 2001. Genetics 159: 423–432] illustrates how biological explanation is a multi-level task, requiring both a “top-down” approach to understanding how a pattern of inheritance or trait might be maintained in populations, as well as “bottom-up” modeling of the dynamics of gene expression.     

Traveling wave solutions from microscopic to macroscopic chemotaxis models

In this paper, we study the existence and nonexistence of traveling wave solutions for the one-dimensional microscopic and macroscopic chemotaxis models. The microscopic model is based on the velocity jump process of Othmer et al. (SIAM J Appl Math 57:1044–1081, 1997). The macroscopic model, which can be shown to be the parabolic limit of the microscopic model, is the classical Keller–Segel model, (Keller and Segel in J Theor Biol 30:225–234; 377–380, 1971). In both models, the chemosensitivity function is given by the derivative of a potential function, Φ(v), which must be unbounded below at some point for the existence of traveling wave solutions. Thus, we consider two examples: F(v) = lnv{\Phi(v) = \ln v} and F(v) = ln[v/(1-v)]{\Phi(v) = \ln[v/(1-v)]}. The mathematical problem reduces to proving the existence or nonexistence of solutions to a nonlinear boundary value problem with variable coefficient on \mathbb R{\mathbb R}. The main purpose of this paper is to identify the relationships between the two models through their traveling waves, from which we can observe how information are lost, retained, or created during the transition from the microscopic model to the macroscopic model. Moreover, the underlying biological implications of our results are discussed.     

The Conserved Motif in Hydrophilic Loop 2/3 and Loop 8/9 of the Lactose Permease of Escherichia coli. Analysis of Suppressor Mutations

The major facilitator superfamily (MFS) of transport proteins, which includes the lactose permease of Escherichia coli, contains a conserved motif G-X-X-X-D/E-R/K-X-G-R/K-R/K in the loops that connect transmembrane segments 2 and 3, and transmembrane segments 8 and 9. In three previous studies (Jessen-Marshall, A.E., & Brooker, R.J. 1996. J. Biol. Chem. 271:1400–1404; Jessen-Marshall, A.E., Parker, N., & Brooker, R.J. 1997. J. Bacteriol. 179:2616–2622; and Pazdernik, N., Cain, S.M., & Brooker, R.J. 1997. J. Biol. Chem. 272:26110–26116), suppressor mutations at twenty different sites were identified which restore function to mutant permeases that have deleterious mutations in the conserved loop 2/3 or loop 8/9 motif. In the current study, several of these second-site suppressor mutations have been separated from the original mutation in the conserved motif. The loop 2/3 suppressors were then coupled to a loop 8/9 mutation (P280L) and the loop 8/9 suppressors were coupled to a loop 2/3 mutation (i.e., G64S) to determine if the suppressors could restore function only to a loop 2/3 mutation, a loop 8/9 mutation, or both. The single parent mutations changing the first position in loop 2/3 (i.e., G64S) and loop 8/9 (i.e., P280L) had less than 4% lactose transport activity. Interestingly, most of the suppressors were very inhibitory when separated from the parent mutation. Two suppressors, A50T and G370V, restored substantial transport activity when individually coupled to the mutation in loop 2/3 and also when coupled to the corresponding mutation in loop 8/9. In other words, these suppressors could alleviate a defect imposed by mutations in either half of the permease. From a kinetic analysis, these suppressors were shown to exert their effects by increasing the V _max values for lactose transport compared with the single G64S and P280L strains. These results are discussed within the context of our model in which the two halves of the lactose permease interact at a rotationally symmetrical interface, and that lactose transport is mediated by conformational changes at the interface. Received: 18 November 1999/Revised: 11 April 2000     

Homologous IRCM-Serine Protease 1 from pituitary,heart atrium and ventricle: A common pro-hormone maturation enzyme?

IRCM-Serine Protease 1 (IRCM-SP1) has recently been isolated and characterized from porcine pituitary anterior and neurointermediate lobes (Cromlishet al., 1986a,J. Biol. Chem. 261:10850–10858; Cromlishet al., 1986b,J. Biol. Chem. 261:10859–10870). This pituitary serine protease was shown to selectively cleave human proopiomelanocortin (POMC)-derived peptides at both pairs of basic residues and C-terminal to specific Arg residues, all known to be cleavedin vivo. Here, a similar enzyme was isolated from rat heart atria and ventricles. Rat IRCM-SP1 was shown to be highly specific for the same cleavage sites in POMC, as the porcine pituitary homologue. Furthermore, the rat and the porcine enzymes cleave rat pro-Atrial Natriuretic Factor (pro-ANF 1–126) to yield ANF 103–126, 102–126 and 99–126 in that order of preference. This suggests thatin vitro the cleavage sites preferred in pro-ANF resemble those found in brain and hypothalamus. The enzyme is nine times more abundant in atria versus ventricles/mg protein. It is concluded that IRCM-SP1, could well represent a common pro-hormone maturation enzyme for POMC and Pro-ANF and possibly many other pro-hormones.     

Preformed GroES Oligomers Are Not Required as Functional Cochaperonins

We have previously shown that the C-terminal sequence of GroES is required for oligomerization [Seale and Horowitz (1995), J. Biol. Chem. 270, 30268–30270]. In this report, we have generated a C-terminal deletion mutant of GroES with a significantly destabilized oligomer and have investigated its function in the chaperonin-assisted protein folding cycle. Removal of the two C-terminal residues of GroES results in a cochaperonin [GroESD(96–97)] that is monomeric at concentrations where GroES function is assessed. Using equilibrium ultracentrifugation, we measured the dissociation constant for the oligomer–monomer equilibrium to be 7.3×10^–34M⁶. The GroESD(96–97) is fully active as a cochaperonin. This mutant is able to inhibit the ATPase activity of GroEL to levels comparable to wild-type GroES. It is also able to assist the refolding of urea-denatured rhodanese by GroEL. While GroESD(96–97) can function at levels comparable to wild-type GroES, higher concentrations of mutant are required to produce the same effect. These results support the idea that the preformed GroES heptamer is not required for function, but they suggest that the oligomeric cochaperonin is most efficient.     

Anomalous spreading speeds of cooperative recursion systems

This work presents an example of a cooperative system of truncated linear recursions in which the interaction between species causes one of the species to have an anomalous spreading speed. By this we mean that this species spreads at a speed which is strictly greater than its spreading speed in isolation from the other species and the speeds at which all the other species actually spread. An ecological implication of this example is discussed in Sect. 5. Our example shows that the formula for the fastest spreading speed given in Lemma 2.3 of our paper (Weinberger et al. in J Math Biol 45:183–218, 2002) is incorrect. However, we find an extra hypothesis under which the formula for the faster spreading speed given in (Weinberger et al. in J Math Biol 45:183–218, 2002) is valid. We also show that the hypotheses of all but one of the theorems of (Weinberger et al. in J Math Biol 45:183–218, 2002) whose proofs rely on Lemma 2.3 imply this extra hypothesis, so that all but one of the theorems of (Weinberger et al. in J Math Biol 45:183–218, 2002) and all the examples given there are valid as they stand.     

Germicide capacity of macrophages (MØ) in the Antarctic fish Notothenia coriiceps (Richardson, 1844) at 0°C

The germicide capability of the macrophage (MØ) of the Antarctic fish Notothenia coriiceps is demonstrated using fluorescence microscopy for the first time. The MØs were able to kill microorganisms by intracellular mechanism and this killing can be stimulated by oyster-derived glycogen. Although the phagocytosis index is lower than in temperate water fish species, this work demonstrates that non-specific defence mechanism plays an important role in the polar environment. There are some studies on inflammation in N. coriiceps [Silva et al. (1998) Polar Biol 20:206–212], parasite–host relation [Silva et al. (1999) Polar Biol 22:417–424] and phagocytosis [Silva et al. (2002) J Fish Biol 60:466–478]. These previous studies have shown that the MØ were able to identify biotic and abiotic factors. However, it can be of interest to study the activity of MØ in microorganism killing, and this work adds new insights of this fundamental process under Antarctic temperatures.     

The complete classification for dynamics in a homosexually-transmitted disease model

A sexually-transmitted disease model for two strains of pathogen in a one-sex, heterogeneously-mixing population was proposed by Li et al. in (J Math Biol 10:1037–1052, 1986). The sufficient and necessary conditions for coexistence and the sufficient conditions for stability of the boundary equilibria were provided. This paper will present a thorough classification of dynamics for this model in terms of the first and second so called reproductive numbers of infection in strains I and J. This classification not only solves a conjecture proposed in (Li et al., J Math Biol 10:1037–1052, 1986) but also gives the sufficient and necessary conditions for the competitive exclusion. Supported by the NSF of China grants 10531030 and 10671143.     

The duration of a sequence of epidemics

The typical duration of an epidemic in a sequence of linearly ordered populations shows a surprising nonmonotonic behaviour with respect to population size, which was noted by Swinton (1998) [Bull. Math. Biol., 60, 215–230]. This paper gives the sketch of a proof of the phenomenon.     

High-Resolution Linkage Map of Mouse Chromosome 13 in the Vicinity of the Host Resistance LocusLgn1

Natural resistance of inbred mouse strains to infection withLegionella pneumophilais controlled by the expression of a single dominant gene on chromosome 13, designatedLgn1.The genetic difference atLgn1is phenotypically expressed as the presence or absence of intracellular replication ofL. pneumophilain host macrophages. In our effort to identify theLgn1gene by positional cloning, we have generated a high-resolution linkage map of theLgn1chromosomal region. For this, we have carried out extensive segregation analysis in a total of 1270 (A/J × C57BL/6J) × A/J informative backcross mice segregating the resistance allele of C57BL/6J and the susceptibility allele of A/J. Additional segregation analyses were carried out in three preexisting panels of C57BL/6J ×Mus spretusinterspecific backcross mice. A total of 39 DNA markers were mapped within an interval of approximately 30 cM overlapping theLgn1region. Combined pedigree analyses for the 5.4-cM segment overlappingLgn1indicated the locus order and the interlocus distances (in cM):D13Mit128–(1.4)–D13Mit194–(0.1)–D13Mit147–(0.9)–D13Mit36–(0.9)–D13Mit146–(0.2)–Lgn1/D13Mit37–(1.0)–D13Mit70.Additional genetic linkage studies of markers not informative in the A/J × C57BL/6J cross positionedD13Mit30, -72, -195,and-203, D13Gor4, D13Hun35,andMtap5in the immediate vicinity of theLgn1locus. The marker density and resolution of this genetic linkage map should allow the construction of a physical map of the region and the isolation of YAC clones overlapping the gene.     

Accuracy of Secondary Structure and Solvent Accessibility Predictions for a Clostridial Neurotoxin C-Fragment

Earlier studies used Rost and Sander's artificial neural network [(1993a), J. Mol. Biol. 232, 584–599] to predict the secondary structures [Lebeda and Olson (1994), Proteins 20, 293–300] and residue solvent accessibilities [Lebeda and Olson (1997), J. Protein Chem. 16, 607–618] of the clostridial neurotoxins. Because the X-ray crystal structure of the 50-kDa C-terminal half of the heavy chain of tetanus toxin was recently determined, this report evaluates the accuracy of these network-derived predictions. For this predominantly -strand-containing fragment, predictions, on a per-residue basis, for both secondary structure and solvent accessibility were about 70% accurate. A more flexible and realistic analysis based on overlapping segments yielded accuracies of over 80% for the three-state secondary structure and for the two-state accessibility predictions. Because the accuracies of these predictions are comparable to those made by Rost and Sander using a dataset of 126 nonhomologous globular proteins, our predictions provide a quantitative foundation for gauging the results when building by homology the structures of related proteins.