Interspecific influence on mobility and Turing instability

In this paper we formulate a multi-patch multi-species model in which the percapita emigration rate of one species depends on the density of some other species. We then focus on Turing instability to examine if and when this cross-emigration response has crucial effects. We find that the type of interaction matters greatly. In the case of competition a cross-emigration response promotes pattern formation by exercising a destabilizing influence; in particular, it may lead to diffusive instability provided that the response is sufficiently strong, which contrasts sharply with the well-known fact that the standard competition system does not exhibit Turing instability. In the case of prey-predator or activator-inhibitor interaction it acts against pattern formation by exerting a stabilizing effect; in particular, the diffusive instability, even though it may happen in a standard system, never occurs when the response is sufficiently strong. We conclude that the cross-emigration response is an important factor that should not be ignored when pattern formation is the issue.     

The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach

Our starting point is a selection-mutation equation describing the adaptive dynamics of a quantitative trait under the influence of an ecological feedback loop. Based on the assumption of small (but frequent) mutations we employ asymptotic analysis to derive a Hamilton-Jacobi equation. Well-established and powerful numerical tools for solving the Hamilton-Jacobi equations then allow us to easily compute the evolution of the trait in a monomorphic population when this evolution is continuous but also when the trait exhibits a jump. By adapting the numerical method we can, at the expense of a significantly increased computing time, also capture the branching event in which a monomorphic population turns dimorphic and subsequently follow the evolution of the two traits in the dimorphic population. From the beginning we concentrate on a caricatural yet interesting model for competition for two resources. This provides the perhaps simplest example of branching and has the great advantage that it can be analyzed and understood in detail.     

Karl-Peter Hadeler: His legacy in mathematical biology

Journal of Mathematical Biology - Karl-Peter Hadeler is a first-generation pioneer in mathematical biology. His work inspired the contributions to this special issue. In this preface we give a...     

An extension of the classification of evolutionarily singular strategies in Adaptive Dynamics

The existing classification of evolutionarily singular strategies in Adaptive Dynamics (Geritz et al. in Evol Ecol 12:35–57, 1998; Metz et al. in Stochastic and spatial structures of dynamical systems, pp 183–231, 1996) assumes an invasion exponent that is differentiable twice as a function of both the resident and the invading trait. Motivated by nested models for studying the evolution of infectious diseases, we consider an extended framework in which the selection gradient exists (so the definition of evolutionary singularities extends verbatim), but where the invasion fitness may lack the smoothness necessary for the classification à la Geritz et al. We derive the classification of singular strategies with respect to convergence stability and invadability and determine the condition for the existence of nearby dimorphisms. In addition to ESSs and invadable strategies, we observe what we call one-sided ESSs: singular strategies that are invadable from one side of the singularity but uninvadable from the other. Studying the regions of mutual invadability in the vicinity of a one-sided ESS, we discover that two isoclines spring in a tangent manner from the singular point at the diagonal of the mutual invadability plot. The way in which the isoclines unfold determines whether these one-sided ESSs act as ESSs or as branching points. We present a computable condition that allows one to determine the relative position of the isoclines (and thus dimorphic dynamics) from the dimorphic as well as from the monomorphic invasion exponent and illustrate our findings with an example from evolutionary epidemiology.     

PACAP mediates the neural proliferative pathway of Mastomys enterochromaffin-like cell transformation.

BACKGROUND AND AIM: Pituitary adenylate-cyclase activating peptide (PACAP) is a more potent proliferative agent than gastrin for rat enterochromaffin-like (ECL) cell proliferation in vitro. The role of this neurotransmitter during gastrin-mediated ECL cell tumor formation and gastrin-autonomous ECL cell neoplasia is unknown. METHODS AND RESULTS: ECL cell transformation was induced in the Mastomys using 16 wk H2 receptor blockade of acid inhibition. Examination of the epithelial fundic mucosa demonstrated that PACAP-immunoreactivity significantly increased in the tumor mucosa compared to the na?ve stomach, and was associated with ECL cells. Na?ve and tumor ECL cells were then purified (approximately 95%) from Mastomys and the presence of all three PACAP/VPAC receptor subtypes was demonstrated by polymerase chain-reaction amplification. Thereafter, cells were maintained in short-term (48 h) primary cultures. PACAP significantly (p<0.05) increased 24 h bromo-deoxyuridine uptake (approximately 4-fold) in both cell types with estimated EC(50) values of approximately 4x10(-16) M and approximately 2x10(-16) M, respectively. Specific receptor antagonists (PAC1/VPAC1) of PACAP competitively inhibited these proliferative effects in na?ve cells. Oligonucleotide antisense directed against PAC1 significantly inhibited PACAP-stimulated DNA synthesis by approximately 85% (p<0.05) in tumor cells. CONCLUSION: PACAP is a potent and effective modulator of ECL cell proliferation. The expression of this neuropeptide and its receptors, particularly PAC1, suggest the existence of a neural regulatory pathway of ECL cell proliferation and transformation.     

Conservative Structure of the Plaque Matrix Protein of Mussels in the Genus Mytilus

: The complementary DNA encoding the byssal plaque matrix protein (fp-2) of the mussel Mytilus coruscus was isolated. The predicted amino acid sequence (474 amino acids) consists of four parts: the signal peptide, the amino-terminal nonrepetitive domain, the central repetitive domain containing 11 repeats of an epidermal growth factor–like motif, and the carboxy-terminal nonrepetitive domain. The amino acid sequence is 82.7%, similar to that of fp-2 of Mytilus galloprovincialis, and the basic structure including number and motif of repeats is highly conservative. Amino acid substitutions are less frequent in ``consensus positions' of the central repetitive domain (13.1%), and most of them are changes from irregular amino acids to regular ones. Thus, the structure of fp-2 was found to be conservative between species. It was presumed that the basic structure of fp-2 is unchangeable to maintain the flexible and durable matrix structure and that variation is not required because fp-2 is protected by other surface proteins.     

Design and development of a fluorescent probe for monitoring hydrogen peroxide using photoinduced electron transfer

A novel fluorescent probe, 7-hydroxy-2-oxo-N-(2-(diphenylphosphino)ethyl)-2H-chromene-3-carboxamide (DPPEA-HC) was developed for use in monitoring hydrogen peroxide (H2O2) production. DPPEA-HC, which consists of a diphenylphosphine moiety and a 7-hydroxycoumarin moiety, reacts with H2O2 to form DPPEA-HC oxide, which is analogous to the reaction of triphenylphosphine with hydroperoxides such as H2O2 to form triphenylphosphine oxide. Photoinduced electron transfer (PET) was applied in the design of DPPEA-HC. Since the diphenylphosphine moiety and the 7-hydroxycoumarin moiety would act as the PET donor and the acceptor, respectively, it would be expected that DPPEA-HC would rationally cancel the PET process via the formation of DPPEA-HC oxide, based on the calculated energy levels of the donor and the acceptor moieties using the B3LYP/6-31G*//AM1 method. The fluorescence intensity of DPPEA-HC increased on the addition of a H2O2 solution in 100 mM sodium phosphate buffer (pH7.4), as predicted from the energy level calculation and a good correlation between increase in the fluorescence of DPPEA-HC and the concentration of H2O2 was observed. DPPEA-HC was also fluoresced by H2O2, which was enzymatically produced in xanthine/xanthine oxidase/superoxide dismutase (XA/XOD/SOD) system. The increase in the fluorescence of DPPEA-HC in the presence of H2O2 immediately ceased on the addition of catalase (CAT), which catalyzes the disproportionation of H2O2. In addition, DPPEA-HC was found to have a much higher selectivity for H2O2 and a greater resistance to autoxidation than 2',7'-dichlorodihydrofluoresein (DCFH). Time-resolved fluorescence measurements of DPPEA-HC and DPPEA-HC oxide confirmed that the fluorescence off/on switching mechanism of DPPEA-HC is based on the PET on/off control.     

Predator migration in response to prey density: What are the consequences?

A predator-prey metapopulation model with two identical patches and only migration of the predator is investigated. Local predator-prey interaction is described by the so-called Rosenzweig-MacArthur model, while the migration term of the predator is put in a nonlinear form, which is derived by extending the Holling time budget argument to migration. In particular, a dimensionless parameter theta is introduced to quantify the migration tendency of predators while they are handling their prey, which gives rise to a family of models connecting two extremes: predators have no inclination to migrate while handling prey (theta = 0) and standard diffusion (theta = 1). Various aspects of the model, including changes in the number and the stability of equilibria and limit cycles, are investigated. We then focus on the key question: "Does spatial structure lead to a substantial damping of the violent oscillations exhibited by many predator-prey models?". It is known that the answer is "yes" if one adopts standard diffusion (theta = 1). However, we present substantial evidence that the answer is "no" if one takes theta = 0. We conclude that the migration submodel is an important constituent of a spatial predator-prey model and that the issue deserves scrutiny, both experimentally and theoretically.