Rotating wave solutions of the FitzHugh–Nagumo equations

This paper will treat the bifurcation and numerical simulation of rotating wave (RW) solutions of the FitzHugh-Nagumo (FHN) equations. These equations are often used as a simple mathematical model of excitable media. The dependence of the solutions on a uniformly applied current, and also on the diffusion coefficients or domain size will be studied. Ranges of applied current and/or diffusion coefficients in which RW solutions are observed will be described using bifurcation theory and continuation methods. The bifurcation of time-periodic solutions of these FHN equations without diffusion is described first. Similar methods are then used to find RW solutions on a circular ring and numerical simulations are described. These results are then extended to investigate RW solutions on annular rings of finite cross-section. Scaling arguments are used to show how the existence of solutions depends on either the diffusion coefficient or on the size of the region.     

Symmetric bursting behaviors in the generalized FitzHugh–Nagumo model

In the current paper, we have investigated the generalized FitzHugh–Nagumo model. We have shown that symmetric bursting behaviors of different types could be observed in this model with an appropriate recovery term. A modified version of this system is used to construct bursting activities. Furthermore, we have shown some numerical examples of delayed Hopf bifurcation and canard phenomenon in the symmetric bursting of super-Hopf/homoclinic type near its super-Hopf and homoclinic bifurcations, respectively.     

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh–Nagumo neuron

Based on the FitzHugh–Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.     

Efficient tuning of potential parameters for liquid–solid interactions

Spherical and cylindrical water droplets on silicon surface are studied to tune the silicon–oxygen interaction. We use molecular dynamics simulations to estimate the contact angle of two different shaped droplets. We found that the cylindrical droplets are independent of the line tension as their three phases curvature is equal zero. Additionally, we compare an analytical model, taking into account or not the Tolman length and we show that for spherical small size droplets, this length is important to be included, in contrast to cylindrical droplets in which the influence of the Tolman length is negligible. We demonstrate that the usual convenient way to exclude linear tension in the general case can give wrong results. Here, we consider cylindrical droplets, since their contact angle does not depend on the droplet size in the range of few to 10ths of nanometres. The droplets are stabilised due to the periodic boundary conditions. This allows us to propose a new parameterisation for nanoscale droplets, which is independent the size of the droplets or its shape, minimising at the same time the calculation procedure. With the proposed methodology, we can extract the epsilon parameter of the interaction potential between a liquid and a solid from the nanoscaled molecular simulation with only as input the macrosized experimental wetting angle for a given temperature.     

Polyamine-induced changes in symbiotic parameters of the Galega orientalis–Rhizobium galegae nitrogen-fixing system

Plants of goat's rue (Galega orientalis) inoculated with Rhizobium galegae strain HAMBI 540 were grown in the presence of putrescine (Put), spermidine (Spd) or spermine (Spm), and several symbiotic characteristics were investigated to delineate the influence of polyamines (PA) on this nitrogen-fixing system. All three PA exerted a concentration-dependent effect on the nodule parameters tested. The increment of nodulation ability and nodule biomass accumulation was extreme (from 2.4- to 4.0-fold) when plants were subjected to 10 and 50 M of various PA. However, at 100 M a negative effect was observed. The acetylene-reduction activity of nodulated roots was increased also in response to treatment with the lower PA concentrations. The level of nitrogenase activity supported by succinate was significantly higher in bacteroids isolated from PA-treated nodules than in bacteroids from control nodules. The symbiotic parameters were also dependent on the type of PA used; the most effective being the diamine Put, while Spm showed a smaller physiological effect with respect to the others. Polyamines altered the ultrastructure of Galega nodule infected cells. After treatment with these substances, pronounced changes in the relative volume of the main components of infected cells and their compartments were observed. The significance of the structural observations and morphometric analyses, their relationship to differences in nitrogen fixation and possible modes of action are discussed.     

The use of the logarithmic transformation in the calculation of the transport parameters of a system that obeys Michaelis–Menten kinetics

1. A logarithmic method is described for the calculation of the transport parameters, K(m) and V(max.)' of a biological system obeying Michaelis-Menten kinetics. 2. This logarithmic method leads to a way of estimating the transport parameters that has not apparently been used previously. It allows the separation of variance due to V(max.) from other variance, and so reduces the fiducial limits that can be placed on an estimation of K(m). 3. The results of studies on the transport of l-histidine and l-monoiodohistidine by rat intestinal sacs in vitro have been used to illustrate the application of the new method. Estimates of the transport parameters have also been made by two alternative procedures. The relative merits of the three methods are discussed.     

The potential therapeutic use of renin–angiotensin system inhibitors in the treatment of inflammatory diseases

Inflammation is a normal part of the immune response to injury or infection but its dysregulation promotes the development of inflammatory diseases, which cause considerable human suffering. Nonsteroidal anti-inflammatory agents are the most commonly prescribed agents for the treatment of inflammatory diseases, but they are accompanied by a broad range of side effects, including gastrointestinal and cardiovascular events. The renin–angiotensin system (RAS) is traditionally known for its role in blood pressure regulation. However, there is increasing evidence that RAS signaling is also involved in the inflammatory response associated with several disease states. Angiotensin II increases blood pressure by binding to angiotensin type 1 (AT₁) receptor, and direct renin inhibitors, angiotensin-converting enzyme (ACE) inhibitors and AT₁ receptor blockers (ARBs) are clinically used as antihypertensive agents. Recent data suggest that these drugs also have anti-inflammatory effects. Therefore, this review summarizes these recent findings for the efficacy of two of the most widely used antihypertensive drug classes, ACE inhibitors and ARBs, to reduce or treat inflammatory diseases such as atherosclerosis, arthritis, steatohepatitis, colitis, pancreatitis, and nephritis.     

Mechanical filtering by the boundary layer and fluid–structure interaction in the superficial neuromast of the fish lateral line system

A great diversity of aquatic animals detects water flow with ciliated mechanoreceptors on the body's surface. In order to understand how these receptors mechanically filter signals, we developed a theoretical model of the superficial neuromast in the fish lateral line system. The cupula of the neuromast was modeled as a cylindrical beam that deflects in response to an oscillating flow field. Its accuracy was verified by comparison with prior measurements of cupular deflection in larval zebrafish (Danio rerio). The model predicts that the boundary layer of flow over the body attenuates low-frequency stimuli. The fluid-structure interaction between this flow and the cupula attenuates high-frequency stimuli. The number and height of hair cell kinocilia and the dimensions of the cupular matrix determine the range of intermediate frequencies to which a neuromast is sensitive. By articulating the individual mechanical contributions of the boundary layer and the components of cupular morphology, this model provides the theoretical framework for understanding how a hydrodynamic receptor filters flow signals.     

The palynological assemblages from the J–K boundary beds of the Bureya Basin,Russian Far East

Palynological assemblages were studied from the coal-bearing Upper Jurassic (Talanja Formation) to the Lower Cretaceous (Dublikan Formation) deposits of the Bureya Basin, Russia. The palynological assemblages from the upper part of the Talanja Formation are dominated by gymnosperms, mainly Ginkgocycadophytus (up to 40%) and conifers related to Pinaceae (up to 70%). The contribution of non-seed plants is not great, but their diversity is considerable. The miospore assemblages of the Talanja sequence are characterized by the last appearance of the spore taxa Staplinisporites pocockii, Camptotriletes cerebriformis, Camptotriletes nitida, and Cingulatisporites sanguinolentus. The palynological assemblage from the Dublikan Formation is dominated by ferns (up to 84%), represented mainly by Cyathidites and Duplexisporites. Among gymnosperms the role of Classopollis increases (making up about 20%). Another feature is the first appearance of the spore taxa Stereisporites bujargiensis, Neoraistrickia rotundiformis, Contignisporites dorsostriatus, Appendicisporites tricostatus, and Concavissimisporites asper.     

Flora of the Kazanian–Urzhumian boundary in the middle Permian of the Russian Platform

Rich fossil plant localities in the upper Guadalupian and the lowermost Lopingian of the Russian Platform are confined to several discrete “levels” or “horizons” divided by intervals that are almost devoid of plant remains. One such “horizon” is located at the boundary between the Upper Kazanian and the Urzhumian of the regional stratigraphic scale. Numerous localities of this level can be grouped into two geographical clusters, the northern one being confined to the Kama River Basin, and the southern one to the Orenburg Region and Southern Bashkortostan. Regarding the southern localities, three floras that are seemingly successive in time can be distinguished. Against a common background of articulates (Paracalamites and Equisetites), the lowermost flora is characterized by the dominance of leaves of Rufloria (Cordaitanthales) with very rare conifers. Conifers (Quadrocladus, Sashinia, Dvinostrobus) and leaves of Phylladoderma (Peltaspermales) are the most abundant elements of the middle assemblage, whereas Rufloria leaves are very seldom found together with the peltasperm Ginkgophyllum and the conifer-like Steirophyllum. The uppermost flora is dominated by Odontopteridium and Ustyugia, two closely related genera of peltasperms, whereas cordaitaleans are totally absent. Comparison with the northern localities, which can be linked to the type sections of the Upper Kazanian and the Urzhumian, enables the dating of these assemblages in terms of the regional stratigraphic scale. All three floras prove to be confined to the uppermost Kazanian, and only the youngest one could also occur in the lowermost Urzhumian. As the stratigraphic ranges of all observed plant taxa exceed the total stratigraphic interval under study, the sequence of the floras seems to be caused by ecological (most likely climatic) factors rather than the actual evolution of plants. In particular, the observed gradual elimination of cordaitaleans confirms the general view on the extinction of this group on the Russian Platform. The southwestern boundary of the occurrence of cordaitaleans on the Russian Platform stretched from the southwest to the northeast, approximately parallel to the palaeolatitudes reconstructed on the basis of palaeomagnetic data. During the Guadalupian it moved to the northeast, which is to the north considering the position of the North Pole of that time. Cordaitaleans were the main peat-forming plants in the Late Palaeozoic of northern Pangea (in the Kuznetsk, Tunguska and Pechora Basins). So their retreat to the north was most likely a consequence and a reflection of the warming and drying of the climate.     

Evolution of the mammary gland from the innate immune system?

The mammary gland is a skin gland unique to the class Mammalia. Despite a growing molecular and histological understanding of the development and physiology of the mammary gland, its functional and morphological origins have remained speculative. Numerous theories on the origin of the mammary gland and lactation exist. The purpose of the mammary gland is to provide the newborn with copious amounts of milk, a unique body fluid that has a dual role of nutrition and immunological protection. Interestingly, antimicrobial enzymes, such as xanthine oxidoreductase or lysozyme, are directly involved in the evolution of the nutritional aspect of milk. We outline that xanthine oxidoreductase evolved a dual role in the mammary gland and hence provide new evidence supporting the hypothesis that the nutritional function of the milk evolved subsequent to its protective function. Therefore, we postulate that the mammary gland evolved from the innate immune system. In addition, we suggest that lactation partly evolved as an inflammatory response to tissue damage and infection, and discuss the observation that the two signaling pathways, NF-kB and Jak/Stat, play central roles in inflammation as well as in lactation.     

On the phylogeny of Early Cardioceratidae (Ammonoidea) and Cadoceratinae from Central Russia at the Bathonian–Callovian boundary

The phylogeny of the Middle Jurassic Cardioceratidae is reconstructed on the basis of a study of their shell morphology and analysis of their stratigraphic distribution. The phylogenetic lineage Cranocephalites → Arctocephalites → Arcticoceras → Paracadoceras is assigned to the subfamily Arctocephalitinae (Upper Bajocian–lowermost Callovian). The subfamily Cadoceratinae (Upper Bajocian–Callovian) also originating from Cranocephalites includes the phylogenetic lineage Greencephalites → Cadoceras → Longaeviceras; and lateral branches Chamoussetia and Platychamoussetia. The origin of the Early Callovian Eckhardites, also assigned to Cardioceratidae, is not established. The generic names Rondiceras and Cadochamoussetia are considered as junior synonyms of Cadoceras and Chamoussetia, respectively. The Early Callovian species Cadoceras bellabimba sp. nov. is described.     

Transient spatio-temporal dynamics of a diffusive plant–herbivore system with Neumann boundary conditions

In many existing predator–prey or plant–herbivore models, the numerical response is assumed to be proportional to the functional response. In this paper, without such an assumption, we consider a diffusive plant–herbivore system with Neumann boundary conditions. Besides stability of spatially homogeneous steady states, we also derive conditions for the occurrence of Hopf bifurcation and steady-state bifurcation and provide geometrical methods to locate the bifurcation values. We numerically explore the complex transient spatio-temporal behaviours induced by these bifurcations. A large variety of different types of transient behaviours including oscillations in one or both of space and time are observed.     

Climatic potential of δ18O of Abies spectabilis from the Nepal Himalaya

A 50-year tree-ring δ¹⁸O chronology of Abies spectabilis growing close to the tree line (3850 m asl) in the Nepal Himalaya is established to explore its dendroclimatic potential. Response function analysis with ambient climatic records revealed that tree-ring δ¹⁸O is primarily governed by rainfall during the monsoon season (June–September), and the regression model accounts for 35% of the variance in rainfall. Extreme dry years identified in instrumental weather data are detected in the δ¹⁸O chronology. Further, tree-ring δ¹⁸O is much more sensitive to rainfall fluctuations than other tree-ring parameters such as width and density typically used in dendroclimatology. Correlation analyses with Niño 3.4 SST reveal time-dependent behavior of ENSO–monsoon relationships.     

Nonmarine ostracodes at the Permian–Triassic boundary of the central part of the East European Platform

Extensive geological and paleontological materials from the upper Permian and the Lower Triassic of the East European Platform had been accumulated by the end of the 20th century. Recently obtained new data indicate the stratigraphic continuity of the East European Permian–Triassic succession. The Permian–Triassic boundary is in many sections associated with the boundary between the Zhukovian and Vokhmian regional stages. New stratigraphic data have led to the revision of the temporal distribution of Zhukovian and Vokhmian ostracodes. In contrast to previous ideas, the rapid development of genus Gerdalia already began in the Zhukovian time rather than in the Vokhmian. At the same time, the first Darwinula of the Triassic type also appeared in the Zhukovian. A proportion of the Permian species were found to cross the boundary between Zhukovian and Vokhmian. The degree of similarity between the Permian and Triassic ostracode assemblages turns out to be much higher than previously recognized.     

Synthesis and evaluation of the antioxidative potential of minoxidil–polyamine conjugates

A series of conjugates (MNX–CO–PA) of minoxidil (MNX) with the polyamines (PAs) putrescine (PUT), spermidine (SPD) and spermine (SPM) as well as dopamine were produced through activation of MNX with N,N′-carbonyldiimidazole, followed by reaction with dopamine or selectively protected PAs and acid-mediated deprotection. These conjugates together with conjugates of the general type MNX–PA or PA–MNX–PA, readily produced using literature protocols, were tested as antioxidants. The most potent inhibitors of lipid peroxidation were the conjugates MNX–SPM (2, 94%), SPM–MNX–SPM (4, 94%) and MNX–N⁴-SPD (7, 91%) and MNX (91%). The most powerful lipoxygenase (LOX) inhibitors were MNX (IC₅₀ = 20 μM) and the conjugates MNX–N⁸-SPD (9, IC₅₀ = 22.1 μM), MNX–CO–dopamine (11, IC₅₀ = 28 μM) and MNX–N¹-SPD (8, IC₅₀ = 30 μM). The most interesting conjugates 2, MNX–CO–PUT (5), 8 and 11 as well as MNX were generally found to exhibit weaker (22–36.5%) or no (conjugate 8) anti-inflammatory activity than indomethacin (47%) with the exception of MNX which showed almost equal potency (49%) to indomethacin. The cytocompatibility of conjugates and MNX at the highest concentration of 100 μM showed a survival percentage of 87–107%, with the exception of conjugates with SPM (compound 2) and MNX–CO–SPM (6), which showed considerable cytotoxicity (survival percentage 8–14%). Molecular docking studies were carried on conjugate 9 and the parent compound MNX and were found to be in accordance with our experimental biological results.     

The distribution of the P–M hybrid dysgenesis system in Drosophila melanogaster strains from Brazil

Wild-caught flies of Drosophila melanogaster from seven natural populations of extreme regions of Brazil (São Luís, MA; Teresina, PI; Rio Cipó, MG; Maringá, PR; São José do Rio Preto, SP; Joinville, SC; and Porto Alegre, RS) were studied with the purpose of evaluating hybrid dysgenesis due to mobilization of P elements and the regulatory capacity of the strains' cytotypes. Diagnostic crosses were made and the strains classified according to their P–M phenotypes. Four strains were classified as moderate P (MA, MG, PI, and SP), two as Q (PR and RS) and one as M′ (SC). Females of southern strains (PR, SC, and RS) presented in A crosses lower degrees of gonadal dysgenesis scores than those from northern strains (MA and PI).