Dynamical analysis of periodic bursting in piece-wise linear planar neuron model

A piece-wise linear planar neuron model, namely, two-dimensional McKean model with periodic drive is investigated in this paper. Periodical bursting phenomenon can be observed in the numerical simulations. By assuming the formal solutions associated with different intervals of this non-autonomous system and introducing the generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the bursting solution induced by the slowly varying periodic drive is presented. It is shown that, the discontinuous Hopf bifurcation occurring at the non-smooth boundaries, i.e., the bifurcation taking place at the thresholds of the stimulation, leads the alternation between the rest state and spiking state. That is, different oscillation modes of this non-autonomous system convert periodically due to the non-smoothness of the vector field and the slow variation of the periodic drive as well.     

Periodic solutions in a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor

We obtain necessary and sufficient conditions on the existence of a unique positive equilibrium point and a set of sufficient conditions on the existence of periodic solutions for a 3-dimensional system which arises from a model of competition between plasmid-bearing and plasmid-free organisms in a chemostat with an inhibitor. Our results improve the corresponding results obtained by Hsu, Luo, and Waltman [1]. Received: 20 November 1997 / Revised version: 12 February 1999 / Published online: 20 December 2000     

环境污染下脉冲输入恒化器模型动力学性质的研究

研究了环境污染下脉冲输入恒化器模型的动力学性质,得到了微生物灭绝周期解的全局稳定性和系统的持续生存.     

Resonance of the epidemic threshold in a periodic environment

Resonance between some natural period of an endemic disease and a seasonal periodic contact rate has been the subject of intensive study. This paper does not focus on resonance for endemic diseases but on resonance for emerging diseases. Periodicity can have an important impact on the initial growth rate and therefore on the epidemic threshold. Resonance occurs when the Euler-Lotka equation has a complex root with an imaginary part (i.e., a natural frequency) close to the angular frequency of the contact rate and a real part not too far from the Malthusian parameter. This is a kind of continuous-time analogue of work by Tuljapurkar on discrete-time population models, which in turn was motivated by the work by Coale on continuous-time demographic models with a periodic birth. We illustrate this resonance phenomenon on several simple epidemic models with contacts varying periodically on a weekly basis, and explain some surprising differences, e.g., between a periodic SEIR model with an exponentially distributed latency and the same model but with a fixed latency.     

一类具有时滞的生化反应模型的Hopf分支

在生物化工用肺炎杆菌与甘油转化为1,3-丙二醇的过程中会出现振荡现象,本文对出现振荡的机理进行了研究,根据生物意义,在模型中引入了时滞项,经分析和计算得到了产生Hopf分支的分支值以及分支值随控制参数变化的规律,并利用时滞微分方程的数值解法绘制了周期解的图形和相图。为这一过程的振荡机理研究提供了理论依据。并可用于指导工艺控制。     

Numerical study of the stability of some autowave solutions in a mathematical model of blood clotting

The stability of some types of solution for a set of equations representing a blood clotting model is examined using numerical methods of solving perturbation problems and the apparatus of adjoint equations. It is concluded that spiral waves are stable in this system, whereas traveling pulses are unstable at parameters corresponding to a chaotic regime in the punctual problem.     

Investigating sensitivity coefficients characterizing the response of a model of tau protein transport in an axon to model parameters

Evaluating the sensitivity of biological models to various model parameters is a critical step towards advancing our understanding of biological systems. In this paper, we investigated sensitivity coefficients for a model simulating transport of tau protein along the axon. This is an important problem due to the relevance of tau transport and agglomeration to Alzheimer’s disease and other tauopathies, such as some forms of parkinsonism. The sensitivity coefficients that we obtained characterize how strongly three observables (the tau concentration, average tau velocity, and the percentage of tau bound to microtubules) depend on model parameters. The fact that the observables strongly depend on a parameter characterizing tau transition from the retrograde to the anterograde kinetic states suggests the importance of motor-driven transport of tau. The observables are sensitive to kinetic constants characterizing tau concentration in the free (cytosolic) state only at small distances from the soma. Cytosolic tau can only be transported by diffusion, suggesting that diffusion-driven transport of tau only plays a role in the proximal axon. Our analysis also shows the location in the axon in which an observable has the greatest sensitivity to a certain parameter. For most parameters, this location is in the proximal axon. This could be useful for designing an experiment aimed at determining the value of this parameter. We also analyzed sensitivity of the average tau velocity, the total tau concentration, and the percentage of microtubule-bound tau to cytosolic diffusivity of tau and diffusivity of bound tau along the MT lattice. The model predicts that at small distances from the soma the effect of these two diffusion processes is comparable.     

Identifyability measures to select the parameters to be estimated in a solid‐state fermentation distributed parameter model

Process modeling can lead to of advantages such as helping in process control, reducing process costs and product quality improvement. This work proposes a solid‐state fermentation distributed parameter model composed by seven differential equations with seventeen parameters to represent the process. Also, parameters estimation with a parameters identifyability analysis (PIA) is performed to build an accurate model with optimum parameters. Statistical tests were made to verify the model accuracy with the estimated parameters considering different assumptions. The results have shown that the model assuming substrate inhibition better represents the process. It was also shown that eight from the seventeen original model parameters were nonidentifiable and better results were obtained with the removal of these parameters from the estimation procedure. Therefore, PIA can be useful to estimation procedure, since it may reduce the number of parameters that can be evaluated. Further, PIA improved the model results, showing to be an important procedure to be taken. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:905–917, 2016     

Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron

Transient increases in spontaneous firing rate of mesencephalic dopaminergic neurons have been suggested to act as a reward prediction error signal. A mechanism previously proposed involves subthreshold calcium-dependent oscillations in all parts of the neuron. In that mechanism, the natural frequency of oscillation varies with diameter of cell processes, so there is a wide variation of natural frequencies on the cell, but strong voltage coupling enforces a single frequency of oscillation under resting conditions. In previous work, mathematical analysis of a simpler system of oscillators showed that the chain of oscillators could produce transient dynamics in which the frequency of the coupled system increased temporarily, as seen in a biophysical model of the dopaminergic neuron. The transient dynamics was shown to be consequence of a slow drift along an invariant subset of phase space, with rate of drift given by a Lyapunov function. In this paper, we show that the same mathematical structure exists for the full biophysical model, giving physiological meaning to the slow drift and the Lyapunov function, which is shown to describe differences in intracellular calcium concentration in different parts of the cell. The duration of transients was long, being comparable to the time constant of calcium disposition. These results indicate that brief changes in input to the dopaminergic neuron can produce long lasting firing rate transients whose form is determined by intrinsic cell properties.     

The stabilizing role of the Sabbath in pre-monarchic Israel:a mathematical model

The three monotheistic cultures have many common institutions and some of them germinated in pre-monarchic Israel. Reasonably, the essential institutions were in place at that starting point; this work explores the possibility that the Sabbath is one of these institutions. Our mathematical examination points to the potential cultural, civic, and social role of the weekly Sabbath, that is, the Sabbath institution, in controlling deviation from social norms. It begins with an analogy between spread of transgression (defined as lack of conformity with social norms) and of biological infection. Borrowing well-known mathematical methods, we derive solution sets of social equilibrium and study their social stability. The work shows how a weekly Sabbath could in theory enhance social resilience in comparison with a similar assembly with a more natural and longer period, say between New Moon and Full Moon. The examination reveals that an efficient Sabbath institution has the potential to ensure a stable organization and suppress occasional appearances of transgression from cultural norms and boundaries. The work suggests the existence of a sharp threshold governed by the “Basic Sabbath Number ש₀”—a critical observance of the Sabbath, or large enough ש₀, is required to ensure suppression of transgression. Subsequently, the model is used to explore an interesting question: how old is the Sabbath? The work is interdisciplinary, combining anthropological concepts with mathematical analysis and with archaeological parallels in regards to the findings.

Electronic supplementary material

The online version of this article (doi:10.1007/s10867-014-9373-9) contains supplementary material, which is available to authorized users.     

The limitations of assessing impacts of land use changes on runoff with a distributed hydrological model: case study of the Hron River

A distributed hydrological model was applied for estimating changes in a runoff regime due to land use changes. The upper Hron river basin, which has an area of 1766 km² and is located in central Slovakia, was selected as the pilot basin. A physically-based rainfall-runoff model with distributed parameters was used for modelling runoff from rainfall and melting snow. The parameters of the model were estimated using climate data from 1981–2000 and from three digital map layers: a land-use map, soil map and digital elevation model. Several scenarios of changes in land use were prepared, and the runoff under the new land use conditions was simulated. Long-term mean annual runoff components and the design maximal mean daily discharges with a return period from 5 to 100 years under the previous and changed land uses were estimated and compared. The simulated runoff changes were confronted with expert judgments and estimates from the literature. Limitations of the use of distributed models for estimating land use changes are discussed.     

SANS/SAXS study of the BSA solvation properties in aqueous urea solutions via a global fit approach

We report on the solvation properties and intermolecular interactions of a model protein (bovine serum albumine, BSA) in urea aqueous solutions, as obtained by combining small-angle neutron and X-ray scattering experiments. According to a global fit strategy, all the whole set of scattering curves are analysed by considering a unique model which includes the BSA structure, the protein-protein interactions and the thermodynamic exchange process of water/urea molecules at the protein solvent interface. As a main result, the equilibrium constant that accounts for the difference in composition between the bulk solvent and the protein solvation layer is derived. Results confirm that urea preferentially sticks to the protein surface, inducing a noticeable change in both the repulsive and the attractive interaction potentials.     

Analysis of the bone metabolism by quantitative computer tomography and clinical chemistry in a primate model (Callithrix jacchus)

Background Common marmosets are widely used as experimental primates; however, little is still known about their bone physiology. Therefore, the aim of our study was to analyse body weight, age and bone‐specific blood parameters in relation to morphological bone parameters. Methods Fifty‐eight common marmosets were analysed for blood calcium (Ca), inorganic phosphor (P_i), alkaline phosphatase (AP) and 17‐β‐estradiol (E2). The examination of bone parameters was undertaken in the lumbar spine by computer tomography. Results There was a correlation between bone mineral density (BMD) and body weight, trabecular area ratio and polar moment as well as between BMD and AP or Ca (only males), whereas there were no correlations between BMD and age, P_i or E2 in all analysed genders. Conclusions Our data support the assumption that the common marmoset is a reliable primate model to study changes in bone metabolism because of the similarity of our results to humans.     

蝮蛇毒致小鼠肾损伤模型的建立

目的探索一种建立蝮蛇毒致肾损伤动物模型的方法。方法将清洁级12周龄雄性昆明小鼠72只,随机分为9组,每组8只,A、B、C组为不同时间的对照组（A-3h,B-3d,C-5d）;D、E、F组为蝮蛇毒1mg／kg肌注组（D-3h,E-3d,F-5d）;G、H、I组为蝮蛇毒2mg／kg肌注组（G-3h,H-3d,I-5d）。按照分组要求计算每组小鼠中每只小鼠需肌注的蝮蛇毒的总量．配制2种不同浓度的蝮蛇毒液．D、E、F、G、H、I组小鼠分别肌注不同浓度的蝮蛇毒液0．15ml,A、B、C组小鼠右臀部注射生理盐水0．15ml以进行对照。结果肌注蝮蛇毒后的小鼠均出现中毒症状,但各组小鼠均无死亡。E、F、H、I组小鼠的肾功能与正常对照组比较有明显差异（P〈0．05）。D、E、F、G、H、I组小鼠均有如下病理学改变：肾被膜下出血．肾皮质充血．肾小球充血。肾小囊扩大．肾小管周围毛细血管充血．肾小管肿胀。小管细胞变性等。结论肌注蝮蛇毒是一种建立蛇毒致小鼠肾损伤动物模型的较好方法。     

Time to the MRCA of a sample in a Wright-Fisher model with variable population size

Determining the expected distribution of the time to the most recent common ancestor of a sample of individuals may deliver important information about the genetic markers and evolution of the population. In this paper, we introduce a new recursive algorithm to calculate the distribution of the time to the most recent common ancestor of the sample from a population evolved by any conditional multinomial sampling model. The most important advantage of our method is that it can be applied to a sample of any size drawn from a population regardless of its size growth pattern. We also present a very efficient method to implement and store the genealogy tree of the population evolved by the Galton–Watson process. In the final section we present results applied to a simulated population with a single bottleneck event and to real populations of known size histories.     

Enhancement of antitumor effect by peptide vaccine therapy in combination with anti-CD4 antibody: Study in a murine model

PurposeThe clinical efficacy of cancer peptide vaccine therapy is insufficient. To enhance the anti-tumor effect of peptide vaccine therapy, we combined this therapy with an anti-CD4 mAb (GK1.5), which is known to deplete CD4⁺ cells, including regulatory T cells (Tregs).MethodsTo determine the treatment schedule, the number of lymphocyte subsets in the peripheral blood of mice was traced by flow cytometry after administration of anti-CD4 mAb. The ovalbumin (OVA)_257–264 peptide vaccine was injected intradermally and anti-CD4 mAb was administered intraperitoneally into C57BL/6 mice at different schedules. We evaluated the enhancement of OVA peptide-specific cytotoxic T lymphocyte (CTL) induction in the combination therapy using the ELISPOT assay, CD107a assay, and cytokine assay. We then examined the in vivo metastasis inhibitory effect by OVA peptide vaccine therapy in combination with anti-CD4 mAb against OVA-expressing thymoma (EG7) in a murine liver metastatic model.ResultsWe showed that peptide-specific CTL induction was enhanced by the peptide vaccine in combination with anti-CD4 mAb and that the optimized treatment schedule had the strongest induction effect of peptide-specific CTLs using an IFN-γ ELISPOT assay. We also confirmed that the CD107a⁺ cells secreted perforin and granzyme B and the amount of IL-2 and TNF produced by these CTLs increased when the peptide vaccine was combined with anti-CD4 mAb. Furthermore, metastasis was inhibited by peptide vaccines in combination with anti-CD4 mAb compared to peptide vaccine alone in a murine liver metastatic model.ConclusionThe use of anti-CD4 mAb in combination with the OVA peptide vaccine therapy increased the number of peptide-specific CTLs and showed a higher therapeutic effect against OVA-expressing tumors. The combination with anti-CD4 mAb may provide a new cancer vaccine strategy.     

Effects of changes in turbidity and phosphate influx on the ecosystem of the Ems estuary as obtained by a computer simulation model

In the Ems estuary the gradients in the concentration of nutrients and in turbidity (the factors that mainly determine the amount of carbon assimilated by phytoplankton) are steep. The effects of changing the turbidity in the estuary and the amount of phosphate discharged by the rivers Ems and Westerwoldsche Aa were analysed, using the simulation model developed by BOEDE (Biological Research Ems-Dollard estuary). The results of several sensitivity runs were compared with the standard run.A 50% reduction of turbidity led to a strong increase in phytoplanktonbiomass, especially in the inner parts of the estuary where turbidity is high. On average, the effects are two to three times larger for the inner part than for the outer part of the estuary. When the turbidity doubles the opposite occurs resulting in a significant decrease of phytoplankton biomass in the upper reaches. In the lower reaches of the estuary a 50% reduction in the river discharge of phosphate is largely compensated for by changes in phosphate transport from the North Sea. This results in a nearly unchanged primary production in the lower reaches as compared with the standard run.In the upper reaches a 50% reduction of phosphate loads results in a strongly reduced primary production.In general, the zooplankton groups (copepods and microzooplankton) are influenced less than the phytoplankton. Benthic fauna is hardly influenced, except for filter feeders; which are strongly affected by the total density of the particles, a parameter which also is directly related to turbidity.     

On the repair of oxidative damage to apoferritin: a model study with the flavonoids quercetin and rutin in aerated and deaerated solutions

Abstract

Ferritin (Ft) impairment through ^?O₂^–, H₂O₂, and ^?OH production occurs in the cases of ketoses, diabetes mellitus, acute intermittent porphyria and tyrosinemia. In addition to ^?Trp and TyrO^? radical production, ferrous iron liberation and Ft synthesis stimulation, site-specific oxidation reactions are induced leading to toxic iron accumulation in organs with high Ft content, for example, liver and brain. To elucidate the potential pathways to Ft recovery, repair of oxidative damage to horse spleen apoferritin (apoFt) and Ft by quercetin (QH) or rutin (RH) was studied in the presence and absence of oxygen. ^?Trp and TyrO^? radicals were produced in pulse radiolysis through apoFt oxidation by ^?Br₂^– radicals. QH and RH bind to apoFt on eight sites with binding constants of ?80,000 and ?32,000 M^?1, respectively. In deaerated solutions, a repair of apoFt radicals is observed involving both bound and free flavonoids. This repair occurs by a fast intra- and a slow inter-molecular electron transfer from bound and free flavonoids, respectively. With QH, the rate constants are 10⁴ s^–1 and 3.5 × 10⁷ M^–1 s^–1 for the intra- and intermolecular repair reactions, respectively. Oxygen does not interfere with repair of apoFt or Ft by bound QH but inhibits 90% of Ft repair by RH. These results taken together indicate that flavonoid antioxidants may help alleviate Ft impairment in diseases involving an oxidative stress.