Simplification of Stochastic Chemical Reaction Models with Fast and Slow Dynamics

Biological systems often involve chemical reactions occurring in low-molecule-number regimes, where fluctuations are not negligible and thus stochastic models are required to capture the system behaviour. The resulting models are generally quite large and complex, involving many reactions and species. For clarity and computational tractability, it is important to be able to simplify these systems to equivalent ones involving fewer elements. While many model simplification approaches have been developed for deterministic systems, there has been limited work on applying these approaches to stochastic modelling. Here, we describe a method that reduces the complexity of stochastic biochemical network models, and apply this method to the reduction of a mammalian signalling cascade and a detailed model of the process of bacterial gene expression. Our results indicate that the simplified model gives an accurate representation for not only the average numbers of all species, but also for the associated fluctuations and statistical parameters.     

Stochastic modelling of animal movement

Modern animal movement modelling derives from two traditions. Lagrangian models, based on random walk behaviour, are useful for multi-step trajectories of single animals. Continuous Eulerian models describe expected behaviour, averaged over stochastic realizations, and are usefully applied to ensembles of individuals. We illustrate three modern research arenas. (i) Models of home-range formation describe the process of an animal ‘settling down’, accomplished by including one or more focal points that attract the animal''s movements. (ii) Memory-based models are used to predict how accumulated experience translates into biased movement choices, employing reinforced random walk behaviour, with previous visitation increasing or decreasing the probability of repetition. (iii) Lévy movement involves a step-length distribution that is over-dispersed, relative to standard probability distributions, and adaptive in exploring new environments or searching for rare targets. Each of these modelling arenas implies more detail in the movement pattern than general models of movement can accommodate, but realistic empiric evaluation of their predictions requires dense locational data, both in time and space, only available with modern GPS telemetry.     

异化金属还原菌的研究进展

微生物利用金属氧化物作呼吸作用的最终电子受体是一种新的代谢途径。该过程微生物利用有机底物异化还原金属氧化物进行生长代谢。异化金属还原菌对于研究探索古生物呼吸形式、界定生命的上限温度等生命科学问题具有重要研究价值,同时在生物整治、微生物燃料电池等方面具有广阔的应用前景。对异化金属还原菌进行了综述,并对这类菌的研究应用给了评述和展望。     

Reduction of diverse electron acceptors by Aeromonas hydrophila

Aeromonas hydrophila ATCC 7966 grew anaerobically on glycerol with nitrate, fumarate, Fe(III), Co(III), or Se(VI) as the sole terminal electron acceptor, but did not ferment glycerol. Final cell yields were directly proportional to the amount of terminal electron acceptor provided. Twenty-four estuarine mesophilic aeromonads were isolated; all reduced nitrate, Fe(III), or Co(III), and five strains reduced Se(VI). Dissimilatory Fe(III) reduction by A. hydrophila may involve cytochromes. Difference spectra obtained with whole cells showed absorption maxima at wavelengths characteristic of c-type cytochromes (419, 522, and 553 nm). Hydrogen-reduced cytochromes within intact cells were oxidized by the addition of Fe(III) or nitrate. Studies with respiratory inhibitors yielded results consistent with a respiratory chain involving succinate (flavin-containing) dehydrogenase, quinones and cytochromes, and a single Fe(III) reductase. Neither anaerobic respiration nor dissimilatory metal reduction by members of the genus Aeromonas have been reported previously. Received: 24 June 1997 / Accepted: 20 October 1997     

绿化带降噪机理及模型研究进展

介绍了目前绿化带降噪机理及不同配置模式的绿化带降噪效果的研究进展。从单变量和多变量两方面总结了已有的绿化带降噪模型,普适性较差,精确性较低是目前已有模型存在的主要问题。同时,对绿化带降噪模型的研究前景进行了展望,认为可以使用非线性生态模型找出影响绿化带降噪量的主要参数,并分析主要参数与降噪量的关系,最终拟合出不同绿化带降噪量的非线性预测模型,从而指导道路绿化带的设计与建设。     

Approach for Qualitative Validation Using Aggregated Data for a Stochastic Simulation Model of the Spread of the Bovine Viral-Diarrhoea Virus in a Dairy Cattle Herd

Qualitative validation consists in showing that a model is able to mimic available observed data. In population level biological models, the available data frequently represent a group status, such as pool testing, rather than the individual statuses. They are aggregated. Our objective was to explore an approach for qualitative validation of a model with aggregated data and to apply it to validate a stochastic model simulating the bovine viral-diarrhoea virus (BVDV) spread within a dairy cattle herd. Repeated measures of the level of BVDV-specific antibodies in the bulk-tank milk (total milk production of a herd) were used to summarise the BVDV herd status. First, a domain of validation was defined to ensure a comparison restricted to dynamics of pathogen spread well identified among observed aggregated data (new herd infection with a wide BVDV spread). For simulations, scenarios were defined and simulation outputs at the individual animal level were aggregated at the herd level using an aggregation function. Comparison was done only for observed data and simulated aggregated outputs that were in the domain of validation. The validity of our BVDV model was not rejected. Drawbacks and ways of improvement of the approach are discussed.     

Evolutionary Branching in a Finite Population: Deterministic Branching vs. Stochastic Branching

Adaptive dynamics formalism demonstrates that, in a constant environment, a continuous trait may first converge to a singular point followed by spontaneous transition from a unimodal trait distribution into a bimodal one, which is called “evolutionary branching.” Most previous analyses of evolutionary branching have been conducted in an infinitely large population. Here, we study the effect of stochasticity caused by the finiteness of the population size on evolutionary branching. By analyzing the dynamics of trait variance, we obtain the condition for evolutionary branching as the one under which trait variance explodes. Genetic drift reduces the trait variance and causes stochastic fluctuation. In a very small population, evolutionary branching does not occur. In larger populations, evolutionary branching may occur, but it occurs in two different manners: in deterministic branching, branching occurs quickly when the population reaches the singular point, while in stochastic branching, the population stays at singularity for a period before branching out. The conditions for these cases and the mean branching-out times are calculated in terms of population size, mutational effects, and selection intensity and are confirmed by direct computer simulations of the individual-based model.     

Dynamics of a Subterranean Trophic Cascade in Space and Time

Trophic cascades, whereby predators indirectly benefit plant biomass by reducing herbivore pressure, form the mechanistic basis for classical biological control of pest insects. Entomopathogenic nematodes (EPN) are lethal to a variety of insect hosts with soil-dwelling stages, making them promising biocontrol agents. EPN biological control programs, however, typically fail because nematodes do not establish, persist and/or recycle over multiple host generations in the field. A variety of factors such as local abiotic conditions, host quantity and quality, and rates of movement affect the probability of persistence. Here, we review results from 13 years of study on the biology and ecology of an endemic population of Heterorhabditis marelatus (Rhabditida: Heterorhabditidae) in a California coastal prairie. In a highly seasonal abiotic environment with intrinsic variation in soils, vegetation structure, and host availability, natural populations of H. marelatus persisted at high incidence at some but not all sites within our study area. Through a set of field and lab experiments, we describe mechanisms and hypotheses to understand the persistence of H. marelatus. We suggest that further ecological study of naturally occurring EPN populations can yield significant insight to improve the practice and management of biological control of soil-dwelling insect pests.     

Geovibrio ferrireducens,a phylogenetically distinct dissimilatory Fe(III)-reducing bacterium

A new, phylogenetically distinct, dissimilatory, Fe(III)-reducing bacterium was isolated from surface sediment of a hydrocarbon-contaminated ditch. The isolate, designated strain PAL-1, was an obligately anaerobic, non-fermentative, motile, gram-negative vibrio. PAL-1 grew in a defined medium with acetate as electron donor and ferric pyrophosphate, ferric oxyhydroxide, ferric citrate, Co(III)-EDTA, or elemental sulfur as sole electron acceptor. PAL-1 also used proline, hydrogen, lactate, propionate, succinate, fumarate, pyruvate, or yeast extract as electron donors for Fe(III) reduction. It is the first bacterium known to couple the oxidation of an amino acid to Fe(III) reduction. PAl-1 did not reduce oxygen, Mn(IV), U(VI), Cr(VI), nitrate, sulfate, sulfite, or thiosulfate with acetate as the electron donor. Cell suspensions of PAL-1 exhibited dithionite-reduced minus air-oxidized difference spectra that were characteristic of c-type cytochromes. Analysis of the 16S rRNA gene sequence of PAL-1 showed that the strain is not related to any of the described metal-reducing bacteria in the Proteobacteria and, together with Flexistipes sinusarabici, forms a separate line of descent within the Bacteria. Phenotypically and phylogenetically, strain PAl-1 differs from all other described bacteria, and represents the type strain of a new genus and species, Geovibrio ferrireducens. Received: 26 September 1995 / Accepted: 28 February 1996     

Reduction of Cr(VI) by "palladized" biomass of Desulfovibrio desulfuricans ATCC 29577

A novel catalytic activity of palladium [Pd(0)]-coated cells of Desulfovibrio desulfuricans ATCC 29577 ["bio-Pd(0)"] is demonstrated. Reduction of 700 microM Cr(VI) occurred within 24 h using formate (25 mM) or hydrogen (1 atm) as the electron donor, under conditions whereby cells lacking bound Pd(0), or palladium metal manufactured via chemical reduction of soluble Pd(II), did not reduce Cr(VI). The biomass-bound Pd(0) also functioned in the continuous removal of 400 microM Cr(VI) from a 1 mM solution under H(2) (flow residence time approximately 5 h), where chemically prepared Pd(0) was ineffective. This demonstrates a new type of active bioinorganic catalysis, whereby the presence of biomass bound to Pd(0) confers a novel catalytic capability not seen with Pd base metal or biomass alone.     

A Stochastic Analysis of a Brownian Ratchet Model for Actin-Based Motility

In recent single-particle tracking (SPT) measurements on Listeria monocytogenes motility in cells [Kuo and McGrath (2000)], the actin-based stochastic dynamics of the bacterium movement has been analyzed statistically in terms of the mean-square displacement (MSD) of the trajectory. We present a stochastic analysis of a simplified polymerization Brownian ratchet (BR) model in which motions are limited by the bacterium movement. Analytical results are obtained and statistical data analyses are investigated. It is shown that the MSD of the stochastic bacterium movement is a monotonic quadratic function while the MSD for detrended trajectories is linear. Both the short-time relaxation and the long-time kinetics in terms the mean velocity and effective diffusion constant of the propelled bacterium are obtained from the MSD analysis. The MSD of the gap between actin tip and the bacterium exhibits an oscillatory behavior when there is a large resistant force from the bacterium. For comparison, a continuous diffusion formalism of the BR model with great analytical simplicity is also studied.     

Estimation of Coupling Strength in Regenerated Lamprey Spinal Cords Based on a Stochastic Phase Model

We present a simple stochastic model of two coupled phase oscillators and a method of fitting the model to experimental spike-train data or to sequences of burst times. We apply the method to data from lesioned isolated lamprey spinal cords. The remaining tracts at the lesion site are either regenerated medial tracts, regenerated lateral tracts, control medial tracts, or control lateral tracts. We show that regenerated tracts on average provide significantly weaker coupling than control tracts. We compare our model-dependent estimate of coupling strength to a measure of coordination based on the size of deflections in the spike-train cross-correlation histogram (CCH). Using simulated data, we show that our estimates are able to detect changes in coupling strength that do not change the size of deflections in the CCH. Our estimates are also more resistant to changes in the level of dynamic noise and to changes in relative oscillator frequency than is the CCH. In simulations with high levels of dynamic noise and in one experimental preparation, we are able detect significant coupling strength although there are no significant deflections in the CCH.     

心肌细胞钙波随机性研究

钙波作为一种胞内的钙释放通道相互触发而产生的连锁反应广泛存在于多种细胞.在心肌中,由于与心律失常的发生有关,心肌细胞中的钙波近年来引起广泛关注.为了在微观上研究钙波的产生和传播过程,利用激光共聚焦钙成像技术对心肌细胞中的钙波进行了成像.实验和分析发现,钙波的起始是钙火花连续随机募集的过程,因此正常细胞中钙波发生概率很低.钙波传播过程中相邻位点开放的时间间隔接近正态分布,显示传播过程具有较大的随机性.且钙波速度越慢,位点间时间间隔的离散度越高.为了进一步研究这种随机性产生的内在机制,构建了一个数值模型对心肌细胞中的钙波进行模拟.研究证明,钙释放位点开放的随机性能够完整地解释实验中观察到的钙波传播的随机行为.实验分析和数值模拟相互印证,首次明确证明,钙波起始和传播过程的随机性,并揭示了该随机性与钙释放位点开放概率的关系.     

Wrapping Up Greenhouse Gas Emissions An Assessment of GHG Emission Reduction Related to Efficient Packaging Use: An Assessment of GHG Emission Reduction Related to Efficient Packaging Use

The use of packaging materials results in greenhouse gas (GHG) emissions through production and transport of materials and packaging and through end-of-life management. In this article, we investigate the potential reduction of GHGs that are related to packaging. For this purpose, we use the dynamic MATTER-MARKAL model in which the western European energy and materials system is modeled. The results show that GHGs related to packaging can technically be reduced by up to 58% in the period 1995–2030. Current European packaging directives will result in a 10% emission reduction. Cost-effective improved material management 1 that includes lightweighting, reusable packages, material recycling, and related strategies can contribute a 22% GHG emission reduction. An additional 13% reduction becomes cost effective when a GHG emission penalty of 100 euros per metric ton 2 (EUR/ton) is introduced (1 EUR 0.9 USD). Generally speaking, improved material management dominates the gains that can be achieved without a penalty or with low GHG emission penalties (up to 100 EUR/ton CO2 equivalent). By contrast, the reduction of emissions in materials production and waste handling dominate when high GHG penalties are applied (between 100 and 500 EUR/ton CO2 equivalent). Given the significant technical potential and the low costs, more attention should be paid to material efficiency improvement in GHG emission reduction strategies.     

一类随机时滞捕食者-食饵模型的动力学行为（英文）

研究了一类含时滞的Harrison型捕食者-食饵模型在随机扰动环境下的动力学行为.对于非时滞和时滞模型分别给出了局部和全局稳定性条件.通过白噪声分别对食饵人口增长率的和捕食者人口死亡率进行随机扰动,构建相应的随机时滞微分方程模型讨论环境噪声对其作用的动力学行为.在一定条件下,随机时滞模型存在随机最终有界的唯一全局正解且解的二阶均值是有界的.最后通过数值模拟对给出的分析结果进行了验证.