栲树不同生长发育阶段的枝系特征分析

对浙江天童国家森林公园内常绿阔叶优势树种栲树(Castanopsis fargesii)不同发育阶段植冠内的分枝式样特征进行了统计分析。结果表明：栲树在不同发育阶段的总体分枝率和逐步分枝率有显著变化,幼苗和幼树阶段的分枝率较低,而成株阶段的分枝率较高;幼树阶段的枝条长度、枝倾角和叶倾角明显大于幼苗和成株阶段,表现为明显的高生长对策;叶片配置在不同枝系上有较大差异,叶片主要集中于植冠内一级枝和二级枝上;叶片的大小从幼苗、幼树到成株阶段逐渐增大。研究结果表明栲树在生活史的不同生长发育阶段,分枝式样表现出一定的可塑性,反映了不同的适应对策。     

Approximating the long-term behaviour of a model for parasitic infection

In a companion paper two stochastic models, useful for the initial behaviour of a parasitic infection, were introduced. Now we analyse the long term behaviour. First a law of large numbers is proved which allows us to analyse the deterministic analogues of the stochastic models. The behaviour of the deterministic models is analogous to the stochastic models in that again three basic reproduction ratios are necessary to fully describe the information needed to separate growth from extinction. The existence of stationary solutions is shown in the deterministic models, which can be used as a justification for simulation of quasi-equilibria in the stochastic models. Host-mortality is included in all models. The proofs involve martingale and coupling methods.     

Ein adaptives und lernfähiges System für diskrete stochastische Prozesse. II

Summary On the adaptive and learning control problems for unknown stochastic systems the estimation of its stochastic transition structure is one of the basic problems for the decision of control inputs to the system. The present paper following the preceding [1] which mainly concerned the decision problem provided of the known stochastic transition structure deals with the practical estimation of the possible supplemental prior information about it. Two examples of computer simulation for the adaptive and learning system controlling the objective system are shown.     

Size-Independent Differences between the Mean of Discrete Stochastic Systems and the Corresponding Continuous Deterministic Systems

In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.     

Space as the final frontier in stochastic simulations of biological systems

Recent technological and theoretical advances are only now allowing the simulation of detailed kinetic models of biological systems that reflect the stochastic movement and reactivity of individual molecules within cellular compartments. The behavior of many systems could not be properly understood without this level of resolution, opening up new perspectives of using computer simulations to accelerate biological research. We review the modeling methodology applied to stochastic spatial models, also to the attention of non-expert potential users. Modeling choices, current limitations and perspectives of improvement of current general-purpose modeling/simulation platforms for biological systems are discussed.     

FERN – a Java framework for stochastic simulation and evaluation of reaction networks

Background  

Stochastic simulation can be used to illustrate the development of biological systems over time and the stochastic nature of these processes. Currently available programs for stochastic simulation, however, are limited in that they either a) do not provide the most efficient simulation algorithms and are difficult to extend, b) cannot be easily integrated into other applications or c) do not allow to monitor and intervene during the simulation process in an easy and intuitive way. Thus, in order to use stochastic simulation in innovative high-level modeling and analysis approaches more flexible tools are necessary.     

不同生境中辽东栎的构型差异

辽东栎具有很强的萌生能力,在东灵山区,存在于多种林分中,对生活在落叶阔叶混交林和次生落叶阔叶灌丛中辽东栎植株的构型进行了比较统计分析,结果表明不同生境中的辽东栎构型具有较大差异。具体表现在：（１）混交林中的辽东栎个体多生活在林隙中,同灌丛中的个体相比,树冠窄小,枝倾角较大,第一枝级枝条（上层）较长,但分枝率较小,叶面积指数较低;（２）枝,叶的方位角,叶倾角（上层）在不同生境中发生显著变化。因此,叶     

Modeling stochastic noise in gene regulatory systems

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steady-states are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.     

SHOOT APICAL MERISTEMS AND MUTATION: FIXATION OF SELECTIVELY NEUTRAL CELL GENOTYPES

Shoot apical meristems are interpreted as either structured, that is having a permanent set of apical initials, or stochastic, having apical initials which represent “... momentary representatives of the continuous meristematic residue at the apex of the relevant layer or zone” (Newman, 1965). The two main parameters of stochastic growth are the average number of apical initials (α) and the number of mitotic cycles (r) of the initials and their daughter cells prior to the random selection of subsequent initials. Mathematical analysis and computer simulation studies of stochastic growth have shown that if one starts with 1 mutant initial and α-1 nonmutant initials, eventually a mosaic plant results. The frequency of shoot apices composed of mutant cells is 1/α and the frequency of shoot apices composed of only nonmutant cells is (1 – α)/α. These asymptotics are only attained after considerable growth, thus mericlinal chimeras can persist for many nodes and give the appearance that a permanent set of initials is present.     

Demographic stochasticity, allee effects, and extinction: the influence of mating system and sex ratio

Demographic stochasticity has a substantial influence on the growth of small populations and consequently on their extinction risk. Mating system is one of several population characteristics that may affect this. We use a stochastic pair-formation model to investigate the combined effects of mating system, sex ratio, and population size on demographic stochasticity and thus on extinction risk. Our model is designed to accommodate a continuous range of mating systems and sex ratios as well as several levels of stochasticity. We show that it is not mating system alone but combinations of mating system and sex ratio that are important in shaping the stochastic dynamics of populations. Specifically, polygyny has the potential to give a high demographic variance and to lower the stochastic population growth rate substantially, thus also shortening the time to extinction, but the outcome is highly dependent on the sex ratio. In addition, population size is shown to be important. We find a stochastic Allee effect that is amplified by polygyny. Our results demonstrate that both mating system and sex ratio must be considered in conservation planning and that appreciating the role of stochasticity is key to understanding their effects.     

桂花植冠的枝系构型分析

采用Strahler法对福建省石峰寨风景区内的不同生长发育阶段桂花(Osmanthus fragrans)的枝系构型进行了统计分析。结果表明:桂花的分枝格局参数,除总体分枝率和逐步分枝率SBR1:2无显著变化外,其余参数因发育阶段的不同,均发生不同程度的变化。枝系构型的比较分析表明:成树阶段高生长不明显,以拓展上层空间为主,幼苗阶段表现出高生长,幼树阶段则表现出从高生长向横向生长过渡的趋势。通过分析叶片配置发现:在不同枝系上,叶片均集中于植冠内一级枝和二级枝上;叶片的大小从幼苗、幼树到成树阶段逐渐增大。这些说明桂花在不同生长发育阶段,枝系构型表现出一定的可塑性,反映了不同的适应对策。     

Hybrid simulation of cellular behavior

MOTIVATION: To be valuable to biological or biomedical research, in silico methods must be scaled to complex pathways and large numbers of interacting molecular species. The correct method for performing such simulations, discrete event simulation by Monte Carlo generation, is computationally costly for large complex systems. Approximation of molecular behavior by continuous models fails to capture stochastic behavior that is essential to many biological phenomena. RESULTS: We present a novel approach to building hybrid simulations in which some processes are simulated discretely, while other processes are handled in a continuous simulation by differential equations. This approach preserves the stochastic behavior of cellular pathways, yet enables scaling to large populations of molecules. We present an algorithm for synchronizing data in a hybrid simulation and discuss the trade-offs in such simulation. We have implemented the hybrid simulation algorithm and have validated it by simulating the statistical behavior of the well-known lambda phage switch. Hybrid simulation provides a new method for exploring the sources and nature of stochastic behavior in cells.     

Growth stress controls negative gravitropism in woody plant stems

In the shoots of woody plant species, reaction-wood fibers are formed on the upper or lower side of the secondary xylem of a leaning trunk or branch wherever large, internal growth stress is generated. Negative gravitropic movement in woody plant stems is proposed to be the result of growth stress generated in the reaction-wood tissue. This study examines the interaction between bending moment due to increasing self-weight and recovery moment resulting from asymmetric growth stress, and tests a hypothesis that describes the relationship based on the structural mechanics "beam theory". Simulations of observed tree branch morphology of Magnolia kobus DC., Juniperus chinensis L., Abies saccharinensis Fr. Schum., and Prunus spachiana Kitamura f. spachiana cv. Plenarosea showed that (i) the growth stress generated in the reaction wood is sufficient to counteract the gravitropic response to increasing self-weight, and (ii) the specific directional angle of the shoot apex or preferred angle of the elongation zone plays an important role in controlling the spatial shape of the branch stem that is peculiar to plant species with large growth stress generated in the reaction-wood tissue.     

A model for radiation-induced bystander effects, with allowance for spatial position and the effects of cell turnover

Bystander effects, whereby cells that are not directly exposed to ionizing radiation exhibit adverse biological effects, have been observed in a number of experimental systems. A novel stochastic model of the radiation-induced bystander effect is developed that takes account of spatial location, cell killing and repopulation. The ionizing radiation dose- and time-responses of this model are explored, and it is shown to exhibit pronounced downward curvature in the high dose-rate region, similar to that observed in many experimental systems, reviewed in the paper. It is also shown to predict the augmentation of effect after fractionated delivery of dose that has been observed in certain experimental systems. It is shown that the generally intractable solution of the full stochastic system can be considerably simplified by assumption of pairwise conditional dependence that varies exponentially over time.     

Toward a stochastic formulation of microbial growth in relation to bioreactor performances: case study of an E. coli fed-batch process

A stochastic microbial growth model has been elaborated in the case of the culture of E. coli in fed-batch and scale-down reactors. This model is based on the stochastic determination of the generation time of the microbial cells. The determination of generation time is determined by choosing the appropriate value on a log-normal distribution. The appropriateness of such distribution is discussed and growth curves are obtained that show good agreement compared with the experimental results. The mean and the standard deviation of the log-normal distribution can be considered to be constant during the batch phase of the culture, but they vary when the fed-batch mode is started. It has been shown that the parameters related to the log-normal distribution are submitted to an exponential evolution. The aim of this study is to explore the bioreactor hydrodynamic effect on microbial growth. Thus, in a second time, the stochastic growth model has been reinforced by data coming from a previous stochastic bioreactor mixing model (1). The connection of these hydrodynamic data with the actual stochastic growth model has allowed us to explain the scale-down effect associated with the glucose concentration fluctuations. It is important to point out that the scale-down effect is induced differently according to the feeding strategy involved in the fed-batch experiments.     

A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

Background  

The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void.     

Growth of branched actin networks against obstacles

A method for simulating the growth of branched actin networks against obstacles has been developed. The method is based on simple stochastic events, including addition or removal of monomers at filament ends, capping of filament ends, nucleation of branches from existing filaments, and detachment of branches; the network structure for several different models of the branching process has also been studied. The models differ with regard to their inclusion of effects such as preferred branch orientations, filament uncapping at the obstacle, and preferential branching at filament ends. The actin ultrastructure near the membrane in lamellipodia is reasonably well produced if preferential branching in the direction of the obstacle or barbed-end uncapping effects are included. Uncapping effects cause the structures to have a few very long filaments that are similar to those seen in pathogen-induced "actin tails." The dependence of the growth velocity, branch spacing, and network density on the rate parameters for the various processes is quite different among the branching models. An analytic theory of the growth velocity and branch spacing of the network is described. Experiments are suggested that could distinguish among some of the branching models.     

Smoldyn on graphics processing units: massively parallel Brownian dynamics simulations

Space is a very important aspect in the simulation of biochemical systems; recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and detailed models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localized fluctuations, transportation phenomena, and diffusion. A common drawback of spatial models lies in their complexity: models can become very large, and their simulation could be time consuming, especially if we want to capture the systems behavior in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to scale up the size of models we are able to simulate, moving from sequential to parallel simulation algorithms. In this paper, we analyze Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of Graphics Processing Units (GPUs). The implementation executes the most computational demanding steps (computation of diffusion, unimolecular, and bimolecular reaction, as well as the most common cases of molecule-surface interaction) on the GPU, computing them in parallel on each molecule of the system. The implementation offers good speed-ups and real time, high quality graphics output     

Crown development in a pioneer tree, Rhus trichocarpa, in relation to the structure and growth of individual branches

Based on an allometric reconstruction, the structure and biomass-allocation patterns of branches and current-year shoots were investigated in branches of various heights in the pioneer tree Rhus trichocarpa, to evaluate how crown development is achieved and limited in association with height. Path analysis was conducted to explore the effects of light availability, basal height and size of individual branches on branch structure and growth. Branch angle was affected by basal height, whereas branch mass was influenced primarily by light availability. This result suggests that branch structure is strongly constrained by basal height, and that trees mediate such constraints under different light environments. Previous-year leaf area and light availability showed positive effects on current-year stem mass. In contrast, branch basal height and mass negatively affected current-year stem mass. Moreover, the length of stems of a given diameter decreased with increasing branch height. Therefore the cost of biomass investment for a unit growth in length is greater for branches of larger size and at upper positions. Vertical growth rate in length decreased with increasing height. Height-dependent changes in stem allometry and angle influenced the reduction in vertical growth rate to a similar degree.