Moment closure approximations for stochastic kinetic models with rational rate laws

Stochastic models are often used when modelling chemical species that have low numbers of molecules. However, as these models become large, it can become computationally expensive to simulate even a single realisation of the system since even efficient simulation techniques have a high computational cost. One possible technique to approximate the stochastic system is moment closure. The moment closure approximation is used to provide analytic approximations to non-linear stochastic models. Until now, this approximation has only been applied to models with polynomial rate laws. In this paper we extend the moment closure method to cover models with rational rate laws.     

The anarchist's guide to ecological theory. Or, we don't need no stinkin' laws

Several ecologists have recently suggested that ecology has several laws. This conclusion contrasts with the views of some philosophers of science, who have suggested that biology cannot have laws. I argue that the debate has been confused because two very different types of law can be recognised: correlative and causal laws. Once we recognise that there is a difference, the argument against causal laws becomes stronger, and instead I suggest that ecologists should recognise that they can and do produce generalisations that are used to build models – nomological machines – that describe the ecological systems they are studying.     

孟德尔豌豆基因克隆的研究进展及其在遗传学教学中的应用

150多年前, 孟德尔进行了豌豆7对相对性状的杂交试验, 发现了遗传学的两个基本规律。1900年, 孟德尔定律被重新发现以后, 人们从生理生化、细胞和分子水平等不同层次上对豌豆的这7个性状进行了深入研究。近年, 随着分子生物学技术的发展, 已有种子形状(R)、茎的长度(Le)、子叶颜色(I)和花的颜色(A)等4个性状的基因被克隆; 未成熟豆荚的颜色(Gp)、花的着生位置(Fa)和豆荚形状(V)的基因已被定位在各自的连锁群上。4个孟德尔基因的鉴定和克隆加深了人们对基因概念的理解：如基因功能的多样性、在分子水平上基因变异原因的多样性、显性和隐性的分子实质等。在遗传学教学中, 把孟德尔基因克隆和研究的最新进展介绍给学生, 在分子水平上诠释经典遗传规律, 有助于提高学生的学习兴趣, 帮助学生全面把握从形式遗传学到分子遗传学的内容和遗传学的发展方向。     

Does population ecology have general laws?

There is a widespread opinion among ecologists that ecology lacks general laws. In this paper I argue that this opinion is mistaken. Taking the case of population dynamics, I point out that there are several very general law-like propositions that provide the theoretical basis for most population dynamics models that were developed to address specific issues. Some of these foundational principles, like the law of exponential growth, are logically very similar to certain laws of physics (Newton's law of inertia, for example, is almost a direct analogue of exponential growth). I discuss two other principles (population self-limitation and resource-consumer oscillations), as well as the more elementary postulates that underlie them. None of the "laws" that I propose for population ecology are new. Collectively ecologists have been using these general principles in guiding development of their models and experiments since the days of Lotka, Volterra, and Gause.     

Toward a generalised tensegrity model describing the mechanical behaviour of the cytoskeleton structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.     

A scaling law for the effects of architecture and allometry on tree vibration modes suggests a biological tuning to modal compartmentalization

Wind is a major ecological factor for plants and a major economical factor for forestry. Mechanical analyses have revealed that the multimodal dynamic behavior of trees is central to wind-tree interactions. Moreover, the trunk and branches influence dynamic modes, both in frequency and location. Because of the complexity of tree architecture, finite element models (FEMs) have been used to analyze such dynamics. However, these models require detailed geometric and architectural data and are tree-specific-two major restraints for their use in most ecological or biological studies. In this work, closed-form scaling laws for modal characteristics were derived from the dimensional analysis of idealized fractal trees that sketched the major architectural and allometrical regularities of real trees. These scaling laws were compared to three-dimensional FEM modal analyses of two completely digitized trees with maximal architectural contrast. Despite their simplifying hypotheses, the models explained most of the spatiotemporal characteristics of modes that involved the trunk and branches, especially for sympodial trees. These scaling laws reduce the tree to (1) a fundamental frequency and (2) one architectural and three biometrical parameters. They also give quantitative insights into the possible biological control of wind excitability of trees through architecture and allometries.     

Systematic Construction of Kinetic Models from Genome-Scale Metabolic Networks

The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.     

Scaling behaviour of different polymer models in dissipative particle dynamics of unentangled melts

We present a dissipative particle dynamics (DPD) study of scaling behaviour for three polymer models. The scaling behaviour is explored for the conformational and dynamic properties of unentangled polymer melts. DPD employs a bead–spring model together with an aggressive coarse-graining to represent polymers at the mesoscale. The first model studied utilises a simple soft repulsion potential for the bead–bead interactions together with a harmonic spring potential to connect beads into a polymer chain. The second model differs from the first model by replacing the harmonic spring with a finitely extensible nonlinear elastic spring. The third model uses realistic coarse-grain potentials for the bead–bead, spring and bending interactions based on the iterative Boltzmann inversion procedure and it corresponds to a mesoscopic model of polyethylene. We systematically vary the chain length and spring constant (in the case of the first and second models), and simulate the conformational properties such as the end-to-end distance or radius of gyration, and dynamic properties such as the centre-of-mass self-diffusion coefficient or viscosity. The scaling of the conformational and dynamic properties with chain length (scaling laws) is compared with the Rouse theory, which is considered as a standard theory for unentangled polymer melts. The comparison shows that simulated scaling laws typically agree with the Rouse scaling laws for the DPD polymer models with more than 10 DPD beads. For the shorter DPD polymers, deviations from the Rouse theory exist and become significant for the dynamic properties, especially for the viscosity of the polymer melts.     

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Young's modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.     

Toward a Generalised Tensegrity Model Describing the Mechanical Behaviour of the Cytoskeleton Structure

The control of many cell functions including growth, migration and mechanotransduction, depends crucially on stress-induced mechanical changes in cell shape and cytoskeleton (CSK) structure. Quantitative studies have been carried out on 6-bar tensegrity models to analyse several mechanical parameters involved in the mechanical responses of adherent cells (i.e. strain hardening, internal stress and scale effects). In the present study, we attempt to generalize some characteristic mechanical laws governing spherical tensegrity structures, with a view of evaluating the mechanical behaviour of the hierarchical multi-modular CSK-structure. The numerical results obtained by studying four different tensegrity models are presented in terms of power laws and point to the existence of unique and constant relationships between the overall structural stiffness and the local properties (length, number and internal stress) of the constitutive components.     

Thermodynamic Constraints in Kinetic Modeling: Thermodynamic‐Kinetic Modeling in Comparison to Other Approaches

Kinetic models of reaction networks may easily violate the laws of thermodynamics and the principle of detailed balance. In large network models, the constraints that are imposed by these laws are particularly difficult to address. This hinders modeling of biochemical reaction networks. Thermodynamic‐kinetic modeling is a method that provides a thermodynamically sound and formally appealing way for deriving dynamic model equations of reaction systems. State variables of this approach are thermokinetic potentials that describe the ability of compounds to drive a reaction. A compound has a parameter called capacity, which is the ratio of its concentration and thermokinetic potential. A reaction is described by its resistance which is the ratio of the thermokinetic driving force and flux. In these aspects, the formalism is similar to the modeling formalism for electrical networks and an analogous graphical representation is possible. The thermodynamic‐kinetic modeling formalism is equivalent to the traditional kinetic modeling formalism with the exception that it is not possible to build thermodynamically infeasible models. Here, the thermodynamic‐kinetic modeling formalism is reviewed, compared to other approaches, and some of its advantages are worked out. In contrast to other approaches, thermodynamic‐kinetic modeling does not rely on an explicit enumeration of stoichiometric cycles. It is capable of describing rate laws far from equilibrium. Further, the parameterization by capacities and resistances is particularly intuitive and powerful.     

A first principles derivation of animal group size distributions

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.     

The changing place of theory in 20th century ecology: from universal laws to array of methodologies

From the beginning of the 20th century ecologists have tried to do self-sufficient hard science that possesses real theory and laws. Early mathematical models were partly borrowed from physics and chemistry. For a long time they were the characteristic feature of theoretical ecology despite the striking absence of supporting empirical data. In the late 1960s a growing disappointment in "classical" theoretical foundations of ecology forced some researchers to propose "pattern-oriented" models that were derived from observation of real populations, communities and ecosystems, rather than from common sense written in mathematical language. However, this view had its own shortcomings, and in the 1980s it was supplemented by a "mechanistic" approach aimed at understanding basic processes and constraints. This shift of attention from general "laws" to "patterns" and later to "mechanisms" corresponds to an evident weakening of demands for theoretical rigour. Although there are great doubts about the existence of universal laws in ecology, ecologists continue to search for generalities. This search has resulted in an elaboration of methodologies that describe post hoc changes in populations, communities and ecosystems, with limited predictive ability.     

52株链霉菌全细胞蛋白组分的数值分类

全细胞可溶性蛋白的凝胶电泳分析作为细菌分类的一种简便而客观的方法得到了广泛应用,在许多报道中已证明蛋白凝胶电泳分析和DNA-DNA杂交的结果有紧密的相关性.目前在许多属中进行了全细胞蛋白组分的数值分类研究,我们对52株链霉菌进行了SDS-PAGE分析,并以全细胞蛋白组分进行聚类分析,以期在全细胞蛋白组分上探讨链霉菌属内种间及种内不同菌株的亲缘关系.     

Does population ecology have general laws?

There is a widespread opinion among ecologists that ecology lacks general laws. In this paper the author argues that this opinion is mistaken. Taking the case of population dynamics, the author points out that there are several very general law-like propositions that provide the theoretical basis for most population dynamics models that were developed to address specific issues. Some of these foundational principles, like the law of exponential growth, are logically very similar to certain law of physics (Newton's law of intertia, for example, is almost a direct analogue of exponential growth). The author discusses two other principles (population self-limitation and resource-consumer oscillations), as well as the more elementary postulates that underlie them. None of the "laws" that the author proposes for population ecology are new. Collectively ecologists have been using these general principles in guiding development of their models and experiments since the days of Lotka, Volterra, and Gause.     

On the evolutionary significance of Mendel's ratios

Length of time in polymorphism is investigated as a possible evolutionary criterion for Mendel's laws in the case of two alleles at one locus and finite population. Deterministic models with constant and random segregation schemes are investigated. In deterministic models the optimum segregation system depends on the zygotic selection and is Mendelian only in symmetric models. In finite population models the initial gene frequencies interact with the segregation to determine mean time to fixation. In deterministic models with random distortion reduction of the variance of the distortion is more likely to produce polymorphism.     

Robust scaling in ecosystems and the meltdown of patch size distributions before extinction

Robust critical systems are characterized by power laws which occur over a broad range of conditions. Their robust behaviour has been explained by local interactions. While such systems could be widespread in nature, their properties are not well understood. Here, we study three robust critical ecosystem models and a null model that lacks spatial interactions. In all these models, individuals aggregate in patches whose size distributions follow power laws which melt down under increasing external stress. We propose that this power-law decay associated with the connectivity of the system can be used to evaluate the level of stress exerted on the ecosystem. We identify several indicators along the transition to extinction. These indicators give us a relative measure of the distance to extinction, and have therefore potential application to conservation biology, especially for ecosystems with self-organization and critical transitions.     

The effect of women's status on infant and child mortality in four rural areas of Bangladesh

In South Asia women are often the primary decision-makers regarding child health care, family health and nutrition. This paper examines the proposition that constraints on women's status adversely affect the survival of their children. Survey data are used to construct indices of women's household autonomy and authority, which are then linked to longitudinal data on survival of their children. Proportional hazard models indicate that enhanced autonomy significantly decreases post-neonatal mortality. Enhanced household authority significantly decreases child mortality. A simulation based on estimated effects of eliminating gender inequality suggests that achieving complete gender equality could reduce child mortality by nearly fifty per cent and post-neonatal mortality by one-third.     

On the origin of hematopoietic stem cells: progress and controversy

Hematopoietic Stem Cells (HSCs) are responsible for the production and replenishment of all blood cell types during the entire life of an organism. Generated during embryonic development, HSCs transit through different anatomical niches where they will expand before colonizing in the bone marrow, where they will reside during adult life. Although the existence of HSCs has been known for more than fifty years and despite extensive research performed in different animal models, there is still uncertainty with respect to the precise origins of HSCs. We review the current knowledge on embryonic hematopoiesis and highlight the remaining questions regarding the anatomical and cellular identities of HSC precursors.     

Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic

Modeling of metabolic pathway dynamics requires detailed kinetic equations at the enzyme level. In particular, the kinetic equations must account for metabolite effectors that contribute significantly to the pathway regulation in vivo. Unfortunately, most kinetic rate laws available in the literature do not consider all the effectors simultaneously, and much kinetic information exists in a qualitative or semiquantitative form. In this article, we present a strategy to incorporate such information into the kinetic equation. This strategy uses fuzzy logic‐based factors to modify algebraic rate laws that account for partial kinetic characteristics. The parameters introduced by the fuzzy factors are then optimized by use of a hybrid of simplex and genetic algorithms. The resulting model provides a flexible form that can simulate various kinetic behaviors. Such kinetic models are suitable for pathway modeling without complete enzyme mechanisms. Three enzymes in Escherichia coli central metabolism are used as examples: phosphoenolpyruvate carboxylase; phosphoenolpyruvate carboxykinase; and pyruvate kinase I. Results show that, with fuzzy logic‐augmented models, the kinetic data can be much better described. In particular, complex behavior, such as allosteric inhibition, can be captured using fuzzy rules. The resulting models, even though they do not provide additional physical meaning in enzyme mechanisms, allow the model to incorporate semiquantitative information in metabolic pathway models. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 62: 722–729, 1999.