Homogeneous nets of neuron-like elements

Propagation and reverberation of excitation patterns are investigated for 1-dimensional and 2-dimensional homogeneous nets of neuron-like elements. A 1-dimensional net has a proper set of excitation patterns which only can be conducted in the net. Such a net has an ability of discriminating and shaping stimulus signals. Two types of self-reproducing reverberatory excitation patterns are shown for 2-dimensional homogeneous nets. An algebraic theory of general homogeneous nets is also developed.     

基于Petri网的基因调控网络建模与分析

如何有效描述与分析复杂的基因调控网络(GRN)是生物学家研究基因表达调控机制的关键步骤.现有大部分方法在建模过程中忽略了生物中广泛存在的协同作用,模型预测结果与实际生物行为之间存在误差.基于混合函数Petri网(HFPN)理论提出了一种对基因调控网络进行定量分析的新方法.首先简要介绍GRN与HFPN的基础理论,然后为HFPN引入两类新元素:逻辑库所与逻辑变迁,描述基因调控网络的逻辑规则以及转录因子间的协同作用,最后构建海胆endo16基因调控网络的Petri网模型,并预测模型在不同位点发生突变时的基因表达水平变化.分析结果与文献实验数据相一致,验证了方法的正确性.     

Suggestion for a possible approach to molecular biology

A hypothetical “self-reproducing living molecule” has been recently frequently discussed in the literature. A physical theory of such a molecule is tentatively outlined. The relational, rather than the quantitative, aspects of the process are emphasized. The process of synthesis of such a molecule from its components is considered as a transition of a complex system between two quantum-mechanical states. The requirement that a “living molecule” should be able to multiply only by self-reproduction but not by a formationde novo leads to the conclusion that the above mentioned transition is a forbidden one. A constellation of conditions under which the forbiddenness is lifted by the presence of an already existing “living molecule” is suggested. The outlined mechanism leads to the conclusion that the property of self-reproduction does not so much reside in the self-reproducing molecule itself as in its relations to other molecules of a system.     

Competitive coexistence of self-reproducing macromolecules.

Several model systems of self-reproducing molecular species subject to the constraint of constant organization are investigated to see under what conditions more than one species may coexist over extended periods of time. It is found that while coexistence is not possible for systems of simple autocatalytic competitors, it can indeed occur if the nature of the reproductive process gives rise to “catalytic niches”. For systems catalyzed by n Michaelis-Menten type enzymes, it is shown that no more than n species may coexist. A precise characterization is provided of “how different” two such enzymes must be in order to allow coexistence of two species. Under certain conditions, one observes a transition from one dominant species to another which may occur either via a coexistent state or directly, but with hysteresis.     

Structural modeling and analysis of signaling pathways based on Petri nets

The purpose of this paper is to discuss how to model and analyze signaling pathways by using Petri net. Firstly, we propose a modeling method based on Petri net by paying attention to the molecular interactions and mechanisms. Then, we introduce a new notion "activation transduction component" in order to describe an enzymic activation process of reactions in signaling pathways and shows its correspondence to a so-called elementary T-invariant in the Petri net models. Further, we design an algorithm to effectively find basic enzymic activation processes by obtaining a series of elementary T-invariants in the Petri net models. Finally, we demonstrate how our method is practically used in modeling and analyzing signaling pathway mediated by thrombopoietin as an example.     

应用生态位模型研究外来入侵物种生态位漂移

由于基础生态位和实际生态位的改变,外来入侵物种在入侵地成功定殖、扩散后常会发生生态位漂移,而物种生态位漂移往往很难直接证明。生态位模型在假设入侵物种的生态位需求保守的前提下,以物种在其原产地的生态位需求为基础,预测其在入侵地的潜在分布,通过比较预测分布与实际分布的差异可以从一定程度上得到外来入侵物种的生态位是否发生漂移的间接证据。以我国入侵杂草胜红蓟在原产地的生态位需求为基础,应用生态位模型预测其在其他地区的潜在分布。研究结果表明,生态位模型可以很好地预测胜红蓟在亚太平洋地区和非洲地区的分布,但在我国,其预测分布与实际分布存在较大差别。胜红蓟在我国预测分布主要为云南、海南、台湾部分地区,而胜红蓟入侵我国后现已广泛分布于长江以南地区,其实际分布比预测分布广泛得多,由此推测胜红蓟在入侵我国后其生态位已经产生了漂移。     

Colored Petri net modeling and simulation of signal transduction pathways

Presented herein is a methodology for quantitatively analyzing the complex signaling network by resorting to colored Petri nets (CPN). The mathematical as well as Petri net models for two basic reaction types were established, followed by the extension to a large signal transduction system stimulated by epidermal growth factor (EGF) in an application study. The CPN models based on the Petri net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the EGF signaling pathway. The usefulness of Petri nets is demonstrated for the quantitative analysis of the signal transduction pathway. Moreover, the trade-offs between modeling capability and simulation efficiency of this pathway are explored, suggesting that the Petri net model can be invaluable in the initial stage of building a dynamic model.     

A simple competition model involving selection

Asimple model system of two self-reproducing objects is considered. A set of equations, similar to Eigen's equation, describing competition of these objects is derived and analyzed under the effect of an ‘ecological constraint’. The relation with other constraints used in the literature is discussed.     

Quantitative measures of organization for multiagent systems

A set of "information theoretic" measures has been developed to quantify the degree of constraint inherent in the organization of a multiagent system. Separate measures can be provided to quantify spatial organization, trophic organization and, more generally, the overall structure of interactions. The additive character of these quantities allows them to be distributed in various fashions among species and places in a way that allows one to assign an "Importance Index" to those taxa and places. In addition, a measure to gauge the degree of adaptation of a species to a particular environment is proffered. The proposed measures allow one to formulate the following hypotheses in quantitative fashion: (1). that any disturbance of an ecosystem at a location associated with a high spatial Importance Index will exert a greater impact on the population dynamics than will a similar disturbance aimed at a place where the values of these indexes are lower; (2). that any disturbance in an ecosystem affecting a particular species with high individual Importance Indexes will cause a greater impact on the overall population dynamics than will a disturbance aimed at a species with a lower values of these indexes; (3). that the ascendancy of evolving system has a propensity to increase. The precise quantitative formulation of these hypothesis would permit them to be tested via multiagent simulation. Estimating the probablities pertaining to these hypotheses presents a number of problems that merit discussion.     

A generalized spatial niche model for aquatic macrophytes

The spatial niches of submerged macrophytes and some relevant statistics for niche extensions and boundaries are described. An interpretation of the potential niche as a probability measure of survival over an n-dimensional gradient space is given. To this end a set of probability measure of is introduced. It is shown that these measures closely relate to statistical concepts found in survival and failure time analysis. By this approach, potential niches are wholly defined as a statistical concept. Realized niches then arise as samples from the specified statistical model: hence appropriate niche location and size measures can be derived.The conceptualized model of the survival niche extends to a general model which describes the shape of realized spatial niches for aquatic macrophytes. This general model was derived from actual vegetation data sampled by diving in many Norwegian lakes. Spatial performance on the vertical gradient can be described by a product of doubly exponential functions. Each of these corresponds to a Gumbel EV1 distribution and expresses the probability distribution of the species' up- and downslope niche boundaries, respectively. Theoretically, both potential and realized niches separate into a persistent and a transient region, each related to ddifferent time scales. The deep-water patchiness, commonly observed for submerged macrophytes, might indicate the transient domain of a realized niche. Published data indicate that the proposed model had widespread applicability, and also relevance to, for example, periphyton.     

Some aspects of the anemia of chronic disorders modeled and analyzed by petri net based approach

Anemia of chronic disorders is a very important phenomenon and iron is a crucial factor of this complex process. To better understand this process and its influence on some other factors we have built a mathematical model of the human body iron homeostasis, which possibly most exactly would reflect the metabolism of iron in the case of anemia and inflammation. The model has been formulated in the language of Petri net theory, which allows for its simulation and precise analysis. The obtained results of the analysis of the model’s behavior, concerning the influence of anemia and inflammation on the transferrin receptors, and hepcidin concentration changes are the valuable complements to the knowledge following from clinical research. This analysis is one of the first attempts to investigate properties and behavior of a not fully understood biological system on a basis of its Petri net based model.     

Predictions of co-contraction depend critically on degrees-of-freedom in the musculoskeletal model

In biomechanics, the calculation of individual muscle forces during movements is based on a model of the musculoskeletal system and a method for extracting a unique set of muscle forces. To obtain a unique set of muscle forces, non-linear, static optimisation is commonly used. However, the optimal solution is dependent on the musculoskeletal geometry, and single joints may be represented using one, two or three degrees-of-freedom. Frequently, a system with multiple degrees-of-freedom is replaced with a system that contains a subset of all the possible degrees-of-freedom. For example, the cat ankle joint is typically modelled as a planar joint with its primary degree-of-freedom (plantar-dorsiflexion), whereas, the actual joint has three rotational degrees-of-freedom. Typically, such simplifications are justified by the idea that the reduced case is contained as a specific solution of the more general case. However, here we demonstrate that the force-sharing solution space of a general, three degrees-of-freedom musculoskeletal system does not necessarily contain the solutions from the corresponding one or two degrees-of-freedom systems. Therefore, solutions of a reduced system, in general, are not sub-set solutions of the actual three degrees-of-freedom system, but are independent solutions that are often incompatible with solutions of the actual system. This result shows that representing a three degrees-of-freedom system as a one or two degrees-of-freedom system gives force-sharing solutions that cannot be extrapolated to the actual system, and vice-versa. These results imply that general solutions cannot be extracted from models with fewer degrees-of-freedom than the actual system. They further emphasise the need for precise geometric representation of the musculoskeletal system, if general force-sharing rules are to be derived.     

Early Cambrian origin of modern food webs: evidence from predator arrow worms

Although palaeontological evidence from exceptional biota demonstrates the existence of diverse marine communities in the Early Cambrian (approx. 540-520 Myr ago), little is known concerning the functioning of the marine ecosystem, especially its trophic structure and the full range of ecological niches colonized by the fauna. The presence of a diverse zooplankton in Early Cambrian oceans is still an open issue. Here we provide compelling evidence that chaetognaths, an important element of modern zooplankton, were present in the Early Cambrian Chengjiang biota with morphologies almost identical to Recent forms. New information obtained from the lowermost Cambrian of China added to previous studies provide convincing evidence that protoconodont-bearing animals also belonged to chaetognaths. Chaetognaths were probably widespread and diverse in the earliest Cambrian. The obvious raptorial function of their circumoral apparatuses (grasping spines) places them among the earliest active predator metazoans. Morphology, body ratios and distribution suggest that the ancestral chaetognaths were planktonic with possible ecological preferences for hyperbenthic niches close to the sea bottom. Our results point to the early introduction of prey-predator relationships into the pelagic realm, and to the increase of trophic complexity (three-level structure) during the Precambrian-Cambrian transition, thus laying the foundations of present-day marine food chains.     

Topological analysis of metabolic networks based on Petri net theory

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.     

基于最大熵生态位元模型的入侵杂草春飞蓬在中国潜在分布区的预测

春飞蓬是源自北美的外来入侵杂草,已入侵我国的上海、江苏、安徽等地,并对当地生态系统造成了危害,表现出巨大的入侵潜力.本文将最大熵生态位元(MaxEnt)模型与地理信息系统相结合,综合分析了影响春飞蓬分布的环境因素,直观和定量地预测了春飞蓬在我国的潜在分布区,并采用接受者操作特性曲线( ROC)分析法对预测结果进行验证.结果表明:春飞蓬在我国有广泛的潜在分布区,主要适生区包括上海、江苏、浙江、安徽、河南、湖北、湖南、江西等地.其目前的实际分布远未达到最大潜在分布范围,仍有可能继续扩散.ROC曲线检验结果表明,MaxEnt模型对春飞蓬在中国潜在分布区的预测精度较高,结果可信.春飞蓬潜在入侵区分布可能主要受温度和降水的影响.应高度重视春飞蓬的危害性,采取灭除已经发生的种群、严格监控向最适分布区入侵等措施阻止春飞蓬的扩散蔓延.     

Human transformation of ecosystems: Comparing protected and unprotected areas with natural baselines

Protected areas serve as reserves of biological diversity and conserve the naturalness of characteristic regional ecosystems. Numerous approaches have been applied to estimate the level of transformation of ecosystems and to compare trends inside and outside of protected areas. In this study, we apply aggregate indicators of anthropogenic pressures on ecosystems and biodiversity in a fine-scale spatial analysis to compare the level of human influence within protected and unprotected areas. The actual state of ecosystems is compared to a natural baseline that is intact or potential natural state. The results show that in a non-protected Central-European landscape, humans appropriate a considerable share of natural ecosystem productivity and carbon stocks, and significantly reduce natural biodiversity and ecosystem services. Human appropriation of net primary production reached more than 60% in total, humans reduced original biodiversity levels by 69%, and net carbon storage was considerably decreased by intensive types of land use. All three indicators significantly differed between protected areas and unprotected areas, suggesting that protected areas maintain higher biodiversity levels, store more carbon and are in total less influenced by human exploitation than average non-protected landscape. Furthermore, we bring evidence that human appropriation of net primary production is negatively related both to biodiversity and ecosystem services indicated by mean species abundance and net carbon storage at the national level. Our results contribute to the quantitative evidence of the impacts of anthropogenic transformation of natural ecosystems on the ecosystem condition, supporting the hypothesis that protected areas significantly reduce anthropogenic pressures and contribute to maintaining critical ecosystem services and biodiversity.     

Evolution is a cooperative process: the biodiversity-related niches differentiation theory (BNDT) can explain why

A. McFayden and G.E. Hutchinson defined a niche as a multidimensional space or hypervolume within the environment that allows an individual or a species to survive, we consider niches as a fundamental ecological variable that regulate species' composition and relation in ecosystems. Successively the niche concept has been associated to the genetic term "phenotype" by MacArthurstressing the importance on what a species or a genome can show outside, either in the environmental functions or in body characteristics. Several indexes have been developed to evaluate the grade of overlapping and similarities of species' niches, even utilizing the theory of information. However, which are the factors that determine the number of species that can coexist in a determinate environment and why a generalist species do not compete until the exclusion of the remaining species to maximize its fitness, is still quite unknown. Moreover, there are few studies and theories that clearly explain why the number of niches is so variable through ecosystems and how can several species live in the same basal niche, intended in a comprehensive sense as the range of basic conditions (temperature, humidity, food-guild, etc.). Here I show that the number of niches in an ecosystem depends on the number of species present in a particular moment and that the species themselves allow the enhancement of niches in terms of space and number. I found that using a three-dimensional model as hypervolume and testing the theory on a Mediterranean, temperate and tropical forest ecosystem it is possible to demonstrate that each species plays a fundamental role in facilitating the colonization by other species by simply modifying the environment and exponentially increasing the available niches' space and number. I resumed these hypothesis, after some preliminary empiric tests, in the Biodiversity-related Niches Differentiation Theory (BNDT), stressing with these definition that the process of niches differentiation is strictly addressed by species. This approach has various consequences, first in consideration of relations among species and second in terms of a better understanding of cooperation/competition dynamics.     

Constructing biological pathway models with hybrid functional Petri nets

In many research projects on modeling and analyzing biological pathways, the Petri net has been recognized as a promising method for representing biological pathways. From the pioneering works by Reddy et al., 1993, and Hofest?dt, 1994, that model metabolic pathways by traditional Petri net, several enhanced Petri nets such as colored Petri net, stochastic Petri net, and hybrid Petri net have been used for modeling biological phenomena. Recently, Matsuno et al., 2003b, introduced the hybrid functional Petri net (HFPN) in order to give a more intuitive and natural modeling method for biological pathways than these existing Petri nets. Although the paper demonstrates the effectiveness of HFPN with two examples of gene regulation mechanism for circadian rhythms and apoptosis signaling pathway, there has been no detailed explanation about the method of HFPN construction for these examples. The purpose of this paper is to describe method to construct biological pathways with the HFPN step-by-step. The method is demonstrated by the well-known glycolytic pathway controlled by the lac operon gene regulatory mechanism.     

Selecting plant species for practical restoration of degraded lands using a multiple‐trait approach

Ecological restoration is essential in rehabilitating degraded areas and safeguarding biodiversity, ecosystem services and human welfare. Using functional traits to plan restoration strategies has been suggested as they are the main ecological attributes that underlie ecosystem processes and services. However, few studies have translated ecological theory into actual restoration practices that can be easily used by different stakeholders. In this article, we applied a multiple‐trait approach to select plant species for the restoration of degraded lands inside the Brazilian Amazon Forests. We selected 10 traits encompassing ease of management, geographical distribution and interactions with animals and other ecosystem services and scored these traits using 118 native species. Then, we ranked all species according to the total number of traits that they exhibited to obtain a list of 53 highly ranked species. In addition, we employed non‐metric multidimensional scaling (NMDS) to assess the variation in these traits across the entire group of species. Based on the results, we selected a subset of species that maximizes functional diversity (high variability). We performed a sparse linear discriminant analysis (SLDA) to highlight a minimum set of traits to effectively discriminate botanical families. The final list of species and their traits highlight the importance of preserving not only the historical reference of a focused ecosystem but also its functional diversity to restore the interaction with local fauna, enrich the food chain and guarantee ecosystem services for local communities.