代谢异速生长理论及其在微生物生态学领域的应用

新陈代谢是生物的基本生理过程,影响生物在不同环境中参与物质循环和能量转化的过程.代谢速率作为生物体重要的生命过程指标,几乎影响所有的生物活性速率,且在很多研究中均表现出异速生长现象.所谓代谢异速是指生物体代谢速率与其个体大小(或质量)之间存在的幂函数关系.代谢异速生长理论的提出,从机制模型角度解释了代谢异速关系这一普遍存在的生命现象.该理论利用分形几何学及流体动力学等原理,从生物能量学角度阐释了异速生长规律的机理,证实了3/4权度指数的存在;但同时有研究表明,权度指数因环境因素等影响处于2/3-1范围之间而非定值.随着研究工作的深入,代谢异速生长理论研究从起初的宏观动植物领域拓展到了微生物领域,在研究微生物的代谢异速生长理论时,可将微生物的可操作分类单元(Operational taxonomic unit,OTU)或具有特定功能的功能群视为一个微生物个体,基于其遗传多样性和功能多样性特征进行表征,以便于将微生物群落多样性与其生态功能性联系起来,使该理论在微生物生态学领域得到有效的补充和完善.尽管细菌具有独特的生物学特性,但与宏观生物系统中观测到的现象表现出明显的一致性.有研究表明,3个农田土壤细菌基于遗传多样性的OTU数的平均周转率分别为0.71、0.80和0.84,介于2/3与1之间,可能与生物代谢异速指数有一定关联,为微生物代谢异速指数的研究提出了一个参考解决方案.鉴于微生物个体特征和生物学特性,在分析代谢速率与个体大小关系中,从微生物单位个体的定义、个体大小表征到计量单位的统一,仍需更多的理论支持.分析了代谢异速生长理论在微生物与生态系统功能关系研究中的可能应用,延伸了该理论的应用范围,并对尚待加强的研究问题进行了评述和展望.     

植物代谢速率与个体生物量关系研究进展

植物的各项生理生态功能（例如,呼吸、生长和繁殖）都与个体生物量成异速生长关系。West, Brown及Enquist基于分形网络结构理论所提出的WBE模型认为：植物的代谢（呼吸）速率正比于个体生物量的3/4次幂。然而,恒定的“3/4异速生长指数”与实测数据、植物生理生态学等研究之间存在矛盾,引发激烈的争论。论文分析了不同回归方法对代谢指数的影响,重点对植物代谢速率与个体生物量异速生长关系研究进展进行了综述,分析并得出了植物代谢指数在小个体时接近1.0,并随着生物量的增加而系统减小,且其密切依赖于氮含量的调控的结论。据此,提出了进一步深入研究植物代谢速率个体生物量关系需要解决的一些科学问题。     

浮游生物异速生长关系研究进展

生物个体的生物学特征(新陈代谢速率等)与个体大小(体积和生物量等)的依赖性关系称为异速生长关系, 这种关系经过尺度转换之后, 还影响着种群、群落和生态系统等。海洋环境较为复杂, 浮游生物的代谢速率不仅受到个体大小影响, 同时光照、温度和营养物质也是重要的影响因素, 因此3/4 规律只有在理想环境状况下才能实现。对于大多数浮游生物来讲, 其尺度因子并非单一的, 存在着多元尺度指数。由于单一和多元尺度指数都忽略了环境温度的影响, 生态学代谢理论在考虑个体大小的基础上, 加上温度这个参数后能够解释不同层次的生态学过程。在综述了异速生长关系发展历史的基础上, 着重探讨了该关系在浮游生物中的研究进展。     

异速生长模型及其应用概述

生物体的许多特征（如代谢速率等）随着个体大小的变化而变化,经常用幂函数形式的异速生长方程来表达,其中影响最为深远的就是新陈代谢速率和个体大小成3／4幂的关系,在简要回顾研究历史的基础上,重点介绍20世纪以来,由West等提出的、目前最为公认的代谢理论模型（分型分配网络模型、生态代谢模型）,包括模型假设条件、数学推导过程、模型在生物学中的应用及关于模型的一些争议。     

WBE 模型及其在生态学中的应用：研究概述

介绍了WBE模型,综述了该模型在生态学中的应用进展。WBE模型,以及以该模型为基础的MTE模型,假设生物体为自相似分形网络结构,提出代谢速率和个体大小之间存在3/4指数关系,分别预测了从个体到生物圈多个尺度上的生物属性之间的异速生长关系,而且部分得到了验证。WBE模型的应用涵盖了个体组织生物量、年生长率,种群密度和生态系统单位面积产量、能量流动率等多个方面;即使在生物圈大尺度上,WBE模型也可用来预测试验中无法直接测量的特征变量的属性,如全球碳储量的估算等。至今,关于WBE和MTE模型仍然存在各种褒贬争论,讨论焦点主要集中于模型建立的前提假设以及权度指数的预测。今后的研究工作应规范试验技术和方法,考虑物种多样性和环境等因素的影响,提出符合各类生物的模型结构体系,使其具有更广泛的应用性和预测性。     

植物种群自疏过程中构件生物量与密度的关系

不论是在对植物种群自疏规律还是在对能量守衡法则的研究中,个体大小(M)大多针对植物地上部分生物量,地下部分和构件生物量及其动态十分重要又多被忽视。以1年生植物荞麦为材料研究了自疏种群地下部分生物量、包括地下部分的个体总生物量以及各构件生物量与密度的关系。结果表明:平均地上生物量和个体总生物量与密度的异速关系指数(γabove-ground和γindividual)分别为-1.293和-1.253,与-4/3无显著性差异(P>0.05),为-4/3自疏法则提供了有力证据;平均根生物量-密度异速指数γroot(-1.128)与-1无显著性差异(P>0.05),与最终产量恒定法则一致;平均茎生物量-密度异速指数γstem(-1.263)接近-4/3(P>0.05),平均叶生物量-密度异速指数γleaf(-1.524)接近-3/2(P>0.05),分别符合-4/3自疏法则与-3/2自疏法则;而繁殖生物量与密度的异速关系指数γreproductive(-2.005)显著小于-3/2、-4/3或-1(P<0.001)。因此,不存在一个对植物不同构件普适的生物量-密度之间的关系。光合产物在地上和地下构件的生物量分配格局以及构件生物量与地上生物量之间特异的异速生长关系导致不同构件具有不同的自疏指数。无论对于地上生物量还是个体总生物量,荞麦种群能量均守衡,而对于地下生物量,荞麦种群能量不守衡。     

甘肃南部7种高寒杜鹃生物量分配的异速生长关系

生物量分配模式影响着植物个体生长和繁殖到整个群落的质量和能量流动等所有层次的功能, 揭示高寒灌丛的生物量分配模式不仅可以掌握植物的生活史策略, 而且对理解灌丛碳汇不确定性具有重要意义。该研究以甘肃南部高山-亚高山区的常绿灌丛——杜鹃(Rhododendron spp.)灌丛的7个典型种为对象, 采用全株收获法研究了不同物种个体水平上各器官生物量的分配比例和异速生长关系。结果表明: 7种高寒杜鹃根、茎、叶生物量的分配平均比例为35.57%、45.61%和18.83%, 各器官生物量分配比例的物种差异显著; 7种高寒杜鹃的叶与茎、叶与根、茎与根以及地上生物量与地下生物量之间既有异速生长关系, 也有等速生长关系, 异速生长指数不完全支持生态代谢理论和小个体等速生长理论的参考值; 各器官异速生长关系的物种差异显著。结合最优分配理论和异速生长理论能更好地解释陇南山地7种高寒杜鹃生物量的变异及适应机制。     

异速生长模型研究概述

最近,关于异速生长模型的讨论再次成为焦点,讨论热点为异速生长指数的取值及其理论解释.本文综述了WBE 97、BMR(99)模型的相关研究,重点介绍了MGL模型及由此模型得到的结果:个体整体的新陈代谢率与个体的质量没有明显依赖关系,其标度指数不是一个固定的值,而是一个区间[2/3,1].考虑的视角从个体整体的新陈代谢率转到单位质量的新陈代谢率,通过对不同物种、不同环境的单位质量新陈代谢率的研究,发现对大多数物种,其值落在一个具有普适性的上、下界的区间内;认为存在单位质量的新陈代谢率最小值确定了个体的大小,并建立基于该最小值的描述个体大小与温度关系的数学模型,该模型得到实验数据验证.     

密度对尖头叶藜生物量分配格局及异速生长的影响

植物器官指示植物不同的功能,而植物器官生物量分配比例的变化表征了植物对资源获取能力的调整。在植物生长发育过程中,植物各器官呈一种明显的异速生长规律。利用异速生长分析方法,通过模拟不同密度(16、44.4、100、400株/m~2)下尖头叶藜(Chenopodium acuminatum)的生长特性,研究密度对尖头叶藜器官生物量分配格局及异速生长的影响。结果表明,随密度增加,尖头叶藜地上和地下器官都存在不同程度的竞争:其中,根和主茎生物量分配增加,茎和地上生物量分配减少,而叶和繁殖生物量分配不随密度变化而变化。研究发现,尖头叶藜各器官间具有显著的异速生长关系:其中叶∶主茎、根∶地上部分、根∶茎、根∶主茎、繁殖器官∶地上部分及繁殖器官∶根生物量间的异速生长不随密度变化而变化,属于表观可塑性;而叶∶地上部分、叶∶根、叶∶茎、茎∶地上部分、主茎∶地上部分、繁殖器官∶茎、繁殖器官∶主茎生物量间具有极显著的异速生长关系,异速指数和个体大小显著受密度变化影响,属于真正可塑性,这表明密度能够影响尖头叶藜各器官的生长变化。尖头叶藜叶∶主茎、叶∶根及主茎∶地上部分生物量间的异速指数在D4-密度时与3/4差异不显著(P0.05),符合生态代谢理论,而在D1—D3密度时与3/4差异显著(P0.05),表明充分竞争的植株更符合代谢理论,而竞争不激烈的植株对资源的投入具有物种特异性。     

四种一年生荒漠植物构件形态与生物量间的异速生长关系

1年生草本植物是古尔班通古特沙漠夏秋季节草本层片的主要组成部分。选择4种藜科1年生草本植物(刺沙蓬、沙蓬、角果藜和对节刺)作为研究对象,对比分析了各物种构件形态特征、生物量分配以及它们之间的异速生长关系。结果表明:沙蓬个体最大,其次为刺沙蓬,角果藜和对节刺个体最小;对节刺具有最大的根冠比(R/S),其次是刺沙蓬,沙蓬和角果藜R/S最小。4种植物构件形态与生物量间均呈显著正相关,表现出强烈的协同变化趋势。R/S与绝大部分指标间呈显著负相关,表明随个体增大地下生物量分配比例逐渐减小。4种植物各构件形态、地上及地下生物量间大部分呈指数1.0的异速生长关系,但各物种间的异速生长指数绝大部分无显著差异且具有共同的异速生长指数。研究表明:尽管物种不同、个体大小迥异,但4种1年生植物构件特征间多具有相同的生长速率和协同变化特征,体现了1年生植物这一生活型内的不同物种对干旱荒漠环境的趋同适应。     

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Scaling, as the translation of information across spatial, temporal, and organizational scales, is essential to predictions and understanding in all sciences and has become a central issue in ecology. A large body of theoretical and empirical evidence concerning allometric scaling in terrestrial individual plants and plant communities has been constructed around the fractal volume-filling theory of West, Brown, and Enquist （the WBE model）. One of the most thought-provoking findings has been that the metabolic rates of plants, like those of animals, scale with their size as a 3/4 power law. The earliest, single most-important study cited in support of the application of the WBE model to terrestrial plants claims that whole-plant resource use in terrestrial plants scales as the 3/4 power of total mass, as predicted by the WBE model. However, in the present study we show that empirical data actually do not support such a claim. More recent studies cited as evidence for 3/4 scaling also suffer from several statistical and data-related problems. Using a forest biomass dataset including 1 266 plots of 17 main forest types across China, we explored the scaling exponents between tree productivity and tree mass and found no universal value across forest stands. We conclude that there is not sufficient evidence to support the existence of a single constant scaling exponent for the metabolism-biomass relationship for terrestrial plants.     

Validation of subject-specific musculoskeletal models using the anatomical reachable 3-D workspace

A novel metric for the validation of musculoskeletal models is proposed, the reachable 3-D workspace (RWS). This new metric was used to compare a generic model scaled in a standard manner to a more subject-specific model. An experimental protocol for assessing the RWS was performed by ten participants for four distinct hand-payload cases. In addition, isometric individual strength measurements were collected for 12 different directions. The strength of subject-specific musculoskeletal models was then computed using the following assumptions: (1) standard routines including the length-mass-fat (LMF) scaling law; (2) the isometric strengths of the muscle elements were optimized to the individual strength measurements using joint strength factors (JSF). The RWS of each participant was subsequently estimated from each of the scaling approaches, LMF and JSF, for the four load cases. The experimental RWS showed that the volume and shape decreased with increasing hand-payload for every participant. The lateral and frontal far-from-torso aspects of the RWS were reduced the most. These trends were reproduced by both strength scaling approaches, but the LMF-scaled models were not able to track the overall RWS volume decrease with increasing payload, since they proved to be weaker than the participants. On the other hand, the optimised JSF subject-specific models performed better on the prediction of the RWS for all payload cases across participants. The RWS can potentially be further used as a subject-specific musculoskeletal model validation, enabling quantification of the volume and shape differences between experimentally and model-predicted RWSs.     

Beyond the '3/4-power law': variation in the intra- and interspecific scaling of metabolic rate in animals

In this review I show that the '3/4-power scaling law' of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory schemes based on multiple boundary constraints and on the scaling of multiple energy-using processes are advocated. It is also stressed that a complete understanding of metabolic scaling will require the identification of both proximate (functional) and ultimate (evolutionary) causes. Four major types of intraspecific metabolic scaling with body mass are recognized [based on the power function R=aMb, where R is respiration (metabolic) rate, a is a constant, M is body mass, and b is the scaling exponent]: Type I: linear, negatively allometric (b<1); Type II: linear, isometric (b=1); Type III: nonlinear, ontogenetic shift from isometric (b=1), or nearly isometric, to negatively allometric (b<1); and Type IV: nonlinear, ontogenetic shift from positively allometric (b>1) to one or two later phases of negative allometry (b<1). Ontogenetic changes in the metabolic intensity of four component processes (i.e. growth, reproduction, locomotion, and heat production) appear to be important in these different patterns of metabolic scaling. These changes may, in turn, be shaped by age (size)-specific patterns of mortality. In addition, major differences in interspecific metabolic scaling are described, especially with respect to mode of temperature regulation, body-size range, and activity level. A 'metabolic-level boundaries hypothesis' focusing on two major constraints (surface-area limits on resource/waste exchange processes and mass/volume limits on power production) can explain much, but not all of this variation. My analysis indicates that further empirical and theoretical work is needed to understand fully the physiological and ecological bases for the considerable variation in metabolic scaling that is observed both within and among species. Recommended approaches for doing this are discussed. I conclude that the scaling of metabolism is not the simple result of a physical law, but rather appears to be the more complex result of diverse adaptations evolved in the context of both physico-chemical and ecological constraints.     

Using two palpable measurements improves the subject-specific femoral modeling

Subject-specific musculoskeletal models are essential to biomedical research and clinical applications, such as customized joint replacement, computer-aided surgical planning, gait analysis and automated segmentation. Generating these models from CT or magnetic resonance imaging (MRI) is time and resource intensive, requiring special skills. Therefore, in many studies individual bone models are approximated by scaling a generic template. Thus, the primary goal of this study was to determine a set of clinically available parameters (palpable measures and demographic data) that could improve the prediction of femoral dimensions, as compared to predicting these variables using uniform scaling based on palpable length. Similar to previous non-homogenous anthropometric scaling methods, the non-homogenous scaling method proposed in this study improved the prediction over uniform scaling of five key femoral measures. Homogenous scaling forces all dimensions of an object to be scaled equally, whereas non-homogenous scaling allows the dimensions to be scaled independently. The largest improvement was in femoral depth, where the coefficient of determination (r²) improved from 0.22 (homogenous) to 0.60 (non-homogeneous). In general, the major advantage of this non-homogenous scaling method is its ability to support the accurate and rapid generation of subject-specific femoral models since all parameters can be collected clinically, without imaging or invasive methods.     

Flexible informatics for linking experimental data to mathematical models via DataRail

MOTIVATION: Linking experimental data to mathematical models in biology is impeded by the lack of suitable software to manage and transform data. Model calibration would be facilitated and models would increase in value were it possible to preserve links to training data along with a record of all normalization, scaling, and fusion routines used to assemble the training data from primary results. RESULTS: We describe the implementation of DataRail, an open source MATLAB-based toolbox that stores experimental data in flexible multi-dimensional arrays, transforms arrays so as to maximize information content, and then constructs models using internal or external tools. Data integrity is maintained via a containment hierarchy for arrays, imposition of a metadata standard based on a newly proposed MIDAS format, assignment of semantically typed universal identifiers, and implementation of a procedure for storing the history of all transformations with the array. We illustrate the utility of DataRail by processing a newly collected set of approximately 22 000 measurements of protein activities obtained from cytokine-stimulated primary and transformed human liver cells. AVAILABILITY: DataRail is distributed under the GNU General Public License and available at http://code.google.com/p/sbpipeline/     

Lipid droplets fusion in adipocyte differentiated 3T3-L1 cells: A Monte Carlo simulation

Several human worldwide diseases like obesity, type 2 diabetes, hepatic steatosis, atherosclerosis and other metabolic pathologies are related to the excessive accumulation of lipids in cells. Lipids accumulate in spherical cellular inclusions called lipid droplets (LDs) whose sizes range from fraction to one hundred of micrometers in adipocytes. It has been suggested that LDs can grow in size due to a fusion process by which a larger LD is obtained with spherical shape and volume equal to the sum of the progenitors’ ones. In this study, the size distribution of two populations of LDs was analyzed in immature and mature (5-days differentiated) 3T3-L1 adipocytes (first and second populations, respectively) after Oil Red O staining. A Monte Carlo simulation of interaction between LDs has been developed in order to quantify the size distribution and the number of fusion events needed to obtain the distribution of the second population size starting from the first one. Four models are presented here based on different kinds of interaction: a surface weighted interaction (R2 Model), a volume weighted interaction (R3 Model), a random interaction (Random model) and an interaction related to the place where the LDs are born (Nearest Model). The last two models mimic quite well the behavior found in the experimental data. This work represents a first step in developing numerical simulations of the LDs growth process. Due to the complex phenomena involving LDs (absorption, growth through additional neutral lipid deposition in existing droplets, de novo formation and catabolism) the study focuses on the fusion process. The results suggest that, to obtain the observed size distribution, a number of fusion events comparable with the number of LDs themselves is needed. Moreover the MC approach results a powerful tool for investigating the LDs growth process.     

Memory effects on scale-free dynamics in foraging Drosophila

The fruit fly, Drosophila melanogaster, displays a scale-free behavior in foraging, i.e., the dwell time on food exhibits a power law distribution. The scaling exponent is generally believed to be stable and the significance of the exponent itself with respect to the scale-free behavior remains elusive. We propose a model whereby the scaling exponent of the scale-free behavior of an animal depends on the memory of the individual. The proposed model is based on the premise that animal behaviors are associated with internal states of the animal. The changes in the scaling exponent are derived by considering losing memory as increasing uncertainty, which is expressed in terms of information entropy of the internal states. Predicted model behaviors agree with experimental results of foraging behavior in wild-type and learning/memory Drosophila mutants. The concept of changes in the scaling exponent due to the amount of memory provides a novel insight into the emergence of a scale-free behavior and the meaning of the scaling exponent.     

Differentiation,ageing, and terminal differentiation: A semantic analysis

The largely unsolved problems in the theoretical analysis of differentiation and ageing involve a substantial component of linguistic (semantic) difficulties. Some of these are simple traps of ambiguity, resulting from metaphorical or analogical employment of established terms—for example, “terminal differentiation” (loss of division potential in vitro) as a borrowing from “differentiation” as used by developmental biologists, or “commitment” by analogy with “determination”. Some difficulties represent a failure to adopt (at least provisionally) an operational (empirical) view—for example, failure to ask what is the nature of the evidence for the view that a fertilized ovum is totipotential, or to scrutinize the evidence for the view that cells “terminally differentiated” in vitro in a conventional medium are in fact moribund under all conditions, or to examine more closely the view that the differentiated state and the cycling state are mutually exclusive.With respect to the problem of ageing, we review some of the critical experiments on ”terminal differentiation” or “clonal senescence”. We then proceed to consider some of the models that have been proposed, including a molecular model proposed by the author which appears to overcome some of the objections to other models. Some of the models exemplify the results of what are ultimately semantic vices.The problems with which these remarks began should indeed yield to the immense and novel resources of molecular biology. But the development of complete analyses demands not only good luck and delicate technique but also critical semantic clarity and severity. Given the best tools, we shall solve major theoretical problems only if we understand quite fully what problem it is that we are trying to solve—and the history of science illustrates that this is not as elementary a matter as it sounds. For the working scientist semantics (and indeed all philosophy of science) is not an indulgence or a frill, but a basic technical resource.     

3dRNAscore: a distance and torsion angle dependent evaluation function of 3D RNA structures

Model evaluation is a necessary step for better prediction and design of 3D RNA structures. For proteins, this has been widely studied and the knowledge-based statistical potential has been proved to be one of effective ways to solve this problem. Currently, a few knowledge-based statistical potentials have also been proposed to evaluate predicted models of RNA tertiary structures. The benchmark tests showed that they can identify the native structures effectively but further improvements are needed to identify near-native structures and those with non-canonical base pairs. Here, we present a novel knowledge-based potential, 3dRNAscore, which combines distance-dependent and dihedral-dependent energies. The benchmarks on different testing datasets all show that 3dRNAscore are more efficient than existing evaluation methods in recognizing native state from a pool of near-native states of RNAs as well as in ranking near-native states of RNA models.