Form, function, and evolution of living organisms

Baselining Urban Ecosystems from Sentinel Species: Fitness, Flows, and Sinks

How can the shape of biodiversity inform us about cities' ecoclimatic fitness and guide their development? Can we use species as the harbingers of climatic extremes? Eco-climatically sensitive species carry information about hydroclimatic change in their distribution, fitness, and preferential gradients of habitat suitability. Conversely, environmental features outside of the species' fitness convey information on potential ecological anomalies in response to extremes to adapt or mitigate, such as through urban parks. Here, to quantify ecosystems' fitness, we propose a novel computational model to extract multivariate functional ecological networks and their basins, which carry the distributed signature of the compounding hydroclimatic pressures on sentinel species. Specifically, we consider butterflies and their habitat suitability (HS) to infer maximum suitability gradients that are meaningful of potential species networks and flows, with the smallest hydroclimatic resistance across urban landscapes. These flows are compared to the distribution of urban parks to identify parks' ecological attractiveness, actual and potential connectivity, and park potential to reduce hydroclimatic impacts. The ecosystem fitness index (EFI) is novelly introduced by combining HS and the divergence of the relative species abundance (RSA) from the optimal log-normal Preston plot. In Shenzhen, as a case study, eco-flow networks are found to be spatially very extended, scale-free, and clustering for low HS gradient and EFI areas, where large water bodies act as sources of ecological corridors draining into urban parks. Conversely, parks with higher HS, HS gradients, and EFIs have small-world connectivity non-overlapping with hydrological networks. Diverging patterns of abundance and richness are inferred as increasing and decreasing with HS. HS is largely determined by temperature and precipitation of the coldest quarter and seasonality, which are critical hydrologic variables. Interestingly, a U-shape pattern is found between abundance and diversity, similar to the one in natural ecosystems. Additionally, both abundance and richness are mildly associated with park area according to a power function, unrelated to longitude but linked to the degree of urbanization or park centrality, counterintuitively. The Preston plot's richness-abundance and abundance-rank patterns were verified to reflect the stationarity or ecological meta-equilibrium with the environment, where both are a reflection of community connectivity. Ecological fitness is grounded on the ecohydrological structure and flows where maximum HS gradients are indicative of the largest eco-changes like climate-driven species flows. These flows, as distributed stress-response functions, inform about the collective eco-fitness of communities, like parks in cities. Flow-based networks can serve as blueprints for designing ecotones that regulate key ecosystem functions, such as temperature and evapotranspiration, while generating cascading ecological benefits across scales. The proposed model, novelly infers HS eco-networks and calculates the EFI, is adaptable to diverse sensitive species and environmental layers, offering a robust tool for precise ecosystem assessment and design.

Does death drive the scaling of life?

The magnitude of many kinds of biological structures and processes scale with organismal size, often in regular ways that can be described by power functions. Traditionally, many of these "biological scaling" relationships have been explained based on internal geometric, physical, and energetic constraints according to universal natural laws, such as the "surface law" and "3/4-power law". However, during the last three decades it has become increasingly apparent that biological scaling relationships vary greatly in response to various external (environmental) factors. In this review, I propose and provide several lines of evidence supporting a new ecological perspective that I call the "mortality theory of ecology" (MorTE). According to this viewpoint, mortality imposes time limits on the growth, development, and reproduction of organisms. Accordingly, small, vulnerable organisms subject to high mortality due to predation and other environmental hazards have evolved faster, shorter lives than larger, more protected organisms. A MorTE also includes various corollary, size-related internal and external causative factors (e.g. intraspecific resource competition, geometric surface area to volume effects on resource supply/transport and the protection of internal tissues from environmental hazards, internal homeostatic regulatory systems, incidence of pathogens and parasites, etc.) that impact the scaling of life. A mortality-centred approach successfully predicts the ranges of body-mass scaling slopes observed for many kinds of biological and ecological traits. Furthermore, I argue that mortality rate should be considered the ultimate (evolutionary) driver of the scaling of life, that is expressed in the context of other proximate (functional) drivers such as information-based biological regulation and spatial (geometric) and energetic (metabolic) constraints.

Exploring the Evolution-Coupling Hypothesis: Do Enzymes' Performance Gains Correlate with Increased Dissipation?

The research literature presents divergent opinions regarding the role of dissipation in living systems, with views ranging from it being useless to it being essential for driving life. The implications of universal thermodynamic evolution are often overlooked or considered controversial. A higher rate of entropy production indicates faster thermodynamic evolution. We calculated enzyme-associated dissipation under steady-state conditions using minimalistic models of enzyme kinetics when all microscopic rate constants are known. We found that dissipation is roughly proportional to the turnover number, and a log-log power-law relationship exists between dissipation and the catalytic efficiency of enzymes. "Perfect" specialized enzymes exhibit the highest dissipation levels and represent the pinnacle of biological evolution. The examples that we analyzed suggested two key points: (a) more evolved enzymes excel in free-energy dissipation, and (b) the proposed evolutionary trajectory from generalist to specialized enzymes should involve increased dissipation for the latter. Introducing stochastic noise in the kinetics of individual enzymes may lead to optimal performance parameters that exceed the observed values. Our findings indicate that biological evolution has opened new channels for dissipation through specialized enzymes. We also discuss the implications of our results concerning scaling laws and the seamless coupling between thermodynamic and biological evolution in living systems immersed in out-of-equilibrium environments.

Tumor Growth, Proliferation and Diffusion in Osteosarcoma

Osteosarcoma is the most common primary bone cancer. According to medical and biological studies, it has a high genetic complexity, thus, to differentiate the mechanisms of appearance and evolution of this disease is a difficult task. In this paper, we use three simplest and well known mathematical models to describe the behavior of several cell lines of osteosarcoma. First, we use a potential law to describe the tumor growth in immunosuppressed mice; with it we show that the variation of tumor growth has a sublinear behavior without the blow-up phenomenon. Second, the logistic model is used to obtain a good aproximation to the rates of proliferation in cell confluency in in vitro experiments. Third, we use a linear reaction-diffusion model; with it, we describe the diffusion behavior for some cell lines. These three models allow us to give a classification of cell lines according to the rates of tumor growth and proliferation and to the diffusion coefficient. A relationship is found between the rates of the tumor growth, the diffusion coefficient and tumorigenicity. Experimental data are extracted from Lauvrak et al. (British Journal of Cancer 109(8):2228-2236, 2013).

Developmental and Evolutionary Heart Adaptations Through Structure-Function Relationships

While the heart works as an efficient pump, it also has a high level of adaptivity by changing its structure to maintain function during healthy and diseased states. In this Review, we present examples of structure-function relationships across species and throughout embryonic development in mammals and birds. We also summarize current research on avian models aiming at understanding how biophysical and biological mechanisms closely interact during heart formation. We conclude by underscoring similarities between cardiac adaptations and structural changes over developmental and evolutionary time scales and how understanding the mechanisms behind these adaptations can help prevent or alleviate the effects of cardiac malformations and contribute to cardiac regeneration efforts.

Scaling of shoot and root respiration of woody and herbaceous plants

Woody and herbaceous plants are the main components of global terrestrial ecosystems, and their growth, adaptation and survival depend largely on the metabolism of shoots and roots. Therefore, understanding size-scaling of metabolic rates in woody and herbaceous plants, and in shoots and roots, is a fundamental issue in ecology. However, few empirical studies have examined metabolic scaling exponents across a wide range of plant sizes. Using whole-plant chamber systems, we measured respiration rates of entire root systems and shoots of 96 woody species (n = 1243) and 33 herbaceous species (n = 463) from various terrestrial biomes, with plant masses spanning nine orders of magnitude. Scaling exponents for relationships between respiration rates and fresh mass were greater in shoots than in roots, and both were greater in herbaceous plants than in woody plants. Furthermore, scaling of whole-plant respiration, including various species, converged separately for woody and herbaceous plants. These findings suggest some general physico-chemical constraints on energy use by shoots and roots of individual plants in various terrestrial biomes, including forests and grasslands. These data will advance our understanding of terrestrial ecosystem structure and function.

Micropattern Fabricated by Acropetal Migration Controlled through Sequential Photo and Thermal Polymerization

Bottom-up patterning technology plays a significant role in both nature and synthetic materials, owing to its inherent advantages such as ease of implementation, spontaneity, and noncontact attributes, etc. However, constrained by the uncontrollability of molecular movement, energy interaction, and stress, obtained micropatterns tend to exhibit an inevitable arched outline, resulting in the limitation of applicability. Herein, inspired by auxin's action mode in apical dominance, a versatile strategy is proposed for fabricating precision self-organizing micropatterns with impressive height based on polymerization-induced acropetal migration. The copolymer containing fluorocarbon chains (low surface energy) and tertiary amine (coinitiator) is designed to self-assemble on the surface of the photo-curing system. The selective exposure under a photomask establishes a photocuring boundary and the radicals would be generated on the surface, which is pivotal in generating a vertical concentration difference of monomer. Subsequent heating treatment activates the material continuously transfers from the unexposed area to the exposed area and is accompanied by the obviously vertical upward mass transfer, resulting in the manufacture of a rectilinear profile micropattern. This strategy significantly broadens the applicability of self-organizing patterns, offering the potential to mitigate the complexity and time-consuming limitations associated with top-down methods.

Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures

Designing and optimizing the structure of urban transportation networks is a challenging task. In this study, we propose a method inspired by optimal transport theory and the principle of economy of scale that uses little information in input to generate structures that are similar to those of public transportation networks. Contrarily to standard approaches, it does not assume any initial backbone network infrastructure but rather extracts this directly from a continuous space using only a few origin and destination points, generating networks from scratch. Analyzing a set of urban train, tram and subway networks, we find a noteworthy degree of similarity in several of the studied cases between simulated and real infrastructures. By tuning one parameter, our method can simulate a range of different subway, tram and train networks that can be further used to suggest possible improvements in terms of relevant transportation properties. Outputs of our algorithm provide naturally a principled quantitative measure of similarity between two networks that can be used to automatize the selection of similar simulated networks.

Tip extension and simultaneous multiple fission in a filamentous bacterium

Organisms display an immense variety of shapes, sizes, and reproductive strategies. At microscopic scales, bacterial cell morphology and growth dynamics are adaptive traits that influence the spatial organization of microbial communities. In one such community-the human dental plaque biofilm-a network of filamentous Corynebacterium matruchotii cells forms the core of bacterial consortia known as hedgehogs, but the processes that generate these structures are unclear. Here, using live-cell time-lapse microscopy and fluorescent D-amino acids to track peptidoglycan biosynthesis, we report an extraordinary example of simultaneous multiple division within the domain Bacteria. We show that C. matruchotii cells elongate at one pole through tip extension, similar to the growth strategy of soil-dwelling Streptomyces bacteria. Filaments elongate rapidly, at rates more than five times greater than other closely related bacterial species. Following elongation, many septa form simultaneously, and each cell divides into 3 to 14 daughter cells, depending on the length of the mother filament. The daughter cells then nucleate outgrowth of new thinner vegetative filaments, generating the classic "whip handle" morphology of this taxon. Our results expand the known diversity of bacterial cell cycles and help explain how this filamentous bacterium can compete for space, access nutrients, and form important interspecies interactions within dental plaque.

Polymerase-Based Signal Delay for Temporally Regulating DNA Involved Reactions, Programming Dynamic Molecular Systems, and Biomimetic Sensing

Complex temporal molecular signals play a pivotal role in the intricate biological pathways of living organisms, and cells exhibit the ability to transmit and receive information by intricately managing the temporal dynamics of their signaling molecules. Although biomimetic molecular networks are successfully engineered outside of cells, the capacity to precisely manipulate temporal behaviors remains limited. In this study, the catalysis activity of isothermal DNA polymerase (DNAP) through combined use of molecular dynamics simulation analysis and fluorescence assays is first characterized. DNAP-driven delay in signal strand release ranged from 100 to 102 min, which is achieved through new strategies including the introduction of primer overhangs, utilization of inhibitory reagents, and alteration of DNA template lengths. The results provide a deeper insight into the underlying mechanisms of temporal control DNAP-mediated primer extension and DNA strand displacement reactions. Then, the regulated DNAP catalysis reactions are applied in temporal modulation of downstream DNA-involved reactions, the establishment of dynamic molecular signals, and the generation of barcodes for multiplexed detection of target genes. The utility of DNAP-based signal delay as a dynamic DNA nanotechnology extends beyond theoretical concepts and achieves practical applications in the fields of cell-free synthetic biology and bionic sensing.

Extrusion-based 3D printing of soft active materials

Active materials are capable of responding to external stimuli, as observed in both natural and synthetic systems, from sensitive plants to temperature-responsive hydrogels. Extrusion-based 3D printing of soft active materials facilitates the fabrication of intricate geometries with spatially programmed compositions and architectures at various scales, further enhancing the functionality of materials. This Feature Article summarizes recent advances in extrusion-based 3D printing of active materials in both non-living (i.e., synthetic) and living systems. It highlights emerging ink formulations and architectural designs that enable programmable properties, with a focus on complex shape morphing and controllable light-emitting patterns. The article also spotlights strategies for engineering living materials that can produce genetically encoded material responses and react to a variety of environmental stimuli. Lastly, it discusses the challenges and prospects for advancements in both synthetic and living composite materials from the perspectives of chemistry, modeling, and integration.

Effects of Geometric Sound on Brainwave Activity Patterns, Autonomic Nervous System Markers, Emotional Response, and Faraday Wave Pattern Morphology

This study introduces Geometric Sound as a subfield of spatial sound featuring audio stimuli which are sonic holograms of mathematically defined 3D shapes. The effects of Geometric Sound on human physiology were investigated through EEG, heart rate, blood pressure, and a combination of questionnaires monitoring 50 healthy participants in two separate experiments. The impact of Geometric Sound on Faraday wave pattern morphology was further studied. The shapes examined, pyramid, cube, and sphere, exhibited varying significant effects on autonomic nervous system markers, brainwave power amplitude, topology, and connectivity patterns, in comparison to both the control (traditional stereo), and recorded baseline where no sound was presented. Brain activity in the Alpha band exhibited the most significant results, additional noteworthy results were observed across analysis paradigms in all frequency bands. Geometric Sound was found to significantly reduce heart rate and blood pressure and enhance relaxation and general well-being. Changes in EEG, heart rate, and blood pressure were primarily shape-dependent, and to a lesser extent sex-dependent. Pyramid Geometric Sound yielded the most significant results in most analysis paradigms. Faraday Waves patterns morphology analysis indicated that identical frequencies result in patterns that correlate with the excitation Geometric Sound shape. We suggest that Geometric Sound shows promise as a noninvasive therapeutic approach for physical and psychological conditions, stress-related disorders, depression, anxiety, and neurotrauma. Further research is warranted to elucidate underlying mechanisms and expand its applications.

A Nonlinear Dynamical View of Kleiber's Law on the Metabolism of Plants and Animals

Kleiber's empirical law, which describes that metabolism increases as the mass to the power 3/4, has arguably remained life sciences' enigma since its formal uncovering in 1930. Why is this behavior sustained over many orders of magnitude? There have been quantitative rationalizations put forward for both plants and animals based on realistic mechanisms. However, universality in scaling laws of this kind, like in critical phenomena, has not yet received substantiation. Here, we provide an account, with quantitative reproduction of the available data, of the metabolism for these two biology kingdoms by means of broad arguments based on statistical mechanics and nonlinear dynamics. We consider iterated renormalization group (RG) fixed-point maps that are associated with an extensive generalized (Tsallis) entropy. We find two unique universality classes that satisfy the 3/4 power law. One corresponds to preferential attachment processes-rich gets richer-and the other to critical processes that suppress the effort for motion. We discuss and generalize our findings to other empirical laws that exhibit similar situations, using data based on general but different concepts that form a conjugate pair that gives rise to the same power-law exponents.

What is complex allometry?

Complex allometry describes a smooth, curvilinear relationship between logarithmic transformations of a biological variable and a corresponding measure for body size when the observations are displayed on a bivariate graph with linear scaling. The curvature in such a display is commonly captured by fitting a quadratic equation to the distribution; and the quadratic term is typically interpreted, in turn, to mean that the mathematically equivalent equation for describing the arithmetic distribution is a two-parameter power equation with an exponent that changes with body size. A power equation with an exponent that is itself a function of body size is virtually uninterpretable, yet numerous attempts have been made in recent years to incorporate such an exponent into theoretical models for the evolution of form and function in both plants and animals. However, the curvature that is described by a quadratic equation fitted to logarithms usually means that an explicit, non-zero intercept is required in the power equation describing the untransformed distribution - not that the exponent in the power equation varies with body size. Misperceptions that commonly accompany reports of complex allometry can be avoided by using nonlinear regression to examine untransformed data.

The Relevance of Time in Biological Scaling

Various phenotypic traits relate to the size of a living system in regular but often disproportionate (allometric) ways. These "biological scaling" relationships have been studied by biologists for over a century, but their causes remain hotly debated. Here, I focus on the patterns and possible causes of the body-mass scaling of the rates/durations of various biological processes and life-history events, i.e., the "pace of life". Many biologists have regarded the rate of metabolism or energy use as the master driver of the "pace of life" and its scaling with body size. Although this "energy perspective" has provided valuable insight, here I argue that a "time perspective" may be equally or even more important. I evaluate various major ways that time may be relevant in biological scaling, including as (1) an independent "fourth dimension" in biological dimensional analyses, (2) a universal "biological clock" that synchronizes various biological rates/durations, (3) a scaling method that uses various biological time periods (allochrony) as scaling metrics, rather than various measures of physical size (allometry), as traditionally performed, (4) an ultimate body-size-related constraint on the rates/timing of biological processes/events that is set by the inevitability of death, and (5) a geological "deep time" approach for viewing the evolution of biological scaling patterns. Although previously proposed universal four-dimensional space-time and "biological clock" views of biological scaling are problematic, novel approaches using allochronic analyses and time perspectives based on size-related rates of individual mortality and species origination/extinction may provide new valuable insights.

Flow similarity model predicts the allometry and allometric covariation of petiole dimensions

Allometric relationships for plants, plant organs and plant parts, have long generated interest among biologists. Several prominent theoretical models based on biomechanical and/or hydraulic arguments have been introduced with mixed support. Here, I test a more recent offering, flow similarity, which is based on the conservation of volumetric flow rate and velocity. Using dimensional data for 935 petioles from 43 angiosperm species, I show that both the intraspecific and interspecific petiole allometries are more closely aligned with the predictions of the flow similarity model than that of elastic or geometric similarity. Further, allometric covariation among empirical scaling exponents falls along predicted functions with clustering around the flow similarity predictions. This work adds to the body of literature highlighting the importance of hydraulics in understanding the physiological basis of plant allometries, identifies previously unknown central tendencies in petiole allometry, and helps to delineate the scope within which the flow similarity model may be applicable.

Reversibly growing crosslinked polymers with programmable sizes and properties

Growth constitutes a powerful method to post-modulate materials' structures and functions without compromising their mechanical performance for sustainable use, but the process is irreversible. To address this issue, we here report a growing-degrowing strategy that enables thermosetting materials to either absorb or release components for continuously changing their sizes, shapes, compositions, and a set of properties simultaneously. The strategy is based on the monomer-polymer equilibrium of networks in which supplying or removing small polymerizable components would drive the networks toward expansion or contraction. Using acid-catalyzed equilibration of siloxane as an example, we demonstrate that the size and mechanical properties of the resulting silicone materials can be significantly or finely tuned in both directions of growth and decomposition. The equilibration can be turned off to yield stable products or reactivated again. During the degrowing-growing circle, material structures are selectively varied either uniformly or heterogeneously, by the availability of fillers. Our strategy endows the materials with many appealing capabilities including environment adaptivity, self-healing, and switchability of surface morphologies, shapes, and optical properties. Since monomer-polymer equilibration exists in many polymers, we envision the expansion of the presented strategy to various systems for many applications.

Declining metabolic scaling parallels an ontogenetic change from elongate to deep-bodied shapes in juvenile Brown trout

Body shape and metabolic rate can be important determinants of animal performance, yet often their effects on influential traits are evaluated in a non-integrated way. This creates an important gap because the integration between shape and metabolism may be crucial to evaluate metabolic scaling theories. Here, we measured standard metabolic rate in 1- and 2-years old juvenile brown trout Salmo trutta, and used a geometric morphometrics approach to extricate the effects of ontogeny and size on the link between shape and metabolic scaling. We evidenced near-isometric ontogenetic scaling of metabolic rate with size, but also a biphasic pattern driven by a significant change in metabolic scaling, from positive to negative allometry. Moreover, the change in metabolic allometry parallels an ontogenetic change from elongate to deep-bodied shapes. This is consistent with the dynamic energy budget (DEB) and surface area (SA) theories, but not with the resource transport network theory which predicts increasing allometric exponents for trends towards more robust, three-dimensional bodies. In addition, we found a relationship between body shape and size independent metabolic rate, with a positive correlation between robustness and metabolic rate, which fits well within the view of Pace-of-Life Syndromes (POLS). Finally, our results align with previous studies that question the universality of metabolic scaling exponents and propose other mechanistic models explaining the diversity of metabolic scaling relationships or emphasizing the potential contribution of ecological factors.

Ontogenetic changes in root and shoot respiration, fresh mass and surface area of Fagus crenata

BACKGROUND AND AIMS

To date, studies on terrestrial plant ecology and evolution have focused primarily on the trade-off patterns in the allocation of metabolic production to roots and shoots in individual plants and the scaling of whole-plant respiration. However, few empirical studies have investigated the root : shoot ratio by considering scaling whole-plant respiration at various sizes throughout ontogeny.

METHODS

Here, using a whole-plant chamber system, we measured the respiration rates, fresh mass and surface area of entire roots and shoots from 377 Fagus crenata individuals, from germinating seeds to mature trees, collected from five different Japanese provenances. Non-linear regression analysis was performed for scaling of root and shoot respiration, fresh mass and surface area with body size.

KEY RESULTS

Whole-plant respiration increased rapidly in germinating seeds. In the seedling to mature tree size range, the scaling of whole-plant respiration to whole-plant fresh mass was expressed as a linear trend on the log-log coordinates (exponent slightly greater than 0.75). In the same body size range, root and shoot respiration vs. whole-plant fresh mass were modelled by upward-convex (exponent decreased from 2.35 to 0.638) and downward-convex trends (exponent increased from -0.918 to 0.864), respectively. The root fraction in whole-plant respiration, fresh mass and surface area shifted continuously throughout ontogeny, increasing in smaller seedlings during early growth stages and decreasing in larger trees.

CONCLUSIONS

Our results suggest a gradual shift in allocation priorities of metabolic energy from roots in seedlings to shoots in mature trees, providing insights into how roots contribute to shoot and whole-plant growth during ontogeny. The models of root : shoot ratio in relation to whole-plant physiology could be applied in tree growth modelling, and in linking the different levels of ecological phenomena, from individuals to ecosystems.

Spatial statistics is a comprehensive tool for quantifying cell neighbor relationships and biological processes via tissue image analysis

Automated microscopy and computational image analysis has transformed cell biology, providing quantitative, spatially resolved information on cells and their constituent molecules from the sub-micron to the whole-organ scale. Here we explore the application of spatial statistics to the cellular relationships within tissue microscopy data and discuss how spatial statistics offers cytometry a powerful yet underused mathematical tool set for which the required data are readily captured using standard protocols and microscopy equipment. We also highlight the often-overlooked need to carefully consider the structural heterogeneity of tissues in terms of the applicability of different statistical measures and their accuracy and demonstrate how spatial analyses offer a great deal more than just basic quantification of biological variance. Ultimately, we highlight how statistical modeling can help reveal the hierarchical spatial processes that connect the properties of individual cells to the establishment of biological function.

Flow similarity, stochastic branching, and quarter-power scaling in plants

The origin of allometric scaling patterns that are multiples of one-fourth has long fascinated biologists. While not universal, quarter-power scaling relationships are common and have been described in all major clades. Several models have been advanced to explain the origin of such patterns, but questions regarding the discordance between model predictions and empirical data have limited their widespread acceptance. Notable among these is a fractal branching model that predicts power-law scaling of both metabolism and physical dimensions. While a power law is a useful first approximation to some data sets, nonlinear data compilations suggest the possibility of alternative mechanisms. Here, we show that quarter-power scaling can be derived using only the preservation of volume flow rate and velocity as model constraints. Applying our model to land plants, we show that incorporating biomechanical principles and allowing different parts of plant branching networks to be optimized to serve different functions predicts nonlinearity in allometric relationships and helps explain why interspecific scaling exponents covary along a fractal continuum. We also demonstrate that while branching may be a stochastic process, due to the conservation of volume, data may still be consistent with the expectations for a fractal network when one examines sub-trees within a tree. Data from numerous sources at the level of plant shoots, stems, and petioles show strong agreement with our model predictions. This theoretical framework provides an easily testable alternative to current general models of plant metabolic allometry.

Variable metabolic scaling breaks the law: from 'Newtonian' to 'Darwinian' approaches

Life's size and tempo are intimately linked. The rate of metabolism varies with body mass in remarkably regular ways that can often be described by a simple power function, where the scaling exponent (b, slope in a log-linear plot) is typically less than 1. Traditional theory based on physical constraints has assumed that b is 2/3 or 3/4, following natural law, but hundreds of studies have documented extensive, systematic variation in b. This overwhelming, law-breaking, empirical evidence is causing a paradigm shift in metabolic scaling theory and methodology from ‘Newtonian’ to ‘Darwinian’ approaches. A new wave of studies focuses on the adaptable regulation and evolution of metabolic scaling, as influenced by diverse intrinsic and extrinsic factors, according to multiple context-dependent mechanisms, and within boundary limits set by physical constraints.

Scaling the leaf length-times-width equation to predict total leaf area of shoots

BACKGROUND AND AIMS

An individual plant consists of different-sized shoots, each of which consists of different-sized leaves. To predict plant-level physiological responses from the responses of individual leaves, modelling this within-shoot leaf size variation is necessary. Within-plant leaf trait variation has been well investigated in canopy photosynthesis models but less so in plant allometry. Therefore, integration of these two different approaches is needed.

METHODS

We focused on an established leaf-level relationship that the area of an individual leaf lamina is proportional to the product of its length and width. The geometric interpretation of this equation is that different-sized leaf laminas from a single species share the same basic form. Based on this shared basic form, we synthesized a new length-times-width equation predicting total shoot leaf area from the collective dimensions of leaves that comprise a shoot. Furthermore, we showed that several previously established empirical relationships, including the allometric relationships between total shoot leaf area, maximum individual leaf length within the shoot and total leaf number of the shoot, can be unified under the same geometric argument. We tested the model predictions using five species, all of which have simple leaves, selected from diverse taxa (Magnoliids, monocots and eudicots) and from different growth forms (trees, erect herbs and rosette herbs).

KEY RESULTS

For all five species, the length-times-width equation explained within-species variation of total leaf area of a shoot with high accuracy (R2 > 0.994). These strong relationships existed despite leaf dimensions scaling very differently between species. We also found good support for all derived predictions from the model (R2 > 0.85).

CONCLUSIONS

Our model can be incorporated to improve previous models of allometry that do not consider within-shoot size variation of individual leaves, providing a cross-scale linkage between individual leaf-size variation and shoot-size variation.

Seeing the forest for the trees through metabolic scaling

We demonstrate that when power scaling occurs for an individual tree and in a forest, there is great resulting simplicity notwithstanding the underlying complexity characterizing the system over many size scales. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions. We show that the effective dimension, D _tree , of a tree is close to 3, whereas a mature forest has D _forest approaching 1. We discuss the energy equivalence rule and show that the metabolic rate-mass relationship is a power law with an exponent D/(D + 1) in both cases leading to a Kleiber's exponent of 3/4 for a tree and 1/2 for a forest. Our work has implications for understanding carbon sequestration and for climate science.

Growing Strategy for Postmodifying Cross-Linked Polymers' Bulky Size, Shape, and Mechanical Properties

Living organisms are open systems that can incorporate externally provided nutrients to vary their appearances and properties, while synthetic materials normally have fixed sizes, shapes, and functions. Herein, we report a strategy for enabling cross-linked polymers to continuously grow with programmable bulky structures and properties. The growing strategy involves repeatable processes including swelling of polymerizable components into the cross-linked polymers, in situ polymerization of the components, and homogenization of the original and newborn polymer networks. Using acrylate-based polymers as an example, we demonstrate that homogenization allows the grown polymer materials to further integrate various polymerizable components to alternate their bulky properties. During the growth, the changes from elastomers to organogels and then to hydrogels with updated covalent-linked functions (i.e., photochromism and thermoresponsiveness) are shown. Since this growing strategy is applicable to different acrylate systems, we envision its great potential in the design of next-generation polymers, smartening systems, and postmodification of cross-linked polymer materials.

Evolution of metabolic scaling among the tetrapod: Effect of phylogeny, the geologic time of class formation and uniformity of species within a class

The metabolic scaling in the animal has been discussed for over 90 years, but no consensus has been reached. Our analysis of 2,126 species of vertebrates reveals a significant allometric exponent heterogeneity. We show that classes of terrestrial vertebrates exhibit the evolution of metabolic scaling. Both the allometric coefficient "a" and the allometric exponent "b" change naturally, but differently depending on the geological time of group formation. The allometric coefficient "a" shows the measure of the evolutionary development of systems that forms resting metabolism in animals. Endothermic classes, such as birds and mammals, have a metabolic rate that is in an order of magnitude higher than that in ectothermic classes, including amphibians and reptiles. In the terrestrial vertebrate phylogeny, we find that the metabolic scaling is characterized by three main allometric exponent values: b = 3/4 (mammals), b > 3/4 (ectotherms, such as amphibians and reptiles), and b < 3/4 (birds). The heterogeneity of the allometric exponent is a natural phenomenon associated with the general evolution of vertebrates. The scaling factor decreases depending on both the external design and the size (birds vs mammals) of the animal. The metabolic rate and uniformity of species within a class increase as the geological start date of formation of the class approaches the present time. The higher the mass-specific standard metabolic rate in the class, the slower metabolic rate grows with increasing body size in this class. Our results lay the groundwork for further exploration of the evolutionary and ecological aspects of the development of metabolic scaling in animals. This article is protected by copyright. All rights reserved.

Phylogeny, body morphology, and trophic level shape intestinal traits in coral reef fishes

Trait-based approaches are increasingly used to study species assemblages and understand ecosystem functioning. The strength of these approaches lies in the appropriate choice of functional traits that relate to the functions of interest. However, trait-function relationships are often supported by weak empirical evidence.Processes related to digestion and nutrient assimilation are particularly challenging to integrate into trait-based approaches. In fishes, intestinal length is commonly used to describe these functions. Although there is broad consensus concerning the relationship between fish intestinal length and diet, evolutionary and environmental forces have shaped a diversity of intestinal morphologies that is not captured by length alone.Focusing on coral reef fishes, we investigate how evolutionary history and ecology shape intestinal morphology. Using a large dataset encompassing 142 species across 31 families collected in French Polynesia, we test how phylogeny, body morphology, and diet relate to three intestinal morphological traits: intestinal length, diameter, and surface area.We demonstrate that phylogeny, body morphology, and trophic level explain most of the interspecific variability in fish intestinal morphology. Despite the high degree of phylogenetic conservatism, taxonomically unrelated herbivorous fishes exhibit similar intestinal morphology due to adaptive convergent evolution. Furthermore, we show that stomachless, durophagous species have the widest intestines to compensate for the lack of a stomach and allow passage of relatively large undigested food particles.Rather than traditionally applied metrics of intestinal length, intestinal surface area may be the most appropriate trait to characterize intestinal morphology in functional studies.

Thiolate end-group regulates ligand arrangement, hydration and affinity for small compounds in monolayer-protected gold nanoparticles

The ability to control the properties of monolayer protected gold nanoparticles (MPNPs) discloses unrevealed features stemming from collective properties of the ligands forming the monolayer and presents opportunities to design new materials. To date, the influence of ligand end-group size and capacity to form hydrogen bonds on structure and hydration of small MPNPs (<5 nm) has been poorly studied. Here, we show that both features determine ligands order, solvent accessibility, capacity to host hydrophobic compounds and interfacial properties of MPNPs. The polarity perceived by a radical probe and its binding constant with the monolayer investigated by electron spin resonance is rationalized by molecular dynamics simulations, which suggest that larger space-filling groups - trimethylammonium, zwitterionic and short polyethylene glycol - favor a radial organization of the thiolates, whereas smaller groups - as sulfonate - promote the formation of bundles. Zwitterionic ligands create a surface network of hydrogen bonds, which affects nanoparticle hydrophobicity and maximize the partition equilibrium constant of the probe. This study discloses the role of the chemistry of the end-group on monolayer features with effects that span from molecular- to nano-scale and opens the door to a shift in the conception of new MPNPs exploiting the end-group as a novel design motif.

Consistent scaling of whole-shoot respiration between Moso bamboo (Phyllostachys pubescens) and trees

Both Moso bamboo (Phyllostachys pubescens) and tree forests have a large biomass; they are considered to play an important role in ecosystem carbon budgets. The scaling relationship between individual whole-shoot (i.e., aboveground parts) respiration and whole-shoot mass provides a clue for comparing the carbon budgets of Moso bamboo and tree forests. However, nobody has empirically demonstrated whether there is a difference between these forest types in the whole-shoot scaling relationship. We developed whole-shoot chambers and measured the shoot respiration of 58 individual mature bamboo shoots from the smallest to the largest in a Moso bamboo forest, and then compared them with that of 254 tree shoots previously measured. For 30 bamboo shoots, we measured the respiration rate of leaves, branches, and culms. We found that the scaling exponent of whole-shoot respiration of bamboo fitted by a simple power function on a log-log scale was 0.843 (95 % CI 0.797-0.885), which was consistent with that of trees, 0.826 (95 % CI 0.799-0.851), but higher than 3/4, the value typifying the Kleiber's rule. The respiration rates of leaves, branches, and culms at the whole-shoot level were proportional to their mass, revealing a constant mean mass-specific respiration of 1.19, 0.224, and 0.0978 µmol CO2 kg- 1 s- 1, respectively. These constant values suggest common traits of organs among physiologically integrated ramets within a genet. Additionally, the larger the shoots, the smaller the allocation of organ mass to the metabolically active leaves, and the larger the allocation to the metabolically inactive culms. Therefore, these shifts in shoot-mass partitioning to leaves and culms caused a negative metabolic scaling of Moso bamboo shoots. The observed convergent metabolic scaling of Moso bamboo and trees may facilitate comparisons of the ecosystem carbon budgets of Moso bamboo and tree forests.

A network-based framework for shape analysis enables accurate characterization of leaf epidermal cells

Cell shape is crucial for the function and development of organisms. Yet, versatile frameworks for cell shape quantification, comparison, and classification remain underdeveloped. Here, we introduce a visibility graph representation of shapes that facilitates network-driven characterization and analyses across shapes encountered in different domains. Using the example of complex shape of leaf pavement cells, we show that our framework accurately quantifies cell protrusions and invaginations and provides additional functionality in comparison to the contending approaches. We further show that structural properties of the visibility graphs can be used to quantify pavement cell shape complexity and allow for classification of plants into their respective phylogenetic clades. Therefore, the visibility graphs provide a robust and unique framework to accurately quantify and classify the shape of different objects.

Allometric co-variation of xylem and stomata across diverse woody seedlings

Leaf stomatal density is known to co-vary with leaf vein density. However, the functional underpinning of this relation, and how it scales to whole-plant water transport anatomy, is still unresolved. We hypothesized that the balance of water exchange between the vapour phase (in stomata) and liquid phase (in vessels) depends on the consistent scaling between the summed stomatal areas and xylem cross-sectional areas, both at the whole-plant and single-leaf level. This predicted size co-variation should be driven by the co-variation of numbers of stomata and terminal vessels. We examined the relationships of stomatal traits and xylem anatomical traits from the entire plant to individual leaves across seedlings of 53 European woody angiosperm species. There was strong and convergent scaling between total stomatal area and stem xylem area per plant and between leaf total stomatal area and midvein xylem area per leaf across all the species, irrespective of variation in leaf habit, growth-form or relative growth rate. Moreover, strong scaling was found between stomatal number and terminal vessel number, whereas not in their respective average areas. Our findings have broad implications for integrating xylem architecture and stomatal distribution and deepen our understanding of the design rules of plants' water transport network.

Exploiting the role of nanoparticle shape in enhancing hydrogel adhesive and mechanical properties

The ability to control nanostructure shape and dimensions presents opportunities to design materials in which their macroscopic properties are dependent upon the nature of the nanoparticle. Although particle morphology has been recognized as a crucial parameter, the exploitation of the potential shape-dependent properties has, to date, been limited. Herein, we demonstrate that nanoparticle shape is a critical consideration in the determination of nanocomposite hydrogel properties. Using translationally relevant calcium-alginate hydrogels, we show that the use of poly(L-lactide)-based nanoparticles with platelet morphology as an adhesive results in a significant enhancement of adhesion over nanoparticle glues comprised of spherical or cylindrical micelles. Furthermore, gel nanocomposites containing platelets showed an enhanced resistance to breaking under strain compared to their spherical and cylindrical counterparts. This study opens the doors to a change in direction in the field of gel nanocomposites, where nanoparticle shape plays an important role in tuning mechanical properties.

The ability to control nanostructure shape and dimensions presents opportunities to design materials in which their macroscopic properties are dependent upon the nature of the nanoparticle. Here the authors show nanoparticle shape is a critical consideration in the determination of nanocomposite hydrogel properties.

Allometric growth in meiofaunal invertebrates: do all kinorhynchs show homogeneous trends?

Allometry determines relevant modifications in metazoan morphology and biology and is affected by many different factors, such as ontogenetic constraints and natural selection. A linear mixed model approach and reduced major axis regression were used to explore evolutionary interspecific allometric trends between the total trunk length and the lengths of the segments and spines in the phylum Kinorhyncha at three taxonomic levels: the whole phylum, the class and the family. Statistically significant results were found in all the trunk segments, meaning that these body units grow proportionally correlated with the body, contrary to the results obtained for the spines. Developmental and morphophysiological constraints could lead to negative allometry in the first and last segments, because these body regions in kinorhynchs are essential to the implementation of some of the main biological functions, such as feeding and locomotion. The differential arrangement of cuticular appendages between the taxonomic groups considered seems to cause different evolutionary trends, because positive allometry may appear if a segment requires more space to accommodate a large number of organs and appendages, and vice versa. The presence of sexual dimorphism could also define positive allometry of a segment, owing to the need to harbour the sexually dimorphic appendages and their associated structures.

Generalized size scaling of metabolic rates based on single-cell measurements with freshwater phytoplankton

Kleiber's law describes the scaling of metabolic rate with body size across several orders of magnitude in size and across taxa and is widely regarded as a fundamental law in biology. The physiological origins of Kleiber's law are still debated and generalizations of the law accounting for deviations from the scaling behavior have been proposed. Most theoretical and experimental studies of Kleiber's law, however, have focused on the relationship between the average body size of a species and its mean metabolic rate, neglecting intraspecific variation of these 2 traits. Here, we propose a theoretical characterization of such variation and report on proof-of-concept experiments with freshwater phytoplankton supporting such framework. We performed joint measurements at the single-cell level of cell volume and nitrogen/carbon uptake rates, as proxies of metabolic rates, of 3 phytoplankton species using nanoscale secondary ion mass spectrometry (NanoSIMS) and stable isotope labeling. Common scaling features of the distribution of nutrient uptake rates and cell volume are found to hold across 3 orders of magnitude in cell size. Once individual measurements of cell volume and nutrient uptake rate within a species are appropriately rescaled by a function of the average cell volume within each species, we find that intraspecific distributions of cell volume and metabolic rates collapse onto a universal curve. Based on the experimental results, this work provides the building blocks for a generalized form of Kleiber's law incorporating intraspecific, correlated variations of nutrient-uptake rates and body sizes.

Methods to label, image, and analyze the complex structural architectures of microvascular networks

Microvascular networks play key roles in oxygen transport and nutrient delivery to meet the varied and dynamic metabolic needs of different tissues throughout the body, and their spatial architectures of interconnected blood vessel segments are highly complex. Moreover, functional adaptations of the microcirculation enabled by structural adaptations in microvascular network architecture are required for development, wound healing, and often invoked in disease conditions, including the top eight causes of death in the Unites States. Effective characterization of microvascular network architectures is not only limited by the available techniques to visualize microvessels but also reliant on the available quantitative metrics that accurately delineate between spatial patterns in altered networks. In this review, we survey models used for studying the microvasculature, methods to label and image microvessels, and the metrics and software packages used to quantify microvascular networks. These programs have provided researchers with invaluable tools, yet we estimate that they have collectively attained low adoption rates, possibly due to limitations with basic validation, segmentation performance, and nonstandard sets of quantification metrics. To address these existing constraints, we discuss opportunities to improve effectiveness, rigor, and reproducibility of microvascular network quantification to better serve the current and future needs of microvascular research.

Body size-dependent energy storage causes Kleiber's law scaling of the metabolic rate in planarians

Kleiber's law, or the 3/4 -power law scaling of the metabolic rate with body mass, is considered one of the few quantitative laws in biology, yet its physiological basis remains unknown. Here, we report Kleiber's law scaling in the planarian Schmidtea mediterranea. Its reversible and life history-independent changes in adult body mass over 3 orders of magnitude reveal that Kleiber's law does not emerge from the size-dependent decrease in cellular metabolic rate, but from a size-dependent increase in mass per cell. Through a combination of experiment and theoretical analysis of the organismal energy balance, we further show that the mass allometry is caused by body size dependent energy storage. Our results reveal the physiological origins of Kleiber's law in planarians and have general implications for understanding a fundamental scaling law in biology.

Methods for imaging mammalian mitochondrial morphology: A prospective on MitoGraph

Mitochondria are found in a variety of shapes, from small round punctate structures to a highly interconnected web. This morphological diversity is important for function, but complicates quantification. Consequently, early quantification efforts relied on various qualitative descriptors that understandably reduce the complexity of the network leading to challenges in consistency across the field. Recent application of state-of-the-art computational tools have resulted in more quantitative approaches. This prospective highlights the implementation of MitoGraph, an open-source image analysis platform for measuring mitochondrial morphology initially optimized for use with Saccharomyces cerevisiae. Here Mitograph was assessed on five different mammalian cells types, all of which were accurately segmented by MitoGraph analysis. MitoGraph also successfully differentiated between distinct mitochondrial morphologies that ranged from entirely fragmented to hyper-elongated. General recommendations are also provided for confocal imaging of labeled mitochondria (using mito-YFP, MitoTracker dyes and immunostaining parameters). Widespread adoption of MitoGraph will help achieve a long-sought goal of consistent and reproducible quantification of mitochondrial morphology.

On the thermodynamic origin of metabolic scaling

The origin and shape of metabolic scaling has been controversial since Kleiber found that basal metabolic rate of animals seemed to vary as a power law of their body mass with exponent 3/4, instead of 2/3, as a surface-to-volume argument predicts. The universality of exponent 3/4 -claimed in terms of the fractal properties of the nutrient network- has recently been challenged according to empirical evidence that observed a wealth of robust exponents deviating from 3/4. Here we present a conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organism to maintain its metabolism. This balance tunes the shape of an additive model from which different effective scalings can be recovered as particular cases, thereby reconciling previously inconsistent empirical evidence in mammals, birds, insects and even plants under a unified framework. This model is biologically motivated, fits remarkably well the data, and also explains additional features such as the relation between energy lost as heat and mass, the role and influence of different climatic environments or the difference found between endotherms and ectotherms.

Covariations in ecological scaling laws fostered by community dynamics

Scaling laws in ecology, intended both as functional relationships among ecologically relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances, and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem type and resource supply rate. The idea that ecological scaling laws are linked has been entertained before, but the full extent of macroecological pattern covariations, the role of the constraints imposed by finite resource supply, and a comprehensive empirical verification are still unexplored. Here, we propose a theoretical scaling framework that predicts the linkages of several macroecological patterns related to species' abundances and body sizes. We show that such a framework is consistent with the stationary-state statistics of a broad class of resource-limited community dynamics models, regardless of parameterization and model assumptions. We verify predicted theoretical covariations by contrasting empirical data and provide testable hypotheses for yet unexplored patterns. We thus place the observed variability of ecological scaling exponents into a coherent statistical framework where patterns in ecology embed constrained fluctuations.

Do Performance-Safety Tradeoffs Cause Hypometric Metabolic Scaling in Animals?

Hypometric scaling of aerobic metabolism in animals has been widely attributed to constraints on oxygen (O₂) supply in larger animals, but recent findings demonstrate that O₂ supply balances with need regardless of size. Larger animals also do not exhibit evidence of compensation for O₂ supply limitation. Because declining metabolic rates (MRs) are tightly linked to fitness, this provides significant evidence against the hypothesis that constraints on supply drive hypometric scaling. As an alternative, ATP demand might decline in larger animals because of performance-safety tradeoffs. Larger animals, which typically reproduce later, exhibit risk-reducing strategies that lower MR. Conversely, smaller animals are more strongly selected for growth and costly neurolocomotory performance, elevating metabolism.

Demystification of animal symmetry: symmetry is a response to mechanical forces

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Symmetry is an eye-catching feature of animal body plans, yet its causes are not well enough understood. The evolution of animal form is mainly due to changes in gene regulatory networks (GRNs). Based on theoretical considerations regarding fundamental GRN properties, it has recently been proposed that the animal genome, on large time scales, should be regarded as a system which can construct both the main symmetries – radial and bilateral – simultaneously; and that the expression of any of these depends on functional constraints. Current theories explain biological symmetry as a pattern mostly determined by phylogenetic constraints, and more by chance than by necessity. In contrast to this conception, I suggest that physical effects, which in many cases act as proximate, direct, tissue-shaping factors during ontogenesis, are also the ultimate causes – i.e. the indirect factors which provide a selective advantage – of animal symmetry, from organs to body plan level patterns. In this respect, animal symmetry is a necessary product of evolution. This proposition offers a parsimonious view of symmetry as a basic feature of the animal body plan, suggesting that molecules and physical forces act in a beautiful harmony to create symmetrical structures, but that the concert itself is directed by the latter.

Reviewers

This article was reviewed by Eugene Koonin, Zoltán Varga and Michaël Manuel.

Ecology of ontogenetic body-mass scaling of gill surface area in a freshwater crustacean

Several studies have documented ecological effects on intraspecific and interspecific body-size scaling of metabolic rate. However, little is known about how various ecological factors may affect the scaling of respiratory structures supporting oxygen uptake for metabolism. To our knowledge, our study is the first to provide evidence for ecological effects on the scaling of a respiratory structure among conspecific populations of any animal. We compared the body-mass scaling of gill surface area (SA) among eight spring-dwelling populations of the amphipod crustacean Gammarus minus Although gill SA scaling was not related to water temperature, conductivity or G. minus population density, it was significantly related to predation regime (and secondarily to pH). Body-mass scaling slopes for gill SA were significantly lower in four populations inhabiting springs with fish predators than for four populations in springs without fish (based on comparing means of the population slopes, or slopes calculated from pooled raw data for each comparison group). As a result, gill SA was proportionately smaller in adult amphipods from springs with versus without fish. This scaling difference paralleled similar differences in the scaling exponents for the rates of growth and resting metabolic rate. We hypothesized that gill SA scaling is shallower in fish-containing versus fishless spring populations of G. minus because of effects of size-selective predation on size-specific growth and activity that in turn affect the scaling of oxygen demand and concomitantly the gill capacity (SA) for oxygen uptake. Although influential theory claims that metabolic scaling is constrained by internal body design, our study builds on previous work to show that the scaling of both metabolism and the respiratory structures supporting it may be ecologically sensitive and evolutionarily malleable.

A general model for metabolic scaling in self-similar asymmetric networks

How a particular attribute of an organism changes or scales with its body size is known as an allometry. Biological allometries, such as metabolic scaling, have been hypothesized to result from selection to maximize how vascular networks fill space yet minimize internal transport distances and resistances. The West, Brown, Enquist (WBE) model argues that these two principles (space-filling and energy minimization) are (i) general principles underlying the evolution of the diversity of biological networks across plants and animals and (ii) can be used to predict how the resulting geometry of biological networks then governs their allometric scaling. Perhaps the most central biological allometry is how metabolic rate scales with body size. A core assumption of the WBE model is that networks are symmetric with respect to their geometric properties. That is, any two given branches within the same generation in the network are assumed to have identical lengths and radii. However, biological networks are rarely if ever symmetric. An open question is: Does incorporating asymmetric branching change or influence the predictions of the WBE model? We derive a general network model that relaxes the symmetric assumption and define two classes of asymmetrically bifurcating networks. We show that asymmetric branching can be incorporated into the WBE model. This asymmetric version of the WBE model results in several theoretical predictions for the structure, physiology, and metabolism of organisms, specifically in the case for the cardiovascular system. We show how network asymmetry can now be incorporated in the many allometric scaling relationships via total network volume. Most importantly, we show that the 3/4 metabolic scaling exponent from Kleiber’s Law can still be attained within many asymmetric networks.

We present a model for incorporating geometrically asymmetric branching into biological resource distribution networks. Our work shows how space-filling and fluid flow principles constrain allowed branching morphologies within the context of our model. Simultaneously, we demonstrate that there is a wide range of asymmetrically branching network architectures that still give rise to 3/4 metabolic scaling exponents.

A lognormal distribution of the lengths of terminal twigs on self-similar branches of elm trees

Lognormal distributions and self-similarity are characteristics associated with a wide range of biological systems. The sequential breakage model has established a link between lognormal distributions and self-similarity and has been used to explain species abundance distributions. To date, however, there has been no similar evidence in studies of multicellular organismal forms. We tested the hypotheses that the distribution of the lengths of terminal stems of Japanese elm trees (Ulmus davidiana), the end products of a self-similar branching process, approaches a lognormal distribution. We measured the length of the stem segments of three elm branches and obtained the following results: (i) each occurrence of branching caused variations or errors in the lengths of the child stems relative to their parent stems; (ii) the branches showed statistical self-similarity; the observed error distributions were similar at all scales within each branch and (iii) the multiplicative effect of these errors generated variations of the lengths of terminal twigs that were well approximated by a lognormal distribution, although some statistically significant deviations from strict lognormality were observed for one branch. Our results provide the first empirical evidence that statistical self-similarity of an organismal form generates a lognormal distribution of organ sizes.

Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?

Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.

The architecture of vascular networks must balance complex demands to efficiently deliver oxygen and resources throughout the entire body. These demands constrain the possible forms of vasculature. Because of these constraints and the indispensable role of vasculature for much of life, scientists have sought to identify systematic patterns in the structural properties of vascular networks and whether these patterns can be predicted from models based on biological and physical principles. These studies have been limited by the lack of extensive, detailed data. Using high-quality vascular network data obtained via our software, Angicart, we identify novel, systematic patterns of asymmetry in sizes and branching angles among sibling vessels from mouse lung and human head and torso. To examine what constraints might underlie these patterns, we investigate several explanations, including various types of optimal branching as well as random branching. The optimal branchings were derived locally with respect to constraints on material costs or power loss. For random branching we allowed the degree of randomness to vary from local to global spatial scales. By comparing predictions with real data, our study suggests that a key component in determining vascular branching is material cost with some randomness at local to intermediate spatial scales.