Scaling properties of cell and organelle size

How size is controlled is a fundamental question in biology. In this review, we discuss the use of scaling relationships—for example, power laws of the form y ∝ xα—to provide a framework for comparison and interpretation of size measurements. Such analysis can illustrate the biological and physical principles underlying observed trends, as has been proposed for the allometric dependence of metabolic rate or limb structure on organism mass. Techniques for measuring size at smaller length-scales continue to improve, leading to more data on the control of size in cells and organelles. Size scaling of these structures is expected to influence growth patterns, functional capacity, and intracellular transport. Furthermore, organelles such as the nucleus, mitochondria, and endoplasmic reticulum show widely varying morphologies which affect their scaling properties. We provide brief summaries of these issues for individual organelles, and conclude with a discussion on how to apply this concept to better understand the mechanisms of size control in the cellular environment.     

Size regulation of multiple organelles competing for a limiting subunit pool

How cells regulate the size of intracellular structures and organelles is a longstanding question. Recent experiments suggest that size control of intracellular structures is achieved through the depletion of a limiting subunit pool in the cytoplasm. While the limiting pool model ensures organelle-to-cell size scaling, it does not provide a mechanism for robust size control of multiple co-existing structures. Here we develop a generalized theory for size-dependent growth of intracellular structures to demonstrate that robust size control of multiple intracellular structures, competing for a limiting subunit pool, is achieved via a negative feedback between the growth rate and the size of the individual structure. This design principle captures size maintenance of a wide variety of subcellular structures, from cytoskeletal filaments to three-dimensional organelles. We identify the feedback motifs for structure size regulation based on known molecular processes, and compare our theory to existing models of size regulation in biological assemblies. Furthermore, we show that positive feedback between structure size and growth rate can lead to bistable size distribution and spontaneous size selection.     

Organelle growth control through limiting pools of cytoplasmic components

The critical importance of controlling the size and number of intracellular organelles has led to a variety of mechanisms for regulating the formation and growth of cellular structures. In this review, we explore a class of mechanisms for organelle growth control that rely primarily on the cytoplasm as a 'limiting pool' of available material. These mechanisms are based on the idea that, as organelles grow, they incorporate subunits from the cytoplasm. If this subunit pool is limited, organelle growth will lead to depletion of subunits from the cytoplasm. Free subunit concentration therefore provides a measure of the number of incorporated subunits and thus the current size of the organelle. Because organelle growth rates are typically a function of subunit concentration, cytoplasmic depletion links organelle size, free subunit concentration, and growth rates, ensuring that as the organelle grows, its rate of growth slows. Thus, a limiting cytoplasmic pool provides a powerful mechanism for size-dependent regulation of growth without recourse to active mechanisms to measure size or modulate growth rates. Variations of this general idea allow not only for size control, but also cell-size-dependent scaling of cellular structures, coordination of growth between similar structures within a cell, and the enforcement of singularity in structure formation, when only a single copy of a structure is desired. Here, we review several examples of such mechanisms in cellular processes as diverse as centriole duplication, centrosome and nuclear size control, cell polarity, and growth of flagella.     

Biological Scaling Problems and Solutions in Amphibians

Size is a primary feature of biological systems that varies at many levels, from the organism to its constituent cells and subcellular structures. Amphibians populate some of the extremes in biological size and have provided insight into scaling mechanisms, upper and lower size limits, and their physiological significance. Body size variation is a widespread evolutionary tactic among amphibians, with miniaturization frequently correlating with direct development that occurs without a tadpole stage. The large genomes of salamanders lead to large cell sizes that necessitate developmental modification and morphological simplification. Amphibian extremes at the cellular level have provided insight into mechanisms that accommodate cell-size differences. Finally, how organelles scale to cell size between species and during development has been investigated at the molecular level, because subcellular scaling can be recapitulated using Xenopus in vitro systems.Size is a fundamental biological feature that impacts physiology at all levels, from organism to organ to cell to subcellular structures/organelles. One basic aspect of size is its absolute value, which has upper and lower limits because of functional requirements. For example, a vertebrate organ, such as an eye or an inner ear, may require a minimum number of cells, or a minimum physical size, to operate. Importantly, surface area and volume scale differently with size, and this also has physiological consequences at both the organism and cellular levels, affecting basic processes, such as desiccation and diffusion. A second important feature of size is scaling relationships, as the overall size of an organism or tissue is determined both by cell size and cell number. At the subcellular level, size scaling may or may not occur depending on the organelle, as absolute values are constrained by the nature and flexibility of constituent molecular building blocks. For example, whereas the size of the nucleus varies significantly and scales with cell size, organelle transport vesicles are of more uniform size owing to the conserved structure of their coat proteins. Extremes in amphibian size and scaling relationships derive primarily from dramatic variations in genome size, and provide instructive examples of size relationships, underlying molecular mechanisms, and above all the remarkable flexibility and power of evolution to adapt biological function across a wide range of size scales.     

Microscaling: why larger anemones have longer cnidae

Scaling analysis provides a quantitative method for describing and comparing how qualities of organisms vary as a function of body size. However, cell level phenomena have been notoriously hard to analyze because animal cells and organelles have such irregular shapes. The intracellular cnidae make good models of scaling at the cell level because they are durable and easy to image and measure. The mean length of unfired tentacle cnidae (spirocysts) varies continuously, and reversibly, with body size for three macrophagous anemone species. Significant differences in spirocyst shape and size relative to body mass are related to differences in tissue functions and species ecologies, strongly suggesting that cnida size, shape, and scaling patterns respond to natural selection. Cnida scaling patterns can be treated as features of cnidarian life histories. Spirocyst scaling exponents (slopes of log cnida dimension vs. log body weight) are similar to each other (0.05-0.09) and to reported values for animal somatic cells (0.017-0.17), but are much smaller than reported values for anemone basal diameters (0.30-0.38). I propose, here, a general, mechanical explanation for microscaling of structural secretory cells and their secretions, including the cnidae. Larger bodies require thicker, pliant sheets of sluggishly respiring extracellular support materials such as mesoglea and basement membrane. Thicker mesoglea can support larger, taller epithelial cells, which in turn provide additional maintenance services for these progressively thicker acellular layers. Ultimately, larger, taller cells can secrete and support larger, longer cnidae.     

Selection on an extreme weapon in the frog‐legged leaf beetle (Sagra femorata)

Biologists have been fascinated with the extreme products of sexual selection for decades. However, relatively few studies have characterized patterns of selection acting on ornaments and weapons in the wild. Here, we measure selection on a wild population of weapon‐bearing beetles (frog‐legged leaf beetles: Sagra femorata) for two consecutive breeding seasons. We consider variation in both weapon size (hind leg length) and in relative weapon size (deviations from the population average scaling relationship between hind leg length and body size), and provide evidence for directional selection on weapon size per se and stabilizing selection on a particular scaling relationship in this population. We suggest that whenever growth in body size is sensitive to external circumstance such as nutrition, then considering deviations from population‐level scaling relationships will better reflect patterns of selection relevant to evolution of the ornament or weapon than will variation in trait size per se. This is because trait‐size versus body‐size scaling relationships approximate underlying developmental reaction norms relating trait growth with body condition in these species. Heightened condition‐sensitive expression is a hallmark of the exaggerated ornaments and weapons favored by sexual selection, yet this plasticity is rarely reflected in the way we think about—and measure—selection acting on these structures in the wild.     

Influence of food,body size,and fragmentation on metabolic rate in a sessile marine invertebrate

Metabolic rates vary among individuals according to food availability and phenotype, most notably body size. Disentangling size from other factors (e.g., age, reproductive status) can be difficult in some groups, but modular organisms may provide an opportunity for manipulating size experimentally. While modular organisms are increasingly used to understand metabolic scaling, the potential of feeding to alter metabolic scaling has not been explored in this group. Here, we perform a series of experiments to examine the drivers of metabolic rate in a modular marine invertebrate, the bryozoan Bugula neritina. We manipulated size and examined metabolic rate in either fed or starved individuals to test for interactions between size manipulation and food availability. Field collected colonies of unknown age showed isometric metabolic scaling, but those colonies in which size was manipulated showed allometric scaling. To further disentangle age effects from size effects, we measured metabolic rate of individuals of known age and again found allometric scaling. Metabolic rate strongly depended on access to food: starvation decreased metabolic rate by 20% and feeding increased metabolic rate by 43%. In comparison to other marine invertebrates, however, the increase in metabolic rate, as well as the duration of the increase (known as specific dynamic action, SDA), were both low. Importantly, neither starvation nor feeding altered the metabolic scaling of our colonies. Overall, we found that field‐collected individuals showed isometric metabolic scaling, whereas metabolic rate of size‐manipulated colonies scaled allometrically with body size. Thus, metabolic scaling is affected by size manipulation but not feeding in this colonial marine invertebrate.     

Organelle Size Scaling of the Budding Yeast Vacuole Is Tuned by Membrane Trafficking Rates

Organelles serve as biochemical reactors in the cell, and often display characteristic scaling trends with cell size, suggesting mechanisms that coordinate their sizes. In this study, we measure the vacuole-cell size scaling trends in budding yeast using optical microscopy and a novel, to our knowledge, image analysis algorithm. Vacuole volume and surface area both show characteristic scaling trends with respect to cell size that are consistent among different strains. Rapamycin treatment was found to increase vacuole-cell size scaling trends for both volume and surface area. Unexpectedly, these increases did not depend on macroautophagy, as similar increases in vacuole size were observed in the autophagy deficient mutants atg1Δ and atg5Δ. Rather, rapamycin appears to act on vacuole size by inhibiting retrograde membrane trafficking, as the atg18Δ mutant, which is defective in retrograde trafficking, shows similar vacuole size scaling to rapamycin-treated cells and is itself insensitive to rapamycin treatment. Disruption of anterograde membrane trafficking in the apl5Δ mutant leads to complementary changes in vacuole size scaling. These quantitative results lead to a simple model for vacuole size scaling based on proportionality between cell growth rates and vacuole growth rates.     

Welcome to Wonderland: The Influence of the Size and Shape of a Virtual Hand On the Perceived Size and Shape of Virtual Objects

The notion of body-based scaling suggests that our body and its action capabilities are used to scale the spatial layout of the environment. Here we present four studies supporting this perspective by showing that the hand acts as a metric which individuals use to scale the apparent sizes of objects in the environment. However to test this, one must be able to manipulate the size and/or dimensions of the perceiver’s hand which is difficult in the real world due to impliability of hand dimensions. To overcome this limitation, we used virtual reality to manipulate dimensions of participants’ fully-tracked, virtual hands to investigate its influence on the perceived size and shape of virtual objects. In a series of experiments, using several measures, we show that individuals’ estimations of the sizes of virtual objects differ depending on the size of their virtual hand in the direction consistent with the body-based scaling hypothesis. Additionally, we found that these effects were specific to participants’ virtual hands rather than another avatar’s hands or a salient familiar-sized object. While these studies provide support for a body-based approach to the scaling of the spatial layout, they also demonstrate the influence of virtual bodies on perception of virtual environments.     

Organelle Size Scaling of the Budding Yeast Vacuole Is Tuned by Membrane Trafficking Rates

Organelles serve as biochemical reactors in the cell, and often display characteristic scaling trends with cell size, suggesting mechanisms that coordinate their sizes. In this study, we measure the vacuole-cell size scaling trends in budding yeast using optical microscopy and a novel, to our knowledge, image analysis algorithm. Vacuole volume and surface area both show characteristic scaling trends with respect to cell size that are consistent among different strains. Rapamycin treatment was found to increase vacuole-cell size scaling trends for both volume and surface area. Unexpectedly, these increases did not depend on macroautophagy, as similar increases in vacuole size were observed in the autophagy deficient mutants atg1Δ and atg5Δ. Rather, rapamycin appears to act on vacuole size by inhibiting retrograde membrane trafficking, as the atg18Δ mutant, which is defective in retrograde trafficking, shows similar vacuole size scaling to rapamycin-treated cells and is itself insensitive to rapamycin treatment. Disruption of anterograde membrane trafficking in the apl5Δ mutant leads to complementary changes in vacuole size scaling. These quantitative results lead to a simple model for vacuole size scaling based on proportionality between cell growth rates and vacuole growth rates.     

A Conceptual Mathematical Model of the Dynamic Self-Organisation of Distinct Cellular Organelles

Formation, degradation and renewal of cellular organelles is a dynamic process based on permanent budding, fusion and inter-organelle traffic of vesicles. These processes include many regulatory proteins such as SNAREs, Rabs and coats. Given this complex machinery, a controversially debated issue is the definition of a minimal set of generic mechanisms necessary to enable the self-organization of organelles differing in number, size and chemical composition. We present a conceptual mathematical model of dynamic organelle formation based on interacting vesicles which carry different types of fusogenic proteins (FP) playing the role of characteristic marker proteins. Our simulations (ODEs) show that a de novo formation of non-identical organelles, each accumulating a different type of FP, requires a certain degree of disproportionation of FPs during budding. More importantly however, the fusion kinetics must indispensably exhibit positive cooperativity among these FPs, particularly for the formation of larger organelles. We compared different types of cooperativity: sequential alignment of corresponding FPs on opposite vesicle/organelles during fusion and pre-formation of FP-aggregates (equivalent, e.g., to SNARE clusters) prior to fusion described by Hill kinetics. This showed that the average organelle size in the system is much more sensitive to the disproportionation strength of FPs during budding if the vesicular transport system gets along with a fusion mechanism based on sequential alignments of FPs. Therefore, pre-formation of FP aggregates within the membranes prior to fusion introduce robustness with respect to organelle size. Our findings provide a plausible explanation for the evolution of a relatively large number of molecules to confer specificity on the fusion machinery compared to the relatively small number involved in the budding process. Moreover, we could speculate that a specific cooperativity which may be described by Hill kinetics (aggregates or Rab/SNARE complex formation) is suitable if maturation/identity switching of organelles play a role (bistability).     

Size and scaling of sexually-selected traits in the lizard, Uta palmeri

Differences between the sexes in overall body size and in the size of other morphological traits, relative to overall body size, are common in many animals. In this study, patterns of growth and scaling of sexually dimorphic tratis are assessedin a lilzard and then used to sugest general developmental mechanisms responsible for sexual size dimorphism (SSD). Adult make Uta palmeri lizards are larger than adult females inoverall body size (snout-vent length, SVL), body mass, jaw length head width, and head depth. Two general growth processes produce this adult SSD. First, juvenile males have greater annual SVL growth rates than do juvenile females, contributing to adult SSD because males will be larger than females in any trait positively correlated with SVL. Secondly, males and females differ in age-related changes in growth of the three head size traits, relative to growth in SVL. Comparing slopes from reduced major axis regressions of each trait on SVL reveals that the sexes do not differ in the scaling of these traits as juveniles, but as adults males have greater slopes than adult females, indicating ontogenetic differences in scaling of these traits in males. Two other topics in SSD are addressed with these data. First, comparing these data on scaling to those of an earlier analysis that used ordinary least squares regression reveals that conclusions about underlying mechanisms in an analysis of scaling can be altered by the choice of a regression model. Secondly, these data indicate that postmaturational differences in scaling contribute to adult sexual size differences, contrary to an earlier study. Shine (1990) found that for many ectotherms, which continue to grow after sexual maturation, post-maturational events contribute little to sexual differences in overall body size. Results for U. palmeri suggest that these findings may only hold for measures of overall body size (e.g. SVL) and may not generalize to traits that exhibit sex difference in scaling.     

Tipping the scales: Evolution of the allometric slope independent of average trait size

The scaling of body parts is central to the expression of morphology across body sizes and to the generation of morphological diversity within and among species. Although patterns of scaling‐relationship evolution have been well documented for over one hundred years, little is known regarding how selection acts to generate these patterns. In part, this is because it is unclear the extent to which the elements of log‐linear scaling relationships—the intercept or mean trait size and the slope—can evolve independently. Here, using the wing–body size scaling relationship in Drosophila melanogaster as an empirical model, we use artificial selection to demonstrate that the slope of a morphological scaling relationship between an organ (the wing) and body size can evolve independently of mean organ or body size. We discuss our findings in the context of how selection likely operates on morphological scaling relationships in nature, the developmental basis for evolved changes in scaling, and the general approach of using individual‐based selection experiments to study the expression and evolution of morphological scaling.     

Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics?

The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions, which can be measured by linear regression on logarithmic axes. We show here that such a procedure does not necessarily mean that the system exhibits self-organized criticality. We first provide an analysis of multisite local field potential (LFP) recordings of brain activity and show that event size distributions defined as negative LFP peaks can be close to power-law distributions. However, this result is not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov–Smirnov test. Similar power-law scaling is observed for surrogate signals, suggesting that power-law scaling may be a generic property of thresholded stochastic processes. We next investigate this problem analytically, and show that, indeed, stochastic processes can produce spurious power-law scaling without the presence of underlying self-organized criticality. However, this power-law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov–Smirnov test. The same analysis was also performed on an artificial network known to display self-organized criticality. In this case, both the graphical representations and the rigorous statistical analysis reveal with no ambiguity that the avalanche size is distributed as a power-law. We conclude that logarithmic representations can lead to spurious power-law scaling induced by the stochastic nature of the phenomenon. This apparent power-law scaling does not constitute a proof of self-organized criticality, which should be demonstrated by more stringent statistical tests.     

Climate change in size-structured ecosystems

One important aspect of climate change is the increase in average temperature, which will not only have direct physiological effects on all species but also indirectly modifies abundances, interaction strengths, food-web topologies, community stability and functioning. In this theme issue, we highlight a novel pathway through which warming indirectly affects ecological communities: by changing their size structure (i.e. the body-size distributions). Warming can shift these distributions towards dominance of small- over large-bodied species. The conceptual, theoretical and empirical research described in this issue, in sum, suggests that effects of temperature may be dominated by changes in size structure, with relatively weak direct effects. For example, temperature effects via size structure have implications for top-down and bottom-up control in ecosystems and may ultimately yield novel communities. Moreover, scaling up effects of temperature and body size from physiology to the levels of populations, communities and ecosystems may provide a crucially important mechanistic approach for forecasting future consequences of global warming.     

Allometric cascade: a model for resolving body mass effects on metabolism

Expanding upon a preliminary communication (Nature 417 (2002) 166), we here further develop a "multiple-causes model" of allometry, where the exponent b is the sum of the influences of multiple contributors to control. The relative strength of each contributor, with its own characteristic value of b(i), is determined by c(i), the control contribution or control coefficient. A more realistic equation for the scaling of metabolism with body size thus can be written as BMR=MR(0)Sigmac(i)(M/M(0))(bi), where MR(0) is the "characteristic metabolic rate" of an animal with a "characteristic body mass", M(0). With M(0) of 1 unit mass (usually kg), MR(0) takes the place of the value a, found in the standard scaling equation, b(i) is the scaling exponent of the process i, and c(i) is its control contribution to overall flux, or the control coefficient of the process i. One can think of this as an allometric cascade, with the b exponent for overall energy metabolism being determined by the b(i) and c(i) values for key steps in the complex pathways of energy demand and energy supply. Key intrinsic factors (such as neural and endocrine processes) or ecological extrinsic factors are considered to act through this system in affecting allometric scaling of energy turnover. Applying this model to maximum vs. BMR data for the first time explains the differing scaling behaviour of these two biological states in mammals, both in the absence and presence of intrinsic regulators such as thyroid hormones (for BMR) and catecholamines (for maximum metabolic rate).     

Tooth scaling and evolutionary dwarfism: an investigation of allometry in human pygmies

Gould has predicted that in rapidly dwarfed lineages the postcanine teeth exhibit a different scaling pattern than is the normal interspecific trend. His prediction of strong negative allometry has not been frequently tested in quantitative detail. Here we present results of scaling analyses of the molar teeth in African pygmies compared with other Africans of larger size and in Philippine pygmies compared with Filipinos of larger size. We find a pattern of strong negative allometry of tooth size to skull and body size in both these comparisons. This scaling pattern is explained by recourse to the developmental bases (known or inferred) of dwarfing in these populations. Body size decrease is related to low levels of the growth control substance insulin-like growth factor I (IGF-I), which does not appear to affect the size of the dentition. The implications of such developmental information for our understanding of allometric patterns in general, and dwarfing events in particular, are discussed.     

Autophagy and mitochondria in Pompe disease: nothing is so new as what has long been forgotten

Macroautophagy (often referred to as autophagy) is an evolutionarily conserved intracellular system by which macromolecules and organelles are delivered to lysosomes for degradation and recycling. Autophagy is robustly induced in response to starvation in order to generate nutrients and energy through the lysosomal degradation of cytoplasmic components. Constitutive, basal autophagy serves as a quality control mechanism for the elimination of aggregated proteins and worn-out or damaged organelles, such as mitochondria. Research during the last decade has made it clear that malfunctioning or failure of this system is associated with a wide range of human pathologies and age-related diseases. Our recent data provide strong evidence for the role of autophagy in the pathogenesis of Pompe disease, a lysosomal glycogen storage disease caused by deficiency of acid alpha-glucosidase (GAA). Large pools of autophagic debris in skeletal muscle cells can be seen in both our GAA knockout model and patients with Pompe disease. In this review, we will focus on these recent data, and comment on the not so recent observations pointing to the involvement of autophagy in skeletal muscle damage in Pompe disease.     

Allometry of behavior

The study of allometric and size scaling relationships is well developed in most biological fields, but lags behind in the area of animal behavior. Part of the reason for this deficit is that scaling relationships of behaviors tend to be inherently more 'noisy' than other biological scaling relationships. However, body size has a pervasive influence on the performance of animals in their environments. For example, the frequently strong relationship between power-to-mass ratios and locomotor performance means that smaller species and individuals enjoy superior locomotor performance (burst acceleration and maneuverability) than larger species, particularly within a clade. We suggest that these size-related functional influences on performance profoundly influence many aspects of animal behavior, such as how animals forage, fight, flee, perceive danger, respond to risk and interact with other individuals. We outline exciting avenues for research on the allometry of behavior by integrating scaling and functional perspectives.