Effects of body size and temperature on population growth

For at least 200 years, since the time of Malthus, population growth has been recognized as providing a critical link between the performance of individual organisms and the ecology and evolution of species. We present a theory that shows how the intrinsic rate of exponential population growth, rmax, and the carrying capacity, K, depend on individual metabolic rate and resource supply rate. To do this, we construct equations for the metabolic rates of entire populations by summing over individuals, and then we combine these population-level equations with Malthusian growth. Thus, the theory makes explicit the relationship between rates of resource supply in the environment and rates of production of new biomass and individuals. These individual-level and population-level processes are inextricably linked because metabolism sets both the demand for environmental resources and the resource allocation to survival, growth, and reproduction. We use the theory to make explicit how and why rmax exhibits its characteristic dependence on body size and temperature. Data for aerobic eukaryotes, including algae, protists, insects, zooplankton, fishes, and mammals, support these predicted scalings for rmax. The metabolic flux of energy and materials also dictates that the carrying capacity or equilibrium density of populations should decrease with increasing body size and increasing temperature. Finally, we argue that body mass and body temperature, through their effects on metabolic rate, can explain most of the variation in fecundity and mortality rates. Data for marine fishes in the field support these predictions for instantaneous rates of mortality. This theory links the rates of metabolism and resource use of individuals to life-history attributes and population dynamics for a broad assortment of organisms, from unicellular organisms to mammals.     

Activation of CD40 favors the growth and vascularization of Kaposi's sarcoma

Although CD40 is expressed by several tumor lines and is up-regulated in tumor vascular endothelium, its role in tumor biology is still unclear. In the present study, we investigated the role of CD40 in the growth and vascularization of Kaposi's sarcoma (KS). In vitro, stimulation of CD40 induced migration of KS cells and inhibited vincristine-induced apoptosis. Similarly, the CD40 engagement on endothelial cells resulted in cell contraction, migration, and prevention of serum withdrawal-apoptosis. To understand the biological relevance of CD40 in vivo, KS cells were engineered to express and release a soluble form of CD40 (KS-sCD40) able to disrupt CD40-CD154 interaction. SCID mice s.c. injected with KS-sCD40 cells developed tumors that were significantly smaller than those induced by control cells (KS-neo). In addition, KS-sCD40 tumors showed several areas of necrosis, diffuse presence of apoptotic cells, and poor vascularization. In contrast, KS-neo tumors showed few or absent areas of necrosis and apoptosis and intense vascularization. Moreover, anti-CD40 Abs stimulated neo-angiogenesis in a murine model in which s.c. implantation of Matrigel was used as a vehicle for the delivery of mediators. These observations provide demonstration that CD40 supports tumor cell survival, growth, and neo-vascularization of KS.     

Testing metabolic ecology theory for allometric scaling of tree size, growth and mortality in tropical forests

The theory of metabolic ecology predicts specific relationships among tree stem diameter, biomass, height, growth and mortality. As demographic rates are important to estimates of carbon fluxes in forests, this theory might offer important insights into the global carbon budget, and deserves careful assessment. We assembled data from 10 old-growth tropical forests encompassing censuses of 367 ha and > 1.7 million trees to test the theory's predictions. We also developed a set of alternative predictions that retained some assumptions of metabolic ecology while also considering how availability of a key limiting resource, light, changes with tree size. Our results show that there are no universal scaling relationships of growth or mortality with size among trees in tropical forests. Observed patterns were consistent with our alternative model in the one site where we had the data necessary to evaluate it, and were inconsistent with the predictions of metabolic ecology in all forests.     

Theoretical predictions for how temperature affects the dynamics of interacting herbivores and plants

Concern about climate change has spurred experimental tests of how warming affects species' abundance and performance. As this body of research grows, interpretation and extrapolation to other species and systems have been limited by a lack of theory. To address the need for theory for how warming affects species interactions, we used consumer-prey models and the metabolic theory of ecology to develop quantitative predictions for how systematic differences between the temperature dependence of heterotrophic and autotrophic population growth lead to temperature-dependent herbivory. We found that herbivore and plant abundances change with temperature in proportion to the ratio of autotrophic to heterotrophic metabolic temperature dependences. This result is consistent across five different formulations of consumer-prey models and over varying resource supply rates. Two models predict that temperature-dependent herbivory causes primary producer abundance to be independent of temperature. This finding contradicts simpler extensions of metabolic theory to abundance that ignore trophic interactions, and is consistent with patterns in terrestrial ecosystems. When applied to experimental data, the model explained 77% and 66% of the variation in phytoplankton and zooplankton abundances, respectively. We suggest that metabolic theory provides a foundation for understanding the effects of temperature change on multitrophic ecological communities.     

Simultaneous in vivo optical quantification of key metabolic and vascular endpoints reveals tumor metabolic diversity in murine breast tumor models

Therapeutically exploiting vascular and metabolic endpoints becomes critical to translational cancer studies because altered vascularity and deregulated metabolism are two important cancer hallmarks. The metabolic and vascular phenotypes of three sibling breast tumor lines with different metastatic potential are investigated in vivo with a newly developed quantitative spectroscopy system. All tumor lines have different metabolic and vascular characteristics compared to normal tissues, and there are strong positive correlations between metabolic (glucose uptake and mitochondrial membrane potential) and vascular (oxygen saturations and hemoglobin concentrations) parameters for metastatic (4T1) tumors but not for micrometastatic (4T07) and nonmetastatic (67NR) tumors. A longitudinal study shows that both vascular and metabolic endpoints of 4T1 tumors increased up to a specific tumor size threshold beyond which these parameters decreased. The synchronous changes between metabolic and vascular parameters, along with the strong positive correlations between these endpoints suggest that 4T1 tumors rely on strong oxidative phosphorylation in addition to glycolysis. This study illustrates the great potential of our optical technique to provide valuable dynamic information about the interplay between the metabolic and vascular status of tumors, with important implications for translational cancer investigations.      

Generation time,life history and the substitution rate of neutral mutations

Our understanding of molecular evolution is hampered by a lack of quantitative predictions about how life-history (LH) traits should correlate with substitution rates. Comparative studies have shown that neutral substitution rates vary substantially between species, and evidence shows that much of this diversity is associated with variation in LH traits. However, while these studies often agree, some unexplained and contradictory results have emerged. Explaining these results is difficult without a clear theoretical understanding of the problem. In this study, we derive predictions for the relationships between LH traits and substitution rates in iteroparous species by using demographic theory to relate commonly measured life-history traits to genetic generation time, and by implication to neutral substitution rates. This provides some surprisingly simple explanations for otherwise confusing patterns, such as the association between fecundity and substitution rates. The same framework can be applied to more complex life histories if full life-tables are available.     

EphB4 controls blood vascular morphogenesis during postnatal angiogenesis

Guidance molecules have attracted interest by demonstration that they regulate patterning of the blood vascular system during development. However, their significance during postnatal angiogenesis has remained unknown. Here, we demonstrate that endothelial cells of human malignant brain tumors also express guidance molecules, such as EphB4 and its ligand ephrinB2. To study their function, EphB4 variants were overexpressed in blood vessels of tumor xenografts. Our studies revealed that EphB4 acts as a negative regulator of blood vessel branching and vascular network formation, switching the vascularization program from sprouting angiogenesis to circumferential vessel growth. In parallel, EphB4 reduces the permeability of the tumor vascular system via activation of the angiopoietin-1/Tie2 system at the endothelium/pericyte interface. Furthermore, overexpression of EphB4 variants in blood vessels during (i) vascularization of non-neoplastic cell grafts and (ii) retinal vascularization revealed that these functions of EphB4 apply to postnatal, non-neoplastic angiogenesis in general. This implies that both neoplastic and non-neoplastic vascularization is driven not only by a vascular initiation program but also by a vascular patterning program mediated by guidance molecules.     

Angiogenesis in the placenta

The mammalian placenta is the organ through which respiratory gases, nutrients, and wastes are exchanged between the maternal and fetal systems. Thus, transplacental exchange provides for all the metabolic demands of fetal growth and development. The rate of transplacental exchange depends primarily on the rates of uterine (maternal placental) and umbilical (fetal placental) blood flows. In fact, increased uterine vascular resistance and reduced uterine blood flow can be used as predictors of high risk pregnancies and are associated with fetal growth retardation. The rates of placental blood flow, in turn, are dependent on placental vascularization, and placental angiogenesis is therefore critical for the successful development of viable, healthy offspring. Recent studies, including gene knockouts in mice, indicate that the vascular endothelial growth factors represent a major class of placental angiogenic factors. Other angiogenic factors, such as the fibroblast growth factors or perhaps the angiopoietins, also may play important roles in placental vascularization. In addition, recent observations suggest that these angiogenic factors interact with the local vasodilator nitric oxide to coordinate placental angiogenesis and blood flow. In the future, regulators of angiogenesis that are currently being developed may provide novel and powerful methods to ensure positive outcomes for most pregnancies.     

On the vegetative biomass partitioning of seed plant leaves, stems, and roots

A central goal of comparative life-history theory is to derive the general rules governing growth, metabolic allocation, and biomass partitioning. Here, we use allometric theory to predict the relationships among annual leaf, stem, and root growth rates (GL, GS, and GR, respectively) across a broad spectrum of seed plant species. Our model predicts isometric scaling relationships among all three organ growth rates: GL is proportional to GS is proportional to GR. It also provides a conceptual basis for understanding the differences in the absolute amounts of biomass allocated to construct the three organ types. Analyses of a large compendium of biomass production rates across diverse seed plant species provide strong statistical support for the predictions of the theory and indicate that reproductive investments may scale isometrically with respect to vegetative organ growth rates. The general rules governing biomass allocation as indexed by the scaling exponents for organ growth rates are remarkably indifferent to plant size and taxonomic affiliation. However, the allometric "constants" for these relationships differ numerically as a function of phenotypic features and local environmental conditions. Nonetheless, at the level of both inter- and intraspecific comparisons, the same proportional biomass allocation pattern holds across extant seed plant species.     

Isoforms of vascular endothelial growth factor act in a coordinate fashion To recruit and expand tumor vasculature

Vascular endothelial growth factor (VEGF) is an essential regulator of vascularization. It is expressed as several splice variants; the major forms contain 120 amino acids, 164 amino acids, and 188 amino acids. We utilized transformed cells nullizygous for VEGF to specifically express each of these isoforms in isolation, in order to determine the role of each in tumorigenic neo-vascularization. We found that only the intermediate isoform, VEGF164, could fully rescue tumor growth; VEGF120 partially rescued tumor growth, and VEGF188 failed completely to rescue tumor expansion. Surprisingly, the vascular density of VEGF188 isoform-expressing tumors is significantly greater than that of wild-type VEGF cells and the other isoform-specific tumors. The failure of the hypervascular VEGF188-expressing tumors to grow may be due to inadequate perfusion of the massive number of microvessels in these tumors; three-dimensional imaging of the tumorigenic vasculature indicated little or no recruitment of the peripheral vasculature. This demonstrates that the VEGF isoforms perform unique functions which together enable tumorigenic vascularization.     

Role of Constitutive Behavior and Tumor-Host Mechanical Interactions in the State of Stress and Growth of Solid Tumors

Mechanical forces play a crucial role in tumor patho-physiology. Compression of cancer cells inhibits their proliferation rate, induces apoptosis and enhances their invasive and metastatic potential. Additionally, compression of intratumor blood vessels reduces the supply of oxygen, nutrients and drugs, affecting tumor progression and treatment. Despite the great importance of the mechanical microenvironment to the pathology of cancer, there are limited studies for the constitutive modeling and the mechanical properties of tumors and on how these parameters affect tumor growth. Also, the contribution of the host tissue to the growth and state of stress of the tumor remains unclear. To this end, we performed unconfined compression experiments in two tumor types and found that the experimental stress-strain response is better fitted to an exponential constitutive equation compared to the widely used neo-Hookean and Blatz-Ko models. Subsequently, we incorporated the constitutive equations along with the corresponding values of the mechanical properties - calculated by the fit - to a biomechanical model of tumor growth. Interestingly, we found that the evolution of stress and the growth rate of the tumor are independent from the selection of the constitutive equation, but depend strongly on the mechanical interactions with the surrounding host tissue. Particularly, model predictions - in agreement with experimental studies - suggest that the stiffness of solid tumors should exceed a critical value compared with that of the surrounding tissue in order to be able to displace the tissue and grow in size. With the use of the model, we estimated this critical value to be on the order of 1.5. Our results suggest that the direct effect of solid stress on tumor growth involves not only the inhibitory effect of stress on cancer cell proliferation and the induction of apoptosis, but also the resistance of the surrounding tissue to tumor expansion.     

A New Model for Size-Dependent Tree Growth in Forests

Tree growth, especially diameter growth of tree stems, is an important issue for understanding the productivity and dynamics of forest stands. Metabolic scaling theory predicted that the 2/3 power of stem diameter at a certain time is a linear function of the 2/3 power of the initial diameter and that the diameter growth rate scales to the 1/3 power of the initial diameter. We tested these predictions of the metabolic scaling theory for 11 Japanese secondary forests at various growth stages. The predictions were not supported by the data, especially in younger stands. Alternatively, we proposed a new theoretical model for stem diameter growth on the basis of six assumptions. All these assumptions were supported by the data. The model produced a nearly linear to curvilinear relationship between the 2/3 power of stem diameters at two different times. It also fitted well to the curvilinear relationship between diameter growth rate and the initial diameter. Our model fitted better than the metabolic scaling theory, suggesting the importance of asymmetric competition among trees, which has not been incorporated in the metabolic scaling theory.     

Vascular Mimicry: A Novel Neovascularization Mechanism Driving Anti-Angiogenic Therapy (AAT) Resistance in Glioblastoma

Glioblastoma (GBM) is a hypervascular neoplasia of the central nervous system with an extremely high rate of mortality. Owing to its hypervascularity, anti-angiogenic therapies (AAT) have been used as an adjuvant to the traditional surgical resection, chemotherapy, and radiation. The benefits of AAT have been transient and the tumors were shown to relapse faster and demonstrated particularly high rates of AAT therapy resistance. Alternative neovascularization mechanisms were shown to be at work in these resilient tumors to counter the AAT therapy insult. Vascular Mimicry (VM) is the uncanny ability of tumor cells to acquire endothelial-like properties and lay down vascular patterned networks reminiscent of host endothelial blood vessels. The VM channels served as an irrigation system for the tumors to meet with the increasing metabolic and nutrient demands of the tumor in the event of the ensuing hypoxia resulting from AAT. In our previous studies, we have demonstrated that AAT accelerates VM in GBM. In this review, we will focus on the origins of VM, visualizing VM in AAT-treated tumors and the development of VM as a resistance mechanism to AAT.     

Anti-tumor activities of the angiogenesis inhibitors interferon-inducible protein-10 and the calreticulin fragment vasostatin

Tumor growth depends upon an adequate supply of oxygen and nutrients achieved through angiogenesis and maintenance of an intact tumor vasculature. Therapy with individual agents that target new vessel formation or existing vessels has suppressed experimental tumor growth, but rarely resulted in the eradication of tumors. We therefore tested the combined anti-tumor activity of vasostatin and interferon-inducible protein-10 (IP-10), agents that differently target the tumor vasculature. Vasostatin, a selective and direct inhibitor of endothelial cell proliferation, significantly reduced Burkitt tumor growth and tumor vessel density. IP-10, an "angiotoxic" chemokine, caused vascular damage and focal necrosis in Burkitt tumors. When combined, vasostatin plus IP-10 reduced tumor growth more effectively than each agent alone, but complete tumor regression was not observed. Microscopically, these tumors displayed focal necrosis and reduction in vessel density. Combination therapy with the inhibitors of angiogenesis vasostatin and IP-10 is effective in reducing the rate of tumor growth but fails to induce tumor regression, suggesting that curative treatment may require supplemental drugs targeting directly the tumor cells.     

Multiscale Metabolic Modeling of C4 Plants: Connecting Nonlinear Genome-Scale Models to Leaf-Scale Metabolism in Developing Maize Leaves

C4 plants, such as maize, concentrate carbon dioxide in a specialized compartment surrounding the veins of their leaves to improve the efficiency of carbon dioxide assimilation. Nonlinear relationships between carbon dioxide and oxygen levels and reaction rates are key to their physiology but cannot be handled with standard techniques of constraint-based metabolic modeling. We demonstrate that incorporating these relationships as constraints on reaction rates and solving the resulting nonlinear optimization problem yields realistic predictions of the response of C4 systems to environmental and biochemical perturbations. Using a new genome-scale reconstruction of maize metabolism, we build an 18000-reaction, nonlinearly constrained model describing mesophyll and bundle sheath cells in 15 segments of the developing maize leaf, interacting via metabolite exchange, and use RNA-seq and enzyme activity measurements to predict spatial variation in metabolic state by a novel method that optimizes correlation between fluxes and expression data. Though such correlations are known to be weak in general, we suggest that developmental gradients may be particularly suited to the inference of metabolic fluxes from expression data, and we demonstrate that our method predicts fluxes that achieve high correlation with the data, successfully capture the experimentally observed base-to-tip transition between carbon-importing tissue and carbon-exporting tissue, and include a nonzero growth rate, in contrast to prior results from similar methods in other systems.     

Trophic interactions and population growth rates: describing patterns and identifying mechanisms

While the concept of population growth rate has been of central importance in the development of the theory of population dynamics, few empirical studies consider the intrinsic growth rate in detail, let alone how it may vary within and between populations of the same species. In an attempt to link theory with data we take two approaches. First, we address the question ''what growth rate patterns does theory predict we should see in time-series?'' The models make a number of predictions, which in general are supported by a comparative study between time-series of harvesting data from 352 red grouse populations. Variations in growth rate between grouse populations were associated with factors that reflected the quality and availability of the main food plant of the grouse. However, while these results support predictions from theory, they provide no clear insight into the mechanisms influencing reductions in population growth rate and regulation. In the second part of the paper, we consider the results of experiments, first at the individual level and then at the population level, to identify the important mechanisms influencing changes in individual productivity and population growth rate. The parasitic nematode Trichostrongylus tenuis is found to have an important influence on productivity, and when incorporated into models with their patterns of distribution between individuals has a destabilizing effect and generates negative growth rates. The hypothesis that negative growth rates at the population level were caused by parasites was demonstrated by a replicated population level experiment. With a sound and tested model framework we then explore the interaction with other natural enemies and show that in general they tend to stabilize variations in growth rate. Interestingly, the models show selective predators that remove heavily infected individuals can release the grouse from parasite-induced regulation and allow equilibrium populations to rise. By contrast, a tick-borne virus that killed chicks simply leads to a reduction in the equilibrium. When humans take grouse they do not appear to stabilize populations and this may be because many of the infective stages are available for infection before harvesting commences. In our opinion, an understanding of growth rates and population dynamics is best achieved through a mechanistic approach that includes a sound experimental approach with the development of models. Models can be tested further to explore how the community of predators and others interact with their prey.