William H. Woodruff

Energetic Limits to Economic Growth

The human population and economy have grown exponentially and now have impacts on climate, ecosystem processes, and biodiversity far exceeding those of any other species. Like all organisms, humans are subject to natural laws and are limited by energy and other resources. In this article, we use a macro ecological approach to integrate perspectives of physics, ecology, and economics with an analysis of extensive global data to show how energy imposes fundamental constraints on economic growth and development. We demonstrate a positive scaling relationship between per capita energy use and per capita gross domestic product (GDP) both across nations and within nations over time. Other indicators of socioeconomic status and ecological impactare correlated with energy use and GDP. We estimate global energy consumption for alternative future scenarios of population growth and standards of living. Large amounts of energy will be required to fuel economic growth, increase standards of living, and lift developing nations out of poverty.

Scaling of number, size, and metabolic rate of cells with body size in mammals.

The size and metabolic rate of cells affect processes from the molecular to the organismal level. We present a quantitative, theoretical framework for studying relationships among cell volume, cellular metabolic rate, body size, and whole-organism metabolic rate that helps reveal the feedback between these levels of organization. We use this framework to show that average cell volume and average cellular metabolic rate cannot both remain constant with changes in body size because of the well known body-size dependence of whole-organism metabolic rate. Based on empirical data compiled for 18 cell types in mammals, we find that many cell types, including erythrocytes, hepatocytes, fibroblasts, and epithelial cells, follow a strategy in which cellular metabolic rate is body size dependent and cell volume is body size invariant. We suggest that this scaling holds for all quickly dividing cells, and conversely, that slowly dividing cells are expected to follow a strategy in which cell volume is body size dependent and cellular metabolic rate is roughly invariant with body size. Data for slowly dividing neurons and adipocytes show that cell volume does indeed scale with body size. From these results, we argue that the particular strategy followed depends on the structural and functional properties of the cell type. We also discuss consequences of these two strategies for cell number and capillary densities. Our results and conceptual framework emphasize fundamental constraints that link the structure and function of cells to that of whole organisms.

Energy Uptake and Allocation during Ontogeny

All organisms face the problem of how to fuel ontogenetic growth. We present a model, empirically grounded in data from birds and mammals, that correctly predicts how growing animals allocate food energy between synthesis of new biomass and maintenance of existing biomass. Previous energy budget models have typically had their bases in rates of either food consumption or metabolic energy expenditure. Our model provides a framework that reconciles these two approaches and highlights the fundamental principles that determine rates of food assimilation and rates of energy allocation to maintenance, biosynthesis, activity, and storage. The model predicts that growth and assimilation rates for all animals should cluster closely around two universal curves. Data for mammals and birds of diverse body sizes and taxa support these predictions.

Bound water in the proton translocation mechanism of the haem-copper oxidases

We address the molecular mechanism by which the haem‐copper oxidases translocate protons. Reduction of O2 to water takes place at a haem iron‐copper (CuB) centre, and protons enter from one side of the membrane through a ‘channel’ structure in the enzyme. Statistical‐mechanical calculations predict bound water molecules within this channel, and mutagenesis experiments show that breaking this water structure impedes proton translocation. Hydrogen‐bonded water molecules connect the channel further via a conserved glutamic acid residue to a histidine ligand of CuB. The glutamic acid side chain may have to move during proton transfer because proton translocation is abolished if it is forced to interact with a nearby lysine or arginine. Perturbing the CuB ligand structure shifts an infrared mode that may be ascribed to the OH stretch of bound water. This is sensitive to mutations of the glutamic acid, supporting its connectivity to the histidine. These results suggest key roles of bound water, the glutamic acid and the histidine copper ligand in the mechanism of proton translocation.

Revisiting a model of ontogenetic growth: estimating model parameters from theory and data.

The ontogenetic growth model (OGM) of West et al. provides a general description of how metabolic energy is allocated between production of new biomass and maintenance of existing biomass during ontogeny. Here, we reexamine the OGM, make some minor modifications and corrections, and further evaluate its ability to account for empirical variation on rates of metabolism and biomass in vertebrates both during ontogeny and across species of varying adult body size. We show that the updated version of the model is internally consistent and is consistent with other predictions of metabolic scaling theory and empirical data. The OGM predicts not only the near universal sigmoidal form of growth curves but also the \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

Physiology (communication arising): Why does metabolic rate scale with body size?

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Resonance Raman studies of Rieske-type proteins

\end{document} scaling of the characteristic times of ontogenetic stages in addition to the curvilinear decline in growth efficiency described by Brody. Additionally, the OGM relates the \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape