Microbes maintain themselves through a variety of processes. Several of these processes can be reduced or shut down entirely when resource availability declines. In pure culture conditions with ample substrate supply, a relationship between the maximum growth rate and the energy invested in maintenance has been reported widely. However, at the other end of the resources spectrum, bacteria are so extremely limited by energy that no growth occurs and metabolism is constrained to the most essential functions only. These minimum energy requirements have been called the basal power requirement. While seemingly different from each other, both aspects are likely components of a continuum of regulated maintenance processes. Here, we analyze cross species tradeoffs in cellular physiology over the range of bacterial size and energy expenditure and determine the contributions to maintenance metabolism at each point along the size-energy spectrum. Furthermore, by exploring the simplest bacteria within this framework-- which are most affected by maintenance constraints-- we uncover which processes become most limiting. For the smallest species, maintenance metabolism converges on total metabolism, where we predict that maintenance is dominated by the repair of proteins. For larger species the relative costs of protein repair decrease and maintenance metabolism is predicted to be dominated by the repair of RNA components. These results provide new insights into which processes are likely to be regulated in environments that are extremely limited by energy.

Population growth rate is a fundamental ecological and evolutionary characteristic of living organisms, but individuals must balance the metabolism devoted to biosynthesis and reproduction against the maintenance of existing structure and other functionality. Here we present a mathematical model that relates metabolic partitioning to the form of growth. The model captures the observed growth trajectory of single cells and individuals for a variety of species and taxa spanning prokaryotes, unicellular eukaryotes, and small multicellular eukaryotes. Our analysis suggests that the per-unit costs of biosynthesis and maintenance are conserved across prokaryotes and eukaryotes. However, the relative metabolic expenditure on growth and maintenance of whole organisms clearly differentiates taxa: prokaryotes spend an increasing fraction of their entire metabolism on growth with increasing cell size, whereas eukaryotes devote a diminishing fraction. These differences allow us to predict the minimum and maximum size for each taxonomic group, anticipating observed evolutionary life-history transitions. The framework provides energetic insights into taxonomic tradeoffs related to growth and metabolism and constrains traits that are important for size-structured modeling of microbial communities and their ecological and biogeochemical effects.

The production of waste as a consequence of human activities is one of the most fundamental challenges facing our society and global ecological systems. Waste generation is rapidly increasing, with corresponding shifts in the structure of our societies, where almost all nations are moving from rural agrarian societies to urban and technological ones. However, the connections between these societal shifts and waste generation have not yet been described. In this study we applied scaling theory to establish a new understanding of waste in urban systems and identified universal scaling laws of waste generation across diverse urban systems worldwide for three forms of waste: wastewater, municipal solid waste, and greenhouse gases. We found that wastewater generation scales superlinearly, municipal solid waste scales linearly, and greenhouse gas emissions scale sublinearly with city size. In specific cases, production can be understood in terms of city size coupled with financial and natural resources. For example, wastewater generation can be understood in terms of the increased economic activity of larger cities, and the deviations from the scaling relationship, indicating relative efficiency, depend on gross domestic product per person and local rainfall. The temporal evolution of these scaling relationships reveals a loss of economies of scale and a general increase in waste production, where sublinear scaling relationships become linear. Our findings suggest general mechanisms controlling waste generation across diverse cities and global urban systems. Our approach offers a systematic framework to uncover these underlying mechanisms that might be key to reducing waste and pursuing a more sustainable future.

Scaling is a general analytical framework used by many disciplines—from physics to biology and the social sciences—to characterize how population-averaged properties of a collective vary with its size. The observation of scale invariance over some range identifies general system types, be they ideal gases, ecosystems or cities. The use of scaling in the analysis of cities quantifies many of their arguably fundamental general characteristics, especially their capacity to create interrelated economies of scale in infrastructure and increasing returns to scale in socio-economic activities. However, the measurement of these effects, and the relationship of observable parameters to theory, hinge on how scaling analysis is used empirically. Here, we show how two equivalent approaches to urban scaling—cross-sectional and temporal—lead to the measurement of different mixtures of the same fundamental parameters describing pure scale and pure temporal phenomena. Specifically, temporal exponents are sensitive to the intensive growth of urban quantities and to circumstances when population growth vanishes, leading to instabilities and infinite divergences. These spurious effects are avoided in cross-sectional scaling, which is more common and closer to theory in terms of quantitative testable expectations for its parameters.

One of the most important classic and contemporary interests in biology is the connection between cellular composition and physiological function. Decades of research have allowed us to understand the detailed relationship between various cellular components and processes for individual species, and have uncovered common functionality across diverse species. However, there still remains the need for frameworks that can mechanistically predict the tradeoffs between cellular functions and elucidate and interpret average trends across species. Here we provide a comprehensive analysis of how cellular composition changes across the diversity of bacteria as connected with physiological function and metabolism, spanning five orders of magnitude in body size. We present an analysis of the trends with cell volume that covers shifts in genomic, protein, cellular envelope, RNA and ribosomal content. We show that trends in protein content are more complex than a simple proportionality with the overall genome size, and that the number of ribosomes is simply explained by cross-species shifts in biosynthesis requirements. Furthermore, we show that the largest and smallest bacteria are limited by physical space requirements. At the lower end of size, cell volume is dominated by DNA and protein content—the requirement for which predicts a lower limit on cell size that is in good agreement with the smallest observed bacteria. At the upper end of bacterial size, we have identified a point at which the number of ribosomes required for biosynthesis exceeds available cell volume. Between these limits we are able to discuss systematic and dramatic shifts in cellular composition. Much of our analysis is connected with the basic energetics of cells where we show that the scaling of metabolic rate is surprisingly superlinear with all cellular components.

Significance: Principle questions in the field of biology concern the evolutionary advantages conferred by the multicellular lifestyle and by the formation of specific multicellular structures. In microbial biofilms, many cells cooperate to form distinct macroscopic patterns. Here we develop and apply a mathematical model, which incorporates empirical values, to show that the tall “ridges” produced by Pseudomonas aeruginosa colony biofilms maximize community growth via enhanced access to oxygen. Production of endogenous redox-active compounds, which mediate electron transfer from cells to oxygen, allows the formation of wider ridges. Externally supplied and endogenously produced oxidant availability controls feature geometry in a manner consistent with the model predictions for optimal geometry.