The quantified cell

The microscopic world of a cell can be as alien to our human-centered intuition as the confinement of quarks within protons or the event horizon of a black hole. We are prone to thinking by analogy—Golgi cisternae stack like pancakes, red blood cells look like donuts—but very little in our human experience is truly comparable to the immensely crowded, membrane-subdivided interior of a eukaryotic cell or the intricately layered structures of a mammalian tissue. So in our daily efforts to understand how cells work, we are faced with a challenge: how do we develop intuition that works at the microscopic scale

The protein cost of metabolic fluxes: prediction from enzymatic rate laws and cost minimization

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell's capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 3.8 and 2.7, respectively, for the two kinds of data. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified

Closed ecosystems extract energy through self-organized nutrient cycles

Our planet is roughly closed to matter, but open to energy input from the sun. However, to harness this energy, organisms must transform matter from one chemical (redox) state to another. For example, photosynthetic organisms can capture light energy by carrying out a pair of electron donor and acceptor transformations (e.g., water to oxygen, CO$_2$ to organic carbon). Closure of ecosystems to matter requires that all such transformations are ultimately balanced, i.e., other organisms must carry out corresponding reverse transformations, resulting in cycles that are coupled to each other. A sustainable closed ecosystem thus requires self-organized cycles of matter, in which every transformation has sufficient thermodynamic favorability to maintain an adequate number of organisms carrying out that process. Here, we propose a new conceptual model that explains the self-organization and emergent features of closed ecosystems. We study this model with varying levels of metabolic diversity and energy input, finding that several thermodynamic features converge across ecosystems. Specifically, irrespective of their species composition, large and metabolically diverse communities self-organize to extract roughly 10% of the maximum extractable energy, or 100 fold more than randomized communities. Moreover, distinct communities implement energy extraction in convergent ways, as indicated by strongly correlated fluxes through nutrient cycles. As the driving force from light increases, however, these features -- fluxes and total energy extraction -- become more variable across communities, indicating that energy limitation imposes tight thermodynamic constraints on collective metabolism.Comment: 10 pages, 4 figure

Thermodynamics drives coenzyme redundancy in metabolism

Coenzymes redistribute a variety of resources (e.g., electrons, phosphate groups, methyl groups) throughout cellular metabolism. For a variety of reactions requiring acceptors or donors of specific resources, there often exist degenerate sets of molecules (e.g., NAD(H) and NADP(H)) that carry out similar functions. Several hypotheses can explain the persistence of coenzyme degeneracy, but none have been tested quantitatively. Here, we use genome-wide metabolic modeling approaches to decompose the selective pressures driving enzymatic specificity for coenzymes in the metabolic network of Escherichia coli. Flux balance modeling predicts that only two enzymes (encoded by leuB and pdxB) are thermodynamically constrained to use NAD(H) over NADP(H). In contrast, structural and sequence analyses reveal widespread conservation of residues that retain selectivity for NAD(H), suggesting that additional forces drive enzyme specificity. Using a model accounting for the cost of oxidoreductase enzyme expression, we find that coenzyme redundancy universally reduces the minimal amount of protein required to catalyze coenzyme-coupled reactions, inducing individual reactions to strongly prefer one coenzyme over another when reactions are near thermodynamic equilibrium. We propose that partitioning of flux across multiple coenzyme pools could be a generic phenomenon of cellular metabolism, and hypothesize that coenzymes typically thought to exist in a single pool (e.g., CoA) may exist in more than one form (e.g., dephospho-CoA)

SARS-CoV-2 (COVID-19) by the numbers

The current SARS-CoV-2 pandemic is a harsh reminder of the fact that, whether in a single human host or a wave of infection across continents, viral dynamics is often a story about the numbers. In this snapshot, our aim is to provide a one-stop, curated graphical source for the key numbers that help us understand the virus driving our current global crisis. The discussion is framed around two broad themes: 1) the biology of the virus itself and 2) the characteristics of the infection of a single human host. Our one-page summary provides the key numbers pertaining to SARS-CoV-2, based mostly on peer-reviewed literature. The numbers reported in summary format are substantiated by the annotated references below. Readers are urged to remember that much uncertainty remains and knowledge of this pandemic and the virus driving it is rapidly evolving. In the paragraphs below we provide 'back of the envelope' calculations that exemplify the insights that can be gained from knowing some key numbers and using quantitative logic. These calculations serve to improve our intuition through sanity checks, but do not replace detailed epidemiological analysis

Prediction from Enzymatic Rate Laws and Cost Minimization

Bacterial growth depends crucially on metabolic fluxes, which are limited by the cell’s capacity to maintain metabolic enzymes. The necessary enzyme amount per unit flux is a major determinant of metabolic strategies both in evolution and bioengineering. It depends on enzyme parameters (such as kcat and KM constants), but also on metabolite concentrations. Moreover, similar amounts of different enzymes might incur different costs for the cell, depending on enzyme-specific properties such as protein size and half-life. Here, we developed enzyme cost minimization (ECM), a scalable method for computing enzyme amounts that support a given metabolic flux at a minimal protein cost. The complex interplay of enzyme and metabolite concentrations, e.g. through thermodynamic driving forces and enzyme saturation, would make it hard to solve this optimization problem directly. By treating enzyme cost as a function of metabolite levels, we formulated ECM as a numerically tractable, convex optimization problem. Its tiered approach allows for building models at different levels of detail, depending on the amount of available data. Validating our method with measured metabolite and protein levels in E. coli central metabolism, we found typical prediction fold errors of 4.1 and 2.6, respectively, for the two kinds of data. This result from the cost-optimized metabolic state is significantly better than randomly sampled metabolite profiles, supporting the hypothesis that enzyme cost is important for the fitness of E. coli. ECM can be used to predict enzyme levels and protein cost in natural and engineered pathways, and could be a valuable computational tool to assist metabolic engineering projects. Furthermore, it establishes a direct connection between protein cost and thermodynamics, and provides a physically plausible and computationally tractable way to include enzyme kinetics into constraint-based metabolic models, where kinetics have usually been ignored or oversimplified