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.

The laws of thermodynamics constrain the action of biochemical systems. However, thermodynamic data on biochemical compounds can be difficult to find and is cumbersome to perform calculations with manually. Even simple thermodynamic questions like ‘how much Gibbs energy is released by ATP hydrolysis at pH 5?’ are complicated excessively by the search for accurate data. To address this problem, eQuilibrator couples a comprehensive and accurate database of thermodynamic properties of biochemical compounds and reactions with a simple and powerful online search and calculation interface. The web interface to eQuilibrator (http://equilibrator.weizmann.ac.il) enables easy calculation of Gibbs energies of compounds and reactions given arbitrary pH, ionic strength and metabolite concentrations. The eQuilibrator code is open-source and all thermodynamic source data are freely downloadable in standard formats. Here we describe the database characteristics and implementation and demonstrate its use.

Contrary to the textbook portrayal of glycolysis as a single pathway conserved across all domains of life, not all sugar-consuming organisms use the canonical Embden-Meyerhoff-Parnass (EMP) glycolytic pathway. Prokaryotic glucose metabolism is particularly diverse, including several alternative glycolytic pathways, the most common of which is the Entner-Doudoroff (ED) pathway. The prevalence of the ED pathway is puzzling as it produces only one ATP per glucose-half as much as the EMP pathway. We argue that the diversity of prokaryotic glucose metabolism may reflect a tradeoff between a pathway's energy (ATP) yield and the amount of enzymatic protein required to catalyze pathway flux. We introduce methods for analyzing pathways in terms of thermodynamics and kinetics and show that the ED pathway is expected to require several-fold less enzymatic protein to achieve the same glucose conversion rate as the EMP pathway. Through genomic analysis, we further show that prokaryotes use different glycolytic pathways depending on their energy supply. Specifically, energy-deprived anaerobes overwhelmingly rely upon the higher ATP yield of the EMP pathway, whereas the ED pathway is common among facultative anaerobes and even more common among aerobes. In addition to demonstrating how protein costs can explain the use of alternative metabolic strategies, this study illustrates a direct connection between an organism's environment and the thermodynamic and biochemical properties of the metabolic pathways it employs.evolution | enzyme cost G lycolysis is the process by which glucose is broken down anaerobically into incompletely oxidized compounds like pyruvate, a process which is usually coupled to the synthesis of ATP. Although the Embden-Meyerhof-Parnas pathway (EMP, often simply "glycolysis") is the nearly ubiquitous glycolytic route among eukaryotes (1, 2), it is not the only game in town. Prokaryotes display impressive diversity in glucose metabolism (2, 3) and natural glycolytic alternatives like the Entner-Doudoroff (ED), and phosphoketolase pathways attest to the fact that there are multiple biologically feasible routes for glucose metabolism (2, 4-8). Natural glycolytic pathways vary in their reaction sequence and in how much ATP they produce per glucose metabolized, ranging from zero to three ATP molecules in most cases (7).The EMP and ED pathways ( Fig. 1 A and B and Fig. S1) are the most common bacterial glycolytic pathways (2, 4, 9), and their general schemes are quite similar: glucose is phosphorylated and then cleaved into two three-carbon units, which are further metabolized to produce ATP (4). In some organisms, these pathways differ slightly in the specific redox cofactors they use (e.g., NAD + vs. NADP + ; Fig. 1B, Fig. S2, and Table S1), but here we focus on the prominent difference in ATP yield. If we take lactate as a representative final product, these two pathways have the same net reaction:and differ primarily in n, the number of ATP produced, and the specific intermediate reaction steps (Fig. 1B, SI T...

Turnover numbers, also known as k cat values, are fundamental properties of enzymes. However, k cat data are scarce and measured in vitro, thus may not faithfully represent the in vivo situation. A basic question that awaits elucidation is: how representative are k cat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate k vivo max , the observed maximal catalytic rate of an enzyme inside cells. Comparison with k cat values from Escherichia coli, yields a correlation of r 2 = 0.62 in log scale (p < 10 −10 ), with a root mean square difference of 0.54 (3.5-fold in linear scale), indicating that in vivo and in vitro maximal rates generally concur. By accounting for the degree of saturation of enzymes and the backward flux dictated by thermodynamics, we further refine the correspondence between k vivo max and k cat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a highthroughput method for extracting enzyme kinetic constants from omics data. (1-6). Many models of cellular metabolism include k cat values, the maximal turnover rates of enzymes, as key inputs to predict the behavior of metabolic pathways and networks (7-9). However, most values have never been measured experimentally. Escherichia coli is the most intensely biochemically characterized organism, but k cat values are available for only about 10% of its ≈ 2, 000 enzyme-reaction pairs (Dataset S1). Indeed, k cat values are missing for several central metabolic enzymes. The scarcity of kinetic data limits the scope of models and necessitates generic parameter assignments that significantly reduce the predictive power of cellular models.Even if a larger collection of k cat values was made available, their current use poses a major difficulty: k cat values are measured through in vitro enzyme assays, representing the initial rate of the reaction, i.e., full substrates saturation and negligible levels of products. Such assays may underrepresent factors like cellular metabolite concentrations, thermodynamic constraints, posttranslational modifications, chaperones, cellular crowding, and activating and inhibiting molecules, which can substantially alter enzyme kinetics in vivo. These omissions call into question the relevance of k cat measurements in vivo (10-12). Furthermore, an effort to measure a large number of k cat values under in vivo-like conditions presents a daunting challenge, given how many unknown biochemical factors might be involved.Several studies grapple with missing k cat values by sampling from the distribution of k cat values measured in vitro or by using measurements of the same enzyme from related species (13-16). These approximations systematically ignore any errors resulting from the differences between in vitro and in vivo environments. Approximations of this sort may also introduce significant errors, as k cat values can deviate by orders of magnitude between isozymes in the same organism as well a...

In metabolism research, thermodynamics is usually used to determine the directionality of a reaction or the feasibility of a pathway. However, the relationship between thermodynamic potentials and fluxes is not limited to questions of directionality: thermodynamics also affects the kinetics of reactions through the flux-force relationship, which states that the logarithm of the ratio between the forward and reverse fluxes is directly proportional to the change in Gibbs energy due to a reaction (ΔrG′). Accordingly, if an enzyme catalyzes a reaction with a ΔrG′ of -5.7 kJ/mol then the forward flux will be roughly ten times the reverse flux. As ΔrG′ approaches equilibrium (ΔrG′ = 0 kJ/mol), exponentially more enzyme counterproductively catalyzes the reverse reaction, reducing the net rate at which the reaction proceeds. Thus, the enzyme level required to achieve a given flux increases dramatically near equilibrium. Here, we develop a framework for quantifying the degree to which pathways suffer these thermodynamic limitations on flux. For each pathway, we calculate a single thermodynamically-derived metric (the Max-min Driving Force, MDF), which enables objective ranking of pathways by the degree to which their flux is constrained by low thermodynamic driving force. Our framework accounts for the effect of pH, ionic strength and metabolite concentration ranges and allows us to quantify how alterations to the pathway structure affect the pathway's thermodynamics. Applying this methodology to pathways of central metabolism sheds light on some of their features, including metabolic bypasses (e.g., fermentation pathways bypassing substrate-level phosphorylation), substrate channeling (e.g., of oxaloacetate from malate dehydrogenase to citrate synthase), and use of alternative cofactors (e.g., quinone as an electron acceptor instead of NAD). The methods presented here place another arrow in metabolic engineers' quiver, providing a simple means of evaluating the thermodynamic and kinetic quality of different pathway chemistries that produce the same molecules.