Competing constraints shape the nonequilibrium limits of cellular decision-making.

Gene regulation is central to cellular function. Yet, despite decades of work, we lack quantitative models that can predict how transcriptional control emerges from molecular interactions at the gene locus. Thermodynamic models of transcription, which assume that gene circuits operate at equilibrium, have previously been employed with considerable success in the context of bacterial systems. However, the presence of ATP-dependent processes within the eukaryotic transcriptional cycle suggests that equilibrium models may be insufficient to capture how eukaryotic gene circuits sense and respond to input transcription factor concentrations. Here, we employ simple kinetic models of transcription to investigate how energy dissipation within the transcriptional cycle impacts the rate at which genes transmit information and drive cellular decisions. We find that biologically plausible levels of energy input can lead to significant gains in how rapidly gene loci transmit information but discover that the regulatory mechanisms underlying these gains change depending on the level of interference from noncognate activator binding. When interference is low, information is maximized by harnessing energy to push the sensitivity of the transcriptional response to input transcription factors beyond its equilibrium limits. Conversely, when interference is high, conditions favor genes that harness energy to increase transcriptional specificity by proofreading activator identity. Our analysis further reveals that equilibrium gene regulatory mechanisms break down as transcriptional interference increases, suggesting that energy dissipation may be indispensable in systems where noncognate factor interference is sufficiently large.

Closed ecosystems extract energy through self-organized nutrient cycles.

Our planet is a self-sustaining ecosystem powered by light energy from the sun, but roughly closed to matter. Many ecosystems on Earth are also approximately closed to matter and recycle nutrients by self-organizing stable nutrient cycles, e.g., microbial mats, lakes, open ocean gyres. However, existing ecological models do not exhibit the self-organization and dynamical stability widely observed in such planetary-scale ecosystems. Here, we advance a conceptual model that explains the self-organization, stability, and emergent features of closed microbial ecosystems. Our model incorporates the bioenergetics of metabolism into an ecological framework. By studying this model, we uncover a crucial thermodynamic feedback loop that enables metabolically diverse communities to almost always stabilize nutrient cycles. Surprisingly, highly diverse communities self-organize to extract [Formula: see text]10[Formula: see text] of the maximum extractable energy, or [Formula: see text]100 fold more than randomized communities. Further, with increasing diversity, distinct ecosystems show strongly correlated fluxes through nutrient cycles. However, as the driving force from light increases, the fluxes of nutrient cycles become more variable and species-dependent. Our results highlight that self-organization promotes the efficiency and stability of complex ecosystems at extracting energy from the environment, even in the absence of any centralized coordination.

Carbon isotope fractionation by an ancestral rubisco suggests that biological proxies for CO2 through geologic time should be reevaluated.

The history of Earth's carbon cycle reflects trends in atmospheric composition convolved with the evolution of photosynthesis. Fortunately, key parts of the carbon cycle have been recorded in the carbon isotope ratios of sedimentary rocks. The dominant model used to interpret this record as a proxy for ancient atmospheric CO2 is based on carbon isotope fractionations of modern photoautotrophs, and longstanding questions remain about how their evolution might have impacted the record. Therefore, we measured both biomass (εp) and enzymatic (εRubisco) carbon isotope fractionations of a cyanobacterial strain (Synechococcus elongatus PCC 7942) solely expressing a putative ancestral Form 1B rubisco dating to ≫1 Ga. This strain, nicknamed ANC, grows in ambient pCO2 and displays larger εp values than WT, despite having a much smaller εRubisco (17.23 ± 0.61‰ vs. 25.18 ± 0.31‰, respectively). Surprisingly, ANC εp exceeded ANC εRubisco in all conditions tested, contradicting prevailing models of cyanobacterial carbon isotope fractionation. Such models can be rectified by introducing additional isotopic fractionation associated with powered inorganic carbon uptake mechanisms present in Cyanobacteria, but this amendment hinders the ability to accurately estimate historical pCO2 from geological data. Understanding the evolution of rubisco and the CO2 concentrating mechanism is therefore critical for interpreting the carbon isotope record, and fluctuations in the record may reflect the evolving efficiency of carbon fixing metabolisms in addition to changes in atmospheric CO2.

Protein cost minimization promotes the emergence of coenzyme redundancy.

SignificanceMetabolism relies on a small class of molecules (coenzymes) that serve as universal donors and acceptors of key chemical groups and electrons. Although metabolic networks crucially depend on structurally redundant coenzymes [e.g., NAD(H) and NADP(H)] associated with different enzymes, the criteria that led to the emergence of this redundancy remain poorly understood. Our combination of modeling and structural and sequence analysis indicates that coenzyme redundancy may not be essential for metabolism but could rather constitute an evolved strategy promoting efficient usage of enzymes when biochemical reactions are near equilibrium. Our work suggests that early metabolism may have operated with fewer coenzymes and that adaptation for metabolic efficiency may have driven the rise of coenzyme diversity in living systems.

Trajectories for the evolution of bacterial CO2-concentrating mechanisms.

Cyanobacteria rely on CO2-concentrating mechanisms (CCMs) to grow in today's atmosphere (0.04% CO2). These complex physiological adaptations require ≈15 genes to produce two types of protein complexes: inorganic carbon (Ci) transporters and 100+ nm carboxysome compartments that encapsulate rubisco with a carbonic anhydrase (CA) enzyme. Mutations disrupting any of these genes prohibit growth in ambient air. If any plausible ancestral form-i.e., lacking a single gene-cannot grow, how did the CCM evolve? Here, we test the hypothesis that evolution of the bacterial CCM was "catalyzed" by historically high CO2 levels that decreased over geologic time. Using an E. coli reconstitution of a bacterial CCM, we constructed strains lacking one or more CCM components and evaluated their growth across CO2 concentrations. We expected these experiments to demonstrate the importance of the carboxysome. Instead, we found that partial CCMs expressing CA or Ci uptake genes grew better than controls in intermediate CO2 levels (≈1%) and observed similar phenotypes in two autotrophic bacteria, Halothiobacillus neapolitanus and Cupriavidus necator. To understand how CA and Ci uptake improve growth, we model autotrophy as colimited by CO2 and HCO3-, as both are required to produce biomass. Our experiments and model delineated a viable trajectory for CCM evolution where decreasing atmospheric CO2 induces an HCO3- deficiency that is alleviated by acquisition of CA or Ci uptake, thereby enabling the emergence of a modern CCM. This work underscores the importance of considering physiology and environmental context when studying the evolution of biological complexity.

Highly active rubiscos discovered by systematic interrogation of natural sequence diversity.

CO2 is converted into biomass almost solely by the enzyme rubisco. The poor carboxylation properties of plant rubiscos have led to efforts that made it the most kinetically characterized enzyme, yet these studies focused on < 5% of its natural diversity. Here, we searched for fast-carboxylating variants by systematically mining genomic and metagenomic data. Approximately 33,000 unique rubisco sequences were identified and clustered into ≈ 1,000 similarity groups. We then synthesized, purified, and biochemically tested the carboxylation rates of 143 representatives, spanning all clusters of form-II and form-II/III rubiscos. Most variants (> 100) were active in vitro, with the fastest having a turnover number of 22 ± 1 s-1 -sixfold faster than the median plant rubisco and nearly twofold faster than the fastest measured rubisco to date. Unlike rubiscos from plants and cyanobacteria, the fastest variants discovered here are homodimers and exhibit a much simpler folding and activation kinetics. Our pipeline can be utilized to explore the kinetic space of other enzymes of interest, allowing us to get a better view of the biosynthetic potential of the biosphere.

eQuilibrator 3.0: a database solution for thermodynamic constant estimation.

eQuilibrator (equilibrator.weizmann.ac.il) is a database of biochemical equilibrium constants and Gibbs free energies, originally designed as a web-based interface. While the website now counts around 1,000 distinct monthly users, its design could not accommodate larger compound databases and it lacked a scalable Application Programming Interface (API) for integration into other tools developed by the systems biology community. Here, we report on the recent updates to the database as well as the addition of a new Python-based interface to eQuilibrator that adds many new features such as a 100-fold larger compound database, the ability to add novel compounds, improvements in speed and memory use, and correction for Mg2+ ion concentrations. Moreover, the new interface can compute the covariance matrix of the uncertainty between estimates, for which we show the advantages and describe the application in metabolic modelling. We foresee that these improvements will make thermodynamic modelling more accessible and facilitate the integration of eQuilibrator into other software platforms.

The total number and mass of SARS-CoV-2 virions.

Quantitatively describing the time course of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection within an infected individual is important for understanding the current global pandemic and possible ways to combat it. Here we integrate the best current knowledge about the typical viral load of SARS-CoV-2 in bodily fluids and host tissues to estimate the total number and mass of SARS-CoV-2 virions in an infected person. We estimate that each infected person carries 109 to 1011 virions during peak infection, with a total mass in the range of 1 µg to 100 µg, which curiously implies that all SARS-CoV-2 virions currently circulating within human hosts have a collective mass of only 0.1 kg to 10 kg. We combine our estimates with the available literature on host immune response and viral mutation rates to demonstrate how antibodies markedly outnumber the spike proteins, and the genetic diversity of virions in an infected host covers all possible single nucleotide substitutions.

Phosphoglycolate salvage in a chemolithoautotroph using the Calvin cycle.

Carbon fixation via the Calvin cycle is constrained by the side activity of Rubisco with dioxygen, generating 2-phosphoglycolate. The metabolic recycling of phosphoglycolate was extensively studied in photoautotrophic organisms, including plants, algae, and cyanobacteria, where it is referred to as photorespiration. While receiving little attention so far, aerobic chemolithoautotrophic bacteria that operate the Calvin cycle independent of light must also recycle phosphoglycolate. As the term photorespiration is inappropriate for describing phosphoglycolate recycling in these nonphotosynthetic autotrophs, we suggest the more general term "phosphoglycolate salvage." Here, we study phosphoglycolate salvage in the model chemolithoautotroph Cupriavidus necator H16 (Ralstonia eutropha H16) by characterizing the proxy process of glycolate metabolism, performing comparative transcriptomics of autotrophic growth under low and high CO2 concentrations, and testing autotrophic growth phenotypes of gene deletion strains at ambient CO2 We find that the canonical plant-like C2 cycle does not operate in this bacterium, and instead, the bacterial-like glycerate pathway is the main route for phosphoglycolate salvage. Upon disruption of the glycerate pathway, we find that an oxidative pathway, which we term the malate cycle, supports phosphoglycolate salvage. In this cycle, glyoxylate is condensed with acetyl coenzyme A (acetyl-CoA) to give malate, which undergoes two oxidative decarboxylation steps to regenerate acetyl-CoA. When both pathways are disrupted, autotrophic growth is abolished at ambient CO2 We present bioinformatic data suggesting that the malate cycle may support phosphoglycolate salvage in diverse chemolithoautotrophic bacteria. This study thus demonstrates a so far unknown phosphoglycolate salvage pathway, highlighting important diversity in microbial carbon fixation metabolism.

Revisiting Trade-offs between Rubisco Kinetic Parameters.

Rubisco is the primary carboxylase of the Calvin cycle, the most abundant enzyme in the biosphere, and one of the best-characterized enzymes. On the basis of correlations between Rubisco kinetic parameters, it is widely posited that constraints embedded in the catalytic mechanism enforce trade-offs between CO2 specificity, SC/O, and maximum carboxylation rate, kcat,C. However, the reasoning that established this view was based on data from ≈20 organisms. Here, we re-examine models of trade-offs in Rubisco catalysis using a data set from ≈300 organisms. Correlations between kinetic parameters are substantially attenuated in this larger data set, with the inverse relationship between kcat,C and SC/O being a key example. Nonetheless, measured kinetic parameters display extremely limited variation, consistent with a view of Rubisco as a highly constrained enzyme. More than 95% of kcat,C values are between 1 and 10 s-1, and no measured kcat,C exceeds 15 s-1. Similarly, SC/O varies by only 30% among Form I Rubiscos and <10% among C3 plant enzymes. Limited variation in SC/O forces a strong positive correlation between the catalytic efficiencies (kcat/KM) for carboxylation and oxygenation, consistent with a model of Rubisco catalysis in which increasing the rate of addition of CO2 to the enzyme-substrate complex requires an equal increase in the O2 addition rate. Altogether, these data suggest that Rubisco evolution is tightly constrained by the physicochemical limits of CO2/O2 discrimination.

Quantum chemistry reveals thermodynamic principles of redox biochemistry.

Thermodynamics dictates the structure and function of metabolism. Redox reactions drive cellular energy and material flow. Hence, accurately quantifying the thermodynamics of redox reactions should reveal design principles that shape cellular metabolism. However, only few redox potentials have been measured, and mostly with inconsistent experimental setups. Here, we develop a quantum chemistry approach to calculate redox potentials of biochemical reactions and demonstrate our method predicts experimentally measured potentials with unparalleled accuracy. We then calculate the potentials of all redox pairs that can be generated from biochemically relevant compounds and highlight fundamental trends in redox biochemistry. We further address the question of why NAD/NADP are used as primary electron carriers, demonstrating how their physiological potential range fits the reactions of central metabolism and minimizes the concentration of reactive carbonyls. The use of quantum chemistry can revolutionize our understanding of biochemical phenomena by enabling fast and accurate calculation of thermodynamic values.

The stringent response regulates adaptation to darkness in the cyanobacterium Synechococcus elongatus.

The cyanobacterium Synechococcus elongatus relies upon photosynthesis to drive metabolism and growth. During darkness, Synechococcus stops growing, derives energy from its glycogen stores, and greatly decreases rates of macromolecular synthesis via unknown mechanisms. Here, we show that the stringent response, a stress response pathway whose genes are conserved across bacteria and plant plastids, contributes to this dark adaptation. Levels of the stringent response alarmone guanosine 3'-diphosphate 5'-diphosphate (ppGpp) rise after a shift from light to dark, indicating that darkness triggers the same response in cyanobacteria as starvation in heterotrophic bacteria. High levels of ppGpp are sufficient to stop growth and dramatically alter many aspects of cellular physiology, including levels of photosynthetic pigments and polyphosphate, DNA content, and the rate of translation. Cells unable to synthesize ppGpp display pronounced growth defects after exposure to darkness. The stringent response regulates expression of a number of genes in Synechococcus, including ribosomal hibernation promoting factor (hpf), which causes ribosomes to dimerize in the dark and may contribute to decreased translation. Although the metabolism of Synechococcus differentiates it from other model bacterial systems, the logic of the stringent response remains remarkably conserved, while at the same time having adapted to the unique stresses of the photosynthetic lifestyle.

pH determines the energetic efficiency of the cyanobacterial CO2 concentrating mechanism.

Many carbon-fixing bacteria rely on a CO2 concentrating mechanism (CCM) to elevate the CO2 concentration around the carboxylating enzyme ribulose bisphosphate carboxylase/oxygenase (RuBisCO). The CCM is postulated to simultaneously enhance the rate of carboxylation and minimize oxygenation, a competitive reaction with O2 also catalyzed by RuBisCO. To achieve this effect, the CCM combines two features: active transport of inorganic carbon into the cell and colocalization of carbonic anhydrase and RuBisCO inside proteinaceous microcompartments called carboxysomes. Understanding the significance of the various CCM components requires reconciling biochemical intuition with a quantitative description of the system. To this end, we have developed a mathematical model of the CCM to analyze its energetic costs and the inherent intertwining of physiology and pH. We find that intracellular pH greatly affects the cost of inorganic carbon accumulation. At low pH the inorganic carbon pool contains more of the highly cell-permeable H2CO3, necessitating a substantial expenditure of energy on transport to maintain internal inorganic carbon levels. An intracellular pH ≈8 reduces leakage, making the CCM significantly more energetically efficient. This pH prediction coincides well with our measurement of intracellular pH in a model cyanobacterium. We also demonstrate that CO2 retention in the carboxysome is necessary, whereas selective uptake of HCO3 (-) into the carboxysome would not appreciably enhance energetic efficiency. Altogether, integration of pH produces a model that is quantitatively consistent with cyanobacterial physiology, emphasizing that pH cannot be neglected when describing biological systems interacting with inorganic carbon pools.

Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro kcat measurements.

Turnover numbers, also known as kcat values, are fundamental properties of enzymes. However, kcat 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 kcat values for the maximal catalytic rates of enzymes in vivo? Here, we harness omics data to calculate kmax(vivo), the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation ofr(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 kmax(vivo) and kcat values. The approach we present here characterizes the quantitative relationship between enzymatic catalysis in vitro and in vivo and offers a high-throughput method for extracting enzyme kinetic constants from omics data.

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 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.

Visual account of protein investment in cellular functions.

Proteomics techniques generate an avalanche of data and promise to satisfy biologists' long-held desire to measure absolute protein abundances on a genome-wide scale. However, can this knowledge be translated into a clearer picture of how cells invest their protein resources? This article aims to give a broad perspective on the composition of proteomes as gleaned from recent quantitative proteomics studies. We describe proteomaps, an approach for visualizing the composition of proteomes with a focus on protein abundances and functions. In proteomaps, each protein is shown as a polygon-shaped tile, with an area representing protein abundance. Functionally related proteins appear in adjacent regions. General trends in proteomes, such as the dominance of metabolism and protein production, become easily visible. We make interactive visualizations of published proteome datasets accessible at www.proteomaps.net. We suggest that evaluating the way protein resources are allocated by various organisms and cell types in different conditions will sharpen our understanding of how and why cells regulate the composition of their proteomes.

Glycolytic strategy as a tradeoff between energy yield and protein cost.

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.

Pathway thermodynamics highlights kinetic obstacles in central metabolism.

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.

Spanning high-dimensional expression space using ribosome-binding site combinatorics.

Protein levels are a dominant factor shaping natural and synthetic biological systems. Although proper functioning of metabolic pathways relies on precise control of enzyme levels, the experimental ability to balance the levels of many genes in parallel is a major outstanding challenge. Here, we introduce a rapid and modular method to span the expression space of several proteins in parallel. By combinatorially pairing genes with a compact set of ribosome-binding sites, we modulate protein abundance by several orders of magnitude. We demonstrate our strategy by using a synthetic operon containing fluorescent proteins to span a 3D color space. Using the same approach, we modulate a recombinant carotenoid biosynthesis pathway in Escherichia coli to reveal a diversity of phenotypes, each characterized by a distinct carotenoid accumulation profile. In a single combinatorial assembly, we achieve a yield of the industrially valuable compound astaxanthin 4-fold higher than previously reported. The methodology presented here provides an efficient tool for exploring a high-dimensional expression space to locate desirable phenotypes.