Avi Flamholz

eQuilibrator—the biochemical thermodynamics calculator

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.

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.

Rethinking glycolysis: on the biochemical logic of metabolic pathways

Metabolic pathways may seem arbitrary and unnecessarily complex. In many cases, a chemist might devise a simpler route for the biochemical transformation, so why has nature chosen such complex solutions? In this review, we distill lessons from a century of metabolic research and introduce new observations suggesting that the intricate structure of metabolic pathways can be explained by a small set of biochemical principles. Using glycolysis as an example, we demonstrate how three key biochemical constraints--thermodynamic favorability, availability of enzymatic mechanisms and the physicochemical properties of pathway intermediates--eliminate otherwise plausible metabolic strategies. Considering these constraints, glycolysis contains no unnecessary steps and represents one of the very few pathway structures that meet cellular demands. The analysis presented here can be applied to metabolic engineering efforts for the rational design of pathways that produce a desired product while satisfying biochemical constraints.

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.

An integrated open framework for thermodynamics of reactions that combines accuracy and coverage

Motivation: The laws of thermodynamics describe a direct, quantitative relationship between metabolite concentrations and reaction directionality. Despite great efforts, thermodynamic data suffer from limited coverage, scattered accessibility and non-standard annotations. We present a framework for unifying thermodynamic data from multiple sources and demonstrate two new techniques for extrapolating the Gibbs energies of unmeasured reactions and conditions. Results: Both methods account for changes in cellular conditions (pH, ionic strength, etc.) by using linear regression over the ΔG○ of pseudoisomers and reactions. The Pseudoisomeric Reactant Contribution method systematically infers compound formation energies using measured K′ and pKa data. The Pseudoisomeric Group Contribution method extends the group contribution method and achieves a high coverage of unmeasured reactions. We define a continuous index that predicts the reversibility of a reaction under a given physiological concentration range. In the characteristic physiological range 3μM–3mM, we find that roughly half of the reactions in Escherichia colis metabolism are reversible. These new tools can increase the accuracy of thermodynamic-based models, especially in non-standard pH and ionic strengths. The reversibility index can help modelers decide which reactions are reversible in physiological conditions. Availability: Freely available on the web at: http://equilibrator.weizmann.ac.il. Website implemented in Python, MySQL, Apache and Django, with all major browsers supported. The framework is open-source (code.google.com/p/milo-lab), implemented in pure Python and tested mainly on Linux. Contact: ron.milo@weizmann.ac.il Supplementary Information: Supplementary data are available at Bioinformatics online.

Profiling of engineering hotspots identifies an allosteric CRISPR-Cas9 switch

The clustered, regularly interspaced, short palindromic repeats (CRISPR)-associated protein Cas9 from Streptococcus pyogenes is an RNA-guided DNA endonuclease with widespread utility for genome modification. However, the structural constraints limiting the engineering of Cas9 have not been determined. Here we experimentally profile Cas9 using randomized insertional mutagenesis and delineate hotspots in the structure capable of tolerating insertions of a PDZ domain without disruption of the enzymes binding and cleavage functions. Orthogonal domains or combinations of domains can be inserted into the identified sites with minimal functional consequence. To illustrate the utility of the identified sites, we construct an allosterically regulated Cas9 by insertion of the estrogen receptor-α ligand-binding domain. This protein showed robust, ligand-dependent activation in prokaryotic and eukaryotic cells, establishing a versatile one-component system for inducible and reversible Cas9 activation. Thus, domain insertion profiling facilitates the rapid generation of new Cas9 functionalities and provides useful data for future engineering of Cas9.

Thermodynamic constraints shape the structure of carbon fixation pathways.

Thermodynamics impose a major constraint on the structure of metabolic pathways. Here, we use carbon fixation pathways to demonstrate how thermodynamics shape the structure of pathways and determine the cellular resources they consume. We analyze the energetic profile of prototypical reactions and show that each reaction type displays a characteristic change in Gibbs energy. Specifically, although carbon fixation pathways display a considerable structural variability, they are all energetically constrained by two types of reactions: carboxylation and carboxyl reduction. In fact, all adenosine triphosphate (ATP) molecules consumed by carbon fixation pathways - with a single exception - are used, directly or indirectly, to power one of these unfavorable reactions. When an indirect coupling is employed, the energy released by ATP hydrolysis is used to establish another chemical bond with high energy of hydrolysis, e.g. a thioester. This bond is cleaved by a downstream enzyme to energize an unfavorable reaction. Notably, many pathways exhibit reduced ATP requirement as they couple unfavorable carboxylation or carboxyl reduction reactions to exergonic reactions other than ATP hydrolysis. In the most extreme example, the reductive acetyl coenzyme A (acetyl-CoA) pathway bypasses almost all ATP-consuming reactions. On the other hand, the reductive pentose phosphate pathway appears to be the least ATP-efficient because it is the only carbon fixation pathway that invests ATP in metabolic aims other than carboxylation and carboxyl reduction. Altogether, our analysis indicates that basic thermodynamic considerations accurately predict the resource investment required to support a metabolic pathway and further identifies biochemical mechanisms that can decrease this requirement.

Design and analysis of metabolic pathways supporting formatotrophic growth for electricity-dependent cultivation of microbes

Electrosynthesis is a promising approach that enables the biological production of commodities, like fuels and fine chemicals, using renewably produced electricity. Several techniques have been proposed to mediate the transfer of electrons from the cathode to living cells. Of these, the electroproduction of formate as a mediator seems especially promising: formate is readily soluble, of low toxicity and can be produced at relatively high efficiency and at reasonable current density. While organisms that are capable of formatotrophic growth, i.e. growth on formate, exist naturally, they are generally less suitable for bulk cultivation and industrial needs. Hence, it may be helpful to engineer a model organism of industrial relevance, such as E. coli, for growth on formate. There are numerous metabolic pathways that can potentially support formatotrophic growth. Here we analyze these diverse pathways according to various criteria including biomass yield, thermodynamic favorability, chemical motive force, kinetics and the practical challenges posed by their expression. We find that the reductive glycine pathway, composed of the tetrahydrofolate system, the glycine cleavage system, serine hydroxymethyltransferase and serine deaminase, is a promising candidate to support electrosynthesis in E. coli. The approach presented here exemplifies how combining different computational approaches into a systematic analysis methodology provides assistance in redesigning metabolism. This article is part of a Special Issue entitled: Metals in Bioenergetics and Biomimetics Systems.

Hydrophobicity and Charge Shape Cellular Metabolite Concentrations

What governs the concentrations of metabolites within living cells? Beyond specific metabolic and enzymatic considerations, are there global trends that affect their values? We hypothesize that the physico-chemical properties of metabolites considerably affect their in-vivo concentrations. The recently achieved experimental capability to measure the concentrations of many metabolites simultaneously has made the testing of this hypothesis possible. Here, we analyze such recently available data sets of metabolite concentrations within E. coli, S. cerevisiae, B. subtilis and human. Overall, these data sets encompass more than twenty conditions, each containing dozens (28-108) of simultaneously measured metabolites. We test for correlations with various physico-chemical properties and find that the number of charged atoms, non-polar surface area, lipophilicity and solubility consistently correlate with concentration. In most data sets, a change in one of these properties elicits a ∼100 fold increase in metabolite concentrations. We find that the non-polar surface area and number of charged atoms account for almost half of the variation in concentrations in the most reliable and comprehensive data set. Analyzing specific groups of metabolites, such as amino-acids or phosphorylated nucleotides, reveals even a higher dependence of concentration on hydrophobicity. We suggest that these findings can be explained by evolutionary constraints imposed on metabolite concentrations and discuss possible selective pressures that can account for them. These include the reduction of solute leakage through the lipid membrane, avoidance of deleterious aggregates and reduction of non-specific hydrophobic binding. By highlighting the global constraints imposed on metabolic pathways, future research could shed light onto aspects of biochemical evolution and the chemical constraints that bound metabolic engineering efforts.

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

Significance The kcat values of enzymes are important for the study of metabolic systems. However, the current use of kcat presents major difficulties, as values for most enzymes have not been experimentally measured, and experimentally available values are often measured under nonphysiological conditions, thereby casting doubt on the relevance of kcat under in vivo conditions. We present an approach that utilizes omics data to quantitatively analyze the relationship between in vitro kcat values and the maximal catalytic rate of enzymes in vivo. Our approach offers a high-throughput method to obtain enzyme kinetic constants, which reflect in vivo conditions, and are useful for more accurate and complete cellular metabolic models. 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 kmaxvivo, the observed maximal catalytic rate of an enzyme inside cells. Comparison with kcat values from Escherichia coli, yields a correlation of r2= 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 kmaxvivo 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.