Commemorating the 1913 Michaelis-Menten paperDie Kinetik der Invertinwirkung: three perspectives

Theory on the rate equations of Michaelis-Menten type enzyme kinetics with competitive inhibition

We derive approximate expressions for pre- and post-steady state regimes of the velocity-substrate-inhibitor spaces of the Michaelis-Menten enzyme kinetic scheme with fully and partial competitive inhibition. Our refinement over the currently available standard quasi steady state approximation (sQSSA) seems to be valid over wide range of enzyme to substrate and enzyme to inhibitor concentration ratios. Further, we show that the enzyme-inhibitor-substrate system can exhibit temporally well-separated two different steady states with respect to both enzyme-substrate and enzyme-inhibitor complexes under certain conditions. We define the ratios fS = vmax/(KMS + e0) and fI = umax/(KMI + e0) as the acceleration factors with respect to the catalytic conversion of substrate and inhibitor into their respective products. Here KMS and KMI are the Michaelis-Menten parameters associated respectively with the binding of substrate and inhibitor with the enzyme, vmax and umax are the respective maximum reaction velocities and e0, s0, and i0 are total enzyme, substrate and inhibitor levels. When (fS/fI) < 1, then enzyme-substrate complex will show multiple steady states and it reaches the full-fledged steady state only after the depletion of enzyme-inhibitor complex. When (fS/fI) > 1, then the enzyme-inhibitor complex will show multiple steady states and it reaches the full-fledged steady state only after the depletion of enzyme-substrate complex. This multi steady-state behavior especially when (fS/fI) ≠ 1 is the root cause of large amount of error in the estimation of various kinetic parameters of fully and partial competitive inhibition schemes using sQSSA. Remarkably, we show that our refined expressions for the reaction velocities over enzyme-substrate-inhibitor space can control this error more significantly than the currently available sQSSA expressions.

Nitrate denitrification rate response to temperature gradient change during river bank infiltration

Nitrate attenuation during river bank infiltration is the key process for reducing nitrogen pollution. Temperature is considered to be an important factor affecting nitrate attenuation. However, the magnitude and mechanism of its impact have not been clear for a long time. In this study, the effects of temperature and temperature gradient on the nitrate denitrification rate were investigated via static batch and dynamic soil column simulation experiments. The results showed that temperature had a significant effect on the denitrification rate. Temperature effects were first observed in denitrifying bacteria. At low temperatures, the microorganism diversity was low, resulting in a lower denitrification rate constant. The static experimental results showed that the denitrification rate at 19 °C was approximately 2.4 times that at 10 °C. The dynamic soil column experiment established an exponential positive correlation between the nitrate denitrification decay kinetic constant and temperature. The affinity of denitrifying enzymes for nitrate in the reaction substrate was ordered as follows: decreasing temperature gradient (30 °C → 10 °C) > zero temperature gradient (10 °C) > increasing temperature gradient condition (0 °C → 10 °C). This study provides a theoretical basis for the biogeochemical processes underlying river bank infiltration, which will help aid in the development and utilization of groundwater resources.

Maud Menten: Pioneering Pediatric-Perinatal Pathologist, Clinician-Scientist, and "the Most Wonderful Human Being in the World"

Maud Menten was born and raised in remote regions of Canada. She obtained her MB/MD at the University of Toronto (1907/1911) and her PhD in biochemistry at the University of Chicago (1916). From 1907 to 1916, she trained at the Rockefeller Institute for Medical Research, the New York Infirmary for Women and Children, Western Reserve University in Cleveland, the Berlin Municipal Hospital in Germany, and the Barnard Free Skin and Cancer Hospital in St Louis. In 1916, she was appointed as pathologist at the Elizabeth Steel Magee Hospital, a charitable maternity hospital in Pittsburgh. She received a faculty appointment at the University of Pittsburgh (1918) and was appointed pathologist at Pittsburgh Children's Hospital (1926). In addition to being one of the first woman academic pathologists, she was likely the first perinatal, the second pediatric-perinatal, and the fourth pediatric pathologist to practice in North America. The importance of Menten's overall scientific contributions place her in the very upper echelon of 20th century pathologists. Her enzyme kinetic work resulted in the Michaelis-Menten equation, and her work in George Crile's laboratory in Cleveland provided a physiological basis for improved surgical outcomes. Her work in Pittsburgh was equally innovative, including initiating the field of enzyme histochemistry.

Early Cannon Development in Females of the "Sanmartinero" Creole Bovine Breed

The variation in the dimensions of the body of living beings in relation to their size, function, or shape is known as allometry. Allometry studies allow the analysis of the function of body structures and their relationship with the performance and survival of breeds and species. The aim of this study was to describe the ontogenetic characteristics of the weight of certain bone elements of the Sanmartinero creole bovine breed, from an early age (6 months) until maturity. A total of 79 females of the Sanmartinero creole bovine breed with an age range of 0.5 to 10 years were studied. Body measurements were obtained individually using standard procedures: cannon perimeter, thoracic perimeter, body length, withers height, and body weight. Functional and production indices were obtained for animals aged more than 3 years (n = 53): corporal index, anamorphosis index, dactylo thoracic index, and the relative thickness of the cannon. The correlation between body weight and the cannon perimeter showed no trend towards a plateau. In the Sanmartinero creole bovine, therefore, a very early development of the cannon perimeter is detected, which could lead to bone fragility in heavier animals. Therefore, data suggest little harmony with appendicular bone development, i.e., with less robust cannons which are those necessary to support body mass. It is suggested that in genetic improvement programs of the Sanmartinero creole bovine, the measurement of the cannon perimeter, the withers height, and the thoracic perimeter should be considered.

MIWE: detecting the critical states of complex biological systems by the mutual information weighted entropy

Complex biological systems often undergo sudden qualitative changes during their dynamic evolution. These critical transitions are typically characterized by a catastrophic progression of the system. Identifying the critical point is critical to uncovering the underlying mechanisms of complex biological systems. However, the system may exhibit minimal changes in its state until the critical point is reached, and in the face of high throughput and strong noise data, traditional biomarkers may not be effective in distinguishing the critical state. In this study, we propose a novel approach, mutual information weighted entropy (MIWE), which uses mutual information between genes to build networks and identifies critical states by quantifying molecular dynamic differences at each stage through weighted differential entropy. The method is applied to one numerical simulation dataset and four real datasets, including bulk and single-cell expression datasets. The critical states of the system can be recognized and the robustness of MIWE method is verified by numerical simulation under the influence of different noises. Moreover, we identify two key transcription factors (TFs), CREB1 and CREB3, that regulate downstream signaling genes to coordinate cell fate commitment. The dark genes in the single-cell expression datasets are mined to reveal the potential pathway regulation mechanism.

Molecular noise-induced activator-inhibitor duality in enzyme inhibition kinetics

Classical theories of enzyme inhibition kinetics predict a monotonic decrease in the mean catalytic activity with the increase in inhibitor concentration. The steady-state result, derived from deterministic mass action kinetics, ignores molecular noise in enzyme-inhibition mechanisms. Here, we present a stochastic generalization of enzyme inhibition kinetics to mesoscopic enzyme concentrations by systematically accounting for molecular noise in competitive and uncompetitive mechanisms of enzyme inhibition. Our work reveals an activator-inhibitor duality as a non-classical effect in the transient regime in which inhibitors tend to enhance enzymatic activity. We introduce statistical measures that quantify this counterintuitive response through the stochastic analog of the Lineweaver-Burk plot that shows a merging of the inhibitor-dependent velocity with the Michaelis-Menten velocity. The statistical measures of mean and temporal fluctuations - fractional enzyme activity and waiting time correlations - show a non-monotonic rise with the increase in inhibitors before subsiding to their baseline value. The inhibitor and substrate dependence of the fractional enzyme activity yields kinetic phase diagrams for non-classical activator-inhibitor duality. Our work links this duality to a molecular memory effect in the transient regime, arising from positive correlations between consecutive product turnover times. The vanishing of memory in the steady state recovers all the classical results.

New Insights into the Cooperativity and Dynamics of Dimeric Enzymes

A survey of protein databases indicates that the majority of enzymes exist in oligomeric forms, with about half of those found in the UniProt database being homodimeric. Understanding why many enzymes are in their dimeric form is imperative. Recent developments in experimental and computational techniques have allowed for a deeper comprehension of the cooperative interactions between the subunits of dimeric enzymes. This review aims to succinctly summarize these recent advancements by providing an overview of experimental and theoretical methods, as well as an understanding of cooperativity in substrate binding and the molecular mechanisms of cooperative catalysis within homodimeric enzymes. Focus is set upon the beneficial effects of dimerization and cooperative catalysis. These advancements not only provide essential case studies and theoretical support for comprehending dimeric enzyme catalysis but also serve as a foundation for designing highly efficient catalysts, such as dimeric organic catalysts. Moreover, these developments have significant implications for drug design, as exemplified by Paxlovid, which was designed for the homodimeric main protease of SARS-CoV-2.

Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism

We present "on the fly" algorithmic criteria for the accuracy and stability (non-stiffness) of reduced models constructed with the quasi-steady state and partial equilibrium approximations. The criteria comprise those introduced in Goussis (Combust Theor Model 16:869-926, 2012) that addressed the case where each fast time scale is due to one reaction and a new one that addresses the case where a fast time scale is due to more than one reactions. The development of these criteria is based on the ability to approximate accurately the fast and slow subspaces of the tangent space. Their validity is assessed on the basis of the Michaelis-Menten reaction mechanism, for which extensive literature is available regarding the validity of the existing various reduced models. The criteria predict correctly the regions in both the parameter and phase spaces where each of these models is valid. The findings are supported by numerical computations at indicative points in the parameter space. Due to their algorithmic character, these criteria can be readily employed for the reduction of large and complex mathematical models.

Mathematical Modeling of ROS Production and Diode-like Behavior in the SDHA/SDHB Subcomplex of Succinate Dehydrogenases in Reverse Quinol-Fumarate Reductase Direction

Succinate dehydrogenase (SDH) plays an important role in reverse electron transfer during hypoxia/anoxia, in particular, in ischemia, when blood supply to an organ is disrupted, and oxygen is not available. It was detected in the voltammetry studies about three decades ago that the SDHA/SDHB subcomplex of SDH can have such a strong nonlinear property as a "tunnel-diode" behavior in reverse quinol-fumarate reductase direction. The molecular and kinetic mechanisms of this phenomenon, that is, a strong drop in the rate of fumarate reduction as the driving force is increased, are still unclear. In order to account for this property of SDH, we developed and analyzed a mechanistic computational model of reverse electron transfer in the SDHA/SDHB subcomplex of SDH. It was shown that a decrease in the rate of succinate release from the active center during fumarate reduction quantitatively explains the experimentally observed tunnel-diode behavior in SDH and threshold values of the electrode potential of about -80 mV. Computational analysis of ROS production in the SDHA/SDHB subcomplex of SDH during reverse electron transfer predicts that the rate of ROS production decreases when the tunnel-diode behavior appears. These results predict a low rate of ROS production by the SDHA/SDHB subcomplex of SDH during ischemia.

Wax based oleogels and their application in sponge cakes

The use of high amounts of saturated fatty acids mainly obtained from tropical fats and oils gains increasing rejection from consumers. Use of liquid plant based oils, however, does not deliver necessary functionalities. In this contribution, sunflower-(SFW), bees-wax (BW), ricebran wax (RBW) and a BW-wax mixture (BW : SFWh) were investigated as a potential alternative fat phase in low-density bakery products. Since the food product matrix is composed of complex ingredients, key-functionalities (foam-stabilization, viscoelastic properties, and oil-binding) were first investigated for pure oleogels as oleofoams. It could be demonstrated that all waxes investigated were able to form oleofoams. The location of wax crystal aggregates, at the oil-air interface or in the bulk, was shown to be a significant factor regarding oil-binding and viscoelastic properties. However, it was not possible to transfer all findings made for the oleofoams to the ones made for the oleogel based sponge cakes. There, all oleogels showed improvement compared to the canola oil variant regarding oil-leaping and visual appearance (volume). Sensory evaluation attested satisfactory results for all wax-based oleogel applications. This contribution aims to deliver novel findings for wax-based oleogels as oleofoams as well as an alternative fat phase in low-density bakery products. The gathered results aim to enable a target-oriented characterization of oleogel applications and hence facilitate future use to deliver beneficial products to the market.

Kinetics of human pyrroline-5-carboxylate reductase in L-thioproline metabolism

L-Thioproline (L-thiazolidine-4-carboxylate, L-T4C) is a cyclic sulfur-containing analog of L-proline found in multiple kingdoms of life. The oxidation of L-T4C leads to L-cysteine formation in bacteria, plants, mammals, and protozoa. The conversion of L-T4C to L-Cys in bacterial cell lysates has been attributed to proline dehydrogenase and L-Δ¹-pyrroline-5-carboxylate (P5C) reductase (PYCR) enzymes but detailed kinetic studies have not been conducted. Here, we characterize the dehydrogenase activity of human PYCR isozymes 1 and 2 with L-T4C using NAD(P)⁺ as the hydride acceptor. Both PYCRs exhibit significant L-T4C dehydrogenase activity; however, PYCR2 displays nearly tenfold higher catalytic efficiency (136 M^-1 s^-1) than PYCR1 (13.7 M^-1 s^-1). Interestingly, no activity was observed with either L-Pro or the analog DL-thiazolidine-2-carboxylate, indicating that the sulfur at the 4-position is critical for PYCRs to utilize L-T4C as a substrate. Inhibition kinetics show that L-Pro is a competitive inhibitor of PYCR1 [Formula: see text] with respect to L-T4C, consistent with these ligands occupying the same binding site. We also confirm by mass spectrometry that L-T4C oxidation by PYCRs leads to cysteine product formation. Our results suggest a new enzyme function for human PYCRs in the metabolism of L-T4C.

Some pioneering Canadian women chemists: lives and contributions

During Dr. Margaret-Ann Armour’s career, she was always passionate about the need to encourage more young women to enter chemistry and chemistry-related careers. One way of doing this is by means of role models, specifically to share stories of previous generations of Canadian women chemists. In fact, it is necessary to make them aware that there were Canadian women chemists, even at the beginning of the 20th century. Yet, no unitary source of information on Canadian women chemists has existed. This contribution will provide six selected life stories to partially remedy this deficiency and to offer those who wish to inspire future generations of women chemists with names and stories from the past. The individuals included here are Maude Menten, Clara Benson, Mary Dover, Bella Marcuse, Carol Edna Robertson (Maass), and Norah Vernon Barry (Toole).

A guide to the Michaelis-Menten equation: steady state and beyond

The modern definition of enzymology is synonymous with the Michaelis-Menten equation instituted by Leonor Michaelis and Maud Menten. Most textbooks, or chapters within, discussing enzymology start with the derivation of the equation under the assumption of rapid equilibrium (as done by Michaelis-Menten) or steady state (as modified by Briggs and Haldane) conditions to highlight the importance of this equation as the bedrock on which interpretation of enzyme kinetic results is dependent. However, few textbooks or monographs take the effort of placing the equation within its right historical context and discuss the assumptions that have gone into its institution. This guide will dwell on these in substantial detail. Further, this guide will attempt to instil a sense of appreciation for the mathematical curve rectangular hyperbola, its unique attributes and how ubiquitous the curve is in biological systems. To conclude, this guide will discuss the limitations of the equation, and the method it embodies, and trace the journey of how investigators are attempting to move beyond the steady-state approach and the Michaelis-Menten equation into full progress curve, pre-steady state and single-turnover kinetic analysis to obtain greater insights into enzyme kinetics and catalysis.

The essence of life revisited: how theories can shed light on it

Disagreement over whether life is inevitable when the conditions can support life remains unresolved, but calculations show that self-organization can arise naturally from purely random effects. Closure to efficient causation, or the need for all specific catalysts used by an organism to be produced internally, implies that a true model of an organism cannot exist, though this does not exclude the possibility that some characteristics can be simulated. Such simulations indicate that there is a limit to how small a self-organizing system can be: much smaller than a bacterial cell, but around the size of a typical virus particle. All current theories of life incorporate, at least implicitly, the idea of catalysis, but they largely ignore the need for metabolic regulation.

Zacharias Dische and the discovery of feedback inhibition: A landmark paper published in the forerunner of Biochimie

Zacharias Dische's discovery of feedback inhibition in metabolism was one of the most important in the history of biochemistry. However, his paper was written and published under very difficult circumstances in wartime and passed almost completely unnoticed. It is almost never cited, and the discovery itself is usually attributed to later work of others. Here I provide a discussion of Dische's work, a translation of his paper into English, and a transcription of the original French version, which is almost unobtainable anywhere.

Two-Stage Continuous Conversion of Carbon Monoxide to Ethylene by Whole Cells of Azotobacter vinelandii

Azotobacter vinelandii is an obligate aerobic diazotroph with a verified transient ability to reduce carbon monoxide to ethylene by its vanadium nitrogenase. In this study, we implemented an industrially relevant continuous two-stage stirred-tank system for in vivo biotransformation of a controlled supply of air enriched with 5% carbon monoxide to 302 μg ethylene g^-1 glucose consumed. To attain this value, the process required overcoming critical oxygen limitations during cell proliferation while simultaneously avoiding the A. vinelandii respiratory protection mechanism that negatively impacts in vivo nitrogenase activity. Additionally, process conditions allowed the demonstration of carbon monoxide's solubility as a reaction-limiting factor and a competitor with dinitrogen for the vanadium nitrogenase active site, implying that excess intracellular carbon monoxide could lead to a cessation of cell proliferation and ethylene formation as shown genetically using a new strain of A. vinelandii deficient in carbon monoxide dehydrogenase.IMPORTANCE Ethylene is an essential commodity feedstock used for the generation of a variety of consumer products, but its generation demands energy-intensive processes and is dependent on nonrenewable substrates. This work describes a continuous biological method for investigating the nitrogenase-mediated carbon monoxide reductive coupling involved in ethylene production using whole cells of Azotobacter vinelandii If eventually adopted by industry, this technology has the potential to significantly reduce the total energy input required and the ethylene recovery costs, as well as decreasing greenhouse gas emissions associated with current production strategies.

A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails

The Michaelis-Menten reaction scheme is among the most influential models in the field of biochemistry, since it led to a very popular expression for the rate of an enzyme-catalysed reaction. After the realisation that this expression is valid in a limited region of the parameter space, two additional expressions were later introduced. The range of validity of these three expressions has been studied thoroughly, since the significance of a reliable rate is not based only on the accuracy of its predictive abilities but also on the physical insight that is acquired in the process of its construction. Here a new expression for the rate is introduced that is valid in practically the full parameter space and reduces to the expressions in the literature, when considering appropriate limits. The new expression is produced by employing algorithmic tools for asymptotic analysis, so that its construction is not hindered by the dimensional form and the complexity of the full model or by a wide parameter range of interest. These tools can be employed for the derivation of enzyme rate expressions of much more complex kinetics mechanisms.

Advantages of Hydrogel-Based 3D-Printed Enzyme Reactors and Their Limitations for Biocatalysis

The development of process steps catalyzed by immobilized enzymes usually encompasses the screening of enzyme variants, as well as the optimization of immobilization protocols and process parameters. Direct immobilization of biocatalysts by physical entrapment into hydrogels can be applied to reduce the effort required for immobilization, as the enzyme-specific optimization of the immobilization procedure is omitted. Physical entrapment is applicable for purified enzymes as well as crude cell extracts. Therefore, it can be used to quickly assess and compare activities of immobilized enzymes. For the application in flow reactors, we developed 3D-printed hydrogel lattices for enzyme entrapment as well as matching housings, also manufactured by 3D-printing. Testing the resulting enzyme reactors for three different enzymes, namely alcohol dehydrogenase from Lactobacillus brevis, benzoylformate decarboxylase from Pseudomonas putida and β-galactosidase from Aspergillus oryzae, and four different enzymatic reactions showed the broad applicability of the approach but also its limitations. The activity of the immobilized biocatalysts was measured in batch experiments and compared to the kinetics of the respective free enzymes in solution. This comparison yields an effectiveness factor, which is a key figure to describe the extent the immobilized catalyst is effectively utilized. For the examined systems the effectiveness factor ranged between 6 and 14% and decreased with increasing absolute activity of the entrapped enzymes due to mass transfer limitations. To test the suitability of the hydrogel lattices for continuous operation, they were inserted into 3D-printed reactor housings and operated at constant flow. Stable product formation could be monitored over a period of 72 h for all four enzymatic systems, including two reactions with redox cofactor regeneration. Comparing calculated and experimental conversion in the continuous setup, higher values of the effectiveness factor in batch experiments also hint at good performance in continuous flow. This can be used to optimize complex biocatalytic reactions on a small scale.

Molecular mechanism of metabolic NAD(P)H-dependent electron-transfer systems: The role of redox cofactors

NAD(P)H-dependent electron-transfer (ET) systems require three functional components: a flavin-containing NAD(P)H-dehydrogenase, one-electron carrier and metal-containing redox center. In principle, these ET systems consist of one-, two- and three-components, and the electron flux from pyridine nucleotide cofactors, NADPH or NADH to final electron acceptor follows a linear pathway: NAD(P)H → flavin → one-electron carrier → metal containing redox center. In each step ET is primarily controlled by one- and two-electron midpoint reduction potentials of protein-bound redox cofactors in which the redox-linked conformational changes during the catalytic cycle are required for the domain-domain interactions. These interactions play an effective ET reactions in the multi-component ET systems. The microsomal and mitochondrial cytochrome P450 (cyt P450) ET systems, nitric oxide synthase (NOS) isozymes, cytochrome b₅ (cyt b₅) ET systems and methionine synthase (MS) ET system include a combination of multi-domain, and their organizations display similarities as well as differences in their components. However, these ET systems are sharing of a similar mechanism. More recent structural information obtained by X-ray and cryo-electron microscopy (cryo-EM) analysis provides more detail for the mechanisms associated with multi-domain ET systems. Therefore, this review summarizes the roles of redox cofactors in the metabolic ET systems on the basis of one-electron redox potentials. In final Section, evolutionary aspects of NAD(P)H-dependent multi-domain ET systems will be discussed.

Rapid Differentiation of Host and Parasitic Exosome Vesicles Using Microfluidic Photonic Crystal Biosensor

Parasite extracellular vesicles (EVs) are potential biomarkers that could be exploited for the diagnosis of infectious disease. This paper reports a rapid bioassay to discriminate parasite and host EVs. The EV detection assay utilizes a label-free photonic crystal (PC) biosensor to detect the EVs using a host-specific transmembrane protein (CD63), which is present on EV secreted by host cells (modeled by murine macrophage cell line J774A.1) but is not expressed on EV secreted by parasitic nematodes such as the gastrointestinal nematode Ascaris suum. The surface of PC is functionalized to recognize CD63, and is sensitive to the changes in refractive index caused by the immobilization of EVs. The biosensor demonstrates a detection limit of 2.18 × 10⁹ EVs/mL and a capability to characterize the affinity constants of antibody-host EV bindings. The discrimination of murine host EVs from parasite EVs indicates the capability of the sensor to differentiate EVs from different origins. The label-free, rapid EV assay could be used to detection parasite infection and facilitate the exosome-based clinic diagnosis and exosome research.

Structural conditions on complex networks for the Michaelis-Menten input-output response

The Michaelis-Menten (MM) fundamental formula describes how the rate of enzyme catalysis depends on substrate concentration. The familiar hyperbolic relationship was derived by timescale separation for a network of three reactions. The same formula has subsequently been found to describe steady-state input-output responses in many biological contexts, including single-molecule enzyme kinetics, gene regulation, transcription, translation, and force generation. Previous attempts to explain its ubiquity have been limited to networks with regular structure or simplifying parametric assumptions. Here, we exploit the graph-based linear framework for timescale separation to derive general structural conditions under which the MM formula arises. The conditions require a partition of the graph into two parts, akin to a "coarse graining" into the original MM graph, and constraints on where and how the input variable occurs. Other features of the graph, including the numerical values of parameters, can remain arbitrary, thereby explaining the formula's ubiquity. For systems at thermodynamic equilibrium, we derive a necessary and sufficient condition. For systems away from thermodynamic equilibrium, especially those with irreversible reactions, distinct structural conditions arise and a general characterization remains open. Nevertheless, our results accommodate, in much greater generality, all examples known to us in the literature.

Quantitative modeling of microalgae based sequestration of atmospheric CO2

A novel modeling method is presented to quantify the sequestration of atmospheric CO₂ by marine microalgae.

Modeling the transformation of atmospheric CO2 into microalgal biomass

Marine phytoplankton acts as a considerable sink of atmospheric CO₂ as it sequesters large quantities of this greenhouse gas for biomass production. To assess microalgae's counterbalancing of global warming, the quantities of CO₂ they fix need to be determined. For this task, it is mandatory to understand which environmental and physiological parameters govern this transformation from atmospheric CO₂ to microalgal biomass. However, experimental analyses are challenging as it has been found that the chemical environment has a major impact on the physiological properties of the microalgae cells (diameter typ. 5-20 μm). Moreover, the cells can only chemically interact with their immediate vicinity and thus compound sequestration needs to be studied on a microscopic spatial scale. Due to these reasons, computer simulations are a more promising approach than the experimental studies. Modeling software has been developed that describes the dissolution of atmospheric CO₂ into oceans followed by the formation of HCO₃^- which is then transported to individual microalgae cells. The second portion of this model describes the competition of different cell species for this HCO₃^-, a nutrient, as well as its uptake and utilization for cell production. Two microalgae species, i.e. Dunaliella salina and Nannochloropsis oculata, were cultured individually and in a competition situation under different atmospheric CO₂ conditions. It is shown that this novel model's predictions of biomass production are in very good agreement with the experimental flow cytometry results. After model validation, it has been applied to long-term prediction of phytoplankton generation. These investigations were motivated by the question whether or not cell production slows down as cultures grow. This is of relevance as a reduced cell production rate means that the increase in a culture's CO₂-sinking capacity slows down as well. One implication resulting from this is that an increase in anthropogenic CO₂ may not be counterbalanced by an increase in phytoplankton production. Modeling studies have found that for several different atmospheric CO₂ levels provided to single-species cultures as well as to species in competing scenarios the cell production rate does slow down over time.

Quantifying enzyme activity in living cells

For over a century, enzymatic activity has been studied in vitro, assuming similar activity in the crowded cellular milieu. Here, we determined in real time the catalytic activity of TEM1-β-lactamase inside living cells and compared the values to those obtained in vitro We found the apparent in vivo catalytic efficiency, k_cat/K_m , to be lower than in vitro, with significant cell-to-cell variability. Surprisingly, the results show that inside the cell the apparent catalytic efficiency decreases, and K_m increases with increasing enzyme concentration. To rationalize these findings, we measured enzyme and substrate diffusion rates in the cell and found the latter to be slower than expected. Simulations showed that for attenuated diffusion the substrate flux becomes rate-limiting, explaining why reaction rates in vivo can be independent on enzyme concentrations. The octanol/water partition of the substrate is 4.5, which is in the range of Food and Drug Administration-approved drugs. This suggests substrate-limited reaction rates to be common. These findings indicate that in vitro data cannot be simply extrapolated to the crowded in vivo environment.

SiGNet: A signaling network data simulator to enable signaling network inference

Network models are widely used to describe complex signaling systems. Cellular wiring varies in different cellular contexts and numerous inference techniques have been developed to infer the structure of a network from experimental data of the network's behavior. To objectively identify which inference strategy is best suited to a specific network, a gold standard network and dataset are required. However, suitable datasets for benchmarking are difficult to find. Numerous tools exist that can simulate data for transcriptional networks, but these are of limited use for the study of signaling networks. Here, we describe SiGNet (Signal Generator for Networks): a Cytoscape app that simulates experimental data for a signaling network of known structure. SiGNet has been developed and tested against published experimental data, incorporating information on network architecture, and the directionality and strength of interactions to create biological data in silico. SiGNet is the first tool to simulate biological signaling data, enabling an accurate and systematic assessment of inference strategies. SiGNet can also be used to produce preliminary models of key biological pathways following perturbation.

Serial deletion reveals structural basis and stability for the core enzyme activity of human glutaminase 1 isoforms: relevance to excitotoxic neurodegeneration

Background

Glutaminase 1 is a phosphate-activated metabolic enzyme that catalyzes the first step of glutaminolysis, which converts glutamine into glutamate. Glutamate is the major neurotransmitter of excitatory synapses, executing important physiological functions in the central nervous system. There are two isoforms of glutaminase 1, KGA and GAC, both of which are generated through alternative splicing from the same gene. KGA and GAC both transcribe 1–14 exons in the N-terminal, but each has its unique C-terminal in the coding sequence. We have previously identified that KGA and GAC are differentially regulated during inflammatory stimulation and HIV infection. Furthermore, glutaminase 1 has been linked to brain diseases such as amyotrophic lateral sclerosis, Alzheimer’s disease, and hepatic encephalopathy. Core enzyme structure of KGA and GAC has been published recently. However, how other coding sequences affect their functional enzyme activity remains unclear.

Methods

We cloned and performed serial deletions of human full-length KGA and GAC from the N-terminal and the C-terminal at an interval of approximately 100 amino acids (AAs). Prokaryotic expressions of the mutant glutaminase 1 protein and a glutaminase enzyme activity assay were used to determine if KGA and GAC have similar efficiency and efficacy to convert glutamine into glutamate.

Results

When 110 AAs or 218 AAs were deleted from the N-terminal or when the unique portions of KGA and GAC that are beyond the 550 AA were deleted from the C-terminal, KGA and GAC retained enzyme activity comparable to the full length proteins. In contrast, deletion of 310 AAs or more from N-terminal or deletion of 450 AAs or more from C-terminal resulted in complete loss of enzyme activity for KGA/GAC. Consistently, when both N- and C-terminal of the KGA and GAC were removed, creating a truncated protein that expressed the central 219 AA - 550 AA, the protein retained enzyme activity. Furthermore, expression of the core 219 AA - 550 AA coding sequence in cells increased extracellular glutamate concentrations to levels comparable to those of full-length KGA and GAC expressions, suggesting that the core enzyme activity of the protein lies within the central 219 AA - 550 AA. Full-length KGA and GAC retained enzyme activities when kept at 4 °C. In contrast, 219 AA - 550 AA truncated protein lost glutaminase activities more readily compared with full-length KGA and GAC, suggesting that the N-terminal and C-terminal coding regions are required for the stability KGA and GAC.

Conclusions

Glutaminase isoforms KGA and GAC have similar efficacy to catalyze the conversion of glutamine to glutamate. The core enzyme activity of glutaminase 1 protein is within the central 219 AA - 550 AA. The N-terminal and C-terminal coding regions of KGA and GAC help maintain the long-term activities of the enzymes.

Mitoenergetic Dysfunction Triggers a Rapid Compensatory Increase in Steady-State Glucose Flux

ATP can be produced in the cytosol by glycolytic conversion of glucose (GLC) into pyruvate. The latter can be metabolized into lactate, which is released by the cell, or taken up by mitochondria to fuel ATP production by the tricarboxylic acid cycle and oxidative phosphorylation (OXPHOS) system. Altering the balance between glycolytic and mitochondrial ATP generation is crucial for cell survival during mitoenergetic dysfunction, which is observed in a large variety of human disorders including cancer. To gain insight into the kinetic properties of this adaptive mechanism we determined here how acute (30 min) inhibition of OXPHOS affected cytosolic GLC homeostasis. GLC dynamics were analyzed in single living C2C12 myoblasts expressing the fluorescent biosensor FLII(12)Pglu-700μδ6 (FLII). Following in situ FLII calibration, the kinetic properties of GLC uptake (V1) and GLC consumption (V2) were determined independently and used to construct a minimal mathematical model of cytosolic GLC dynamics. After validating the model, it was applied to quantitatively predict V1 and V2 at steady-state (i.e., when V1 = V2 = Vsteady-state) in the absence and presence of OXPHOS inhibitors. Integrating model predictions with experimental data on lactate production, cell volume, and O2 consumption revealed that glycolysis and mitochondria equally contribute to cellular ATP production in control myoblasts. Inhibition of OXPHOS induced a twofold increase in Vsteady-state and glycolytic ATP production flux. Both in the absence and presence of OXPHOS inhibitors, GLC was consumed at near maximal rates, meaning that GLC consumption is rate-limiting under steady-state conditions. Taken together, we demonstrate here that OXPHOS inhibition increases steady-state GLC uptake and consumption in C2C12 myoblasts. This activation fully compensates for the reduction in mitochondrial ATP production, thereby maintaining the balance between cellular ATP supply and demand.

Computational modeling analysis of mitochondrial superoxide production under varying substrate conditions and upon inhibition of different segments of the electron transport chain

A computational mechanistic model of superoxide (O2•-) formation in the mitochondrial electron transport chain (ETC) was developed to facilitate the quantitative analysis of factors controlling mitochondrial O2•- production and assist in the interpretation of experimental studies. The model takes into account all individual electron transfer reactions in Complexes I and III. The model accounts for multiple, often seemingly contradictory observations on the effects of ΔΨ and ΔpH, and for the effects of multiple substrate and inhibitor conditions, including differential effects of Complex III inhibitors antimycin A, myxothiazol and stigmatellin. Simulation results confirm that, in addition to O2•- formation in Complex III and at the flavin site of Complex I, the quinone binding site of Complex I is an additional superoxide generating site that accounts for experimental observations on O2•- production during reverse electron transfer. However, our simulation results predict that, when cytochrome c oxidase is inhibited during oxidation of succinate, ROS production at this site is eliminated and almost all superoxide in Complex I is generated by reduced FMN, even when the redox pressure for reverse electron transfer from succinate is strong. In addition, the model indicates that conflicting literature data on the kinetics of electron transfer in Complex III involving the iron-sulfur protein-cytochrome bL complex can be resolved in favor of a dissociation of the protein only after electron transfer to cytochrome bH. The model predictions can be helpful in understanding factors driving mitochondrial superoxide formation in intact cells and tissues.

Model-assisted analysis of sugar metabolism throughout tomato fruit development reveals enzyme and carrier properties in relation to vacuole expansion

A kinetic model combining enzyme activity measurements and subcellular compartmentation was parameterized to fit the sucrose, hexose, and glucose-6-P contents of pericarp throughout tomato (Solanum lycopersicum) fruit development. The model was further validated using independent data obtained from domesticated and wild tomato species and on transgenic lines. A hierarchical clustering analysis of the calculated fluxes and enzyme capacities together revealed stage-dependent features. Cell division was characterized by a high sucrolytic activity of the vacuole, whereas sucrose cleavage during expansion was sustained by both sucrose synthase and neutral invertase, associated with minimal futile cycling. Most importantly, a tight correlation between flux rate and enzyme capacity was found for fructokinase and PPi-dependent phosphofructokinase during cell division and for sucrose synthase, UDP-glucopyrophosphorylase, and phosphoglucomutase during expansion, thus suggesting an adaptation of enzyme abundance to metabolic needs. In contrast, for most enzymes, flux rates varied irrespectively of enzyme capacities, and most enzymes functioned at <5% of their maximal catalytic capacity. One of the major findings with the model was the high accumulation of soluble sugars within the vacuole together with organic acids, thus enabling the osmotic-driven vacuole expansion that was found during cell division.

Modeling the respiratory chain complexes with biothermokinetic equations - the case of complex I

The mitochondrial respiratory chain plays a crucial role in energy metabolism and its dysfunction is implicated in a wide range of human diseases. In order to understand the global expression of local mutations in the rate of oxygen consumption or in the production of adenosine triphosphate (ATP) it is useful to have a mathematical model in which the changes in a given respiratory complex are properly modeled. Our aim in this paper is to provide thermodynamics respecting and structurally simple equations to represent the kinetics of each isolated complexes which can, assembled in a dynamical system, also simulate the behavior of the respiratory chain, as a whole, under a large set of different physiological and pathological conditions. On the example of the reduced nicotinamide adenine dinucleotide (NADH)-ubiquinol-oxidoreductase (complex I) we analyze the suitability of different types of rate equations. Based on our kinetic experiments we show that very simple rate laws, as those often used in many respiratory chain models, fail to describe the kinetic behavior when applied to a wide concentration range. This led us to adapt rate equations containing the essential parameters of enzyme kinetic, maximal velocities and Henri-Michaelis-Menten like-constants (KM and KI) to satisfactorily simulate these data.