Validity of the Michaelis-Menten equation--steady-state or reactant stationary assumption: that is the question

The reprotoxic adverse side effects of neurogenic and neuroprotective drugs: current use of human organoid modeling as a potential alternative to preclinical models

The management of neurological disorders heavily relies on neurotherapeutic drugs, but notable concerns exist regarding their possible negative effects on reproductive health. Traditional preclinical models often fail to accurately predict reprotoxicity, highlighting the need for more physiologically relevant systems. Organoid models represent a promising approach for concurrently studying neurotoxicity and reprotoxicity, providing insights into the complex interplay between neurotherapeutic drugs and reproductive systems. Herein, we have examined the molecular mechanisms underlying neurotherapeutic drug-induced reprotoxicity and discussed experimental findings from case studies. Additionally, we explore the utility of organoid models in elucidating the reproductive complications of neurodrug exposure. Have discussed the principles of organoid models, highlighting their ability to recapitulate neurodevelopmental processes and simulate drug-induced toxicity in a controlled environment. Challenges and future perspectives in the field have been addressed with a focus on advancing organoid technologies to improve reprotoxicity assessment and enhance drug safety screening. This review underscores the importance of organoid models in unraveling the complex relationship between neurotherapeutic drugs and reproductive health.

Discovery and application of food catalysts to promote the coupling of PQQ (quinone) with amines

Background

Biocatalysts (enzymes) play a crucial role in catalyzing specific reactions across various industries, often offering environmentally friendly and sustainable alternatives to chemical catalysts. However, their catalytic activities are susceptible to denaturation. In this study, we present the discovery of novel protein-based biocatalysts derived from processed foods, including skimmed milk, soy milk, cheese, and dried tofu. These food catalysts exhibit high availability, low cost, safety, and thermo-stability.

Results

Focusing on the physiologically intriguing coenzyme pyrroloquinoline quinone (PQQ), we observed that the reaction with glycine to form imidazolopyrroquinoline (IPQ) did not proceed efficiently when PQQ was present at very low concentrations. Surprisingly, in the presence of protein-based foods, this reaction was significantly accelerated. Notably, skimmed milk enhanced the PQQ detection limit (600 times lower) during high-performance liquid chromatography (HPLC) following IPQ derivatization. Milk appears to facilitate the reaction between PQQ and various amino acids, primary amines, and secondary amines. Further investigations revealed that food catalysis operates through a non-enzymatic mechanism. Additionally, nuclear magnetic resonance spectroscopy demonstrated that milk components interacted with amino substrates due to the ability of amines to react with quinones on colloidal surfaces.

Conclusion

These practical food catalysts not only contribute to environmental safety but also hold significance across diverse scientific domains. Non-enzymatic protein catalysts find applications in biocatalysis, organic synthesis, food technology, analytical chemistry, and fundamental nutritional and evolutionary studies.

Modeling cancer progression: an integrated workflow extending data-driven kinetic models to bio-mechanical PDE models

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

HetMM: A Michaelis-Menten model for non-homogeneous enzyme mixtures

The Michaelis-Menten model requires its reaction velocities to come from a preparation of homogeneous enzymes, with identical or near-identical catalytic activities. However, this condition is not always met. We introduce a kinetic model that relaxes this requirement, by assuming there are an unknown number of enzyme species drawn from a probability distribution whose standard deviation is estimated. Through simulation studies, we demonstrate the method accurately discriminates between homogeneous and heterogeneous data, even with moderate levels of experimental error. We applied this model to three homogeneous and three heterogeneous biological systems, showing that the standard and heterogeneous models outperform respectively. Lastly, we show that heterogeneity is not readily distinguished from negatively cooperative binding under the Hill model. These two distinct attributes-inequality in catalytic ability and interference between binding sites-yield similar Michaelis-Menten curves that are not readily resolved without further experimentation. Our user-friendly software package allows homogeneity testing and parameter estimation.

Enhancing ROS-Inducing Nanozyme through Intraparticle Electron Transport

Iron oxide nanoparticles (IONPs) have garnered significant attention as a promising platform for reactive oxygen species (ROS)-dependent disease treatment, owing to their remarkable biocompatibility and Fenton catalytic activity. However, the low catalytic activity of IONPs is a major hurdle in their clinical translation. To overcome this challenge, IONPs of different compositions are examined for their Fenton reaction under pharmacologically relevant conditions. The results show that wüstite (FeO) nanoparticles exhibit higher catalytic activity than magnetite (Fe3 O4 ) or maghemite (γ-Fe2 O3 ) of matched size and coating, despite having a similar surface oxidation state. Further analyses suggest that the high catalytic activity of wüstite nanoparticles can be attributed to the presence of internal low-valence iron (Fe0 and Fe2+ ), which accelerates the recycling of surface Fe3+ to Fe2+ through intraparticle electron transport. Additionally, ultrasmall wüstite nanoparticles are generated by tuning the thermodecomposition-based nanocrystal synthesis, resulting in a Fenton reaction rate 5.3 times higher than that of ferumoxytol, an FDA-approved IONP. Compared with ferumoxytol, wüstite nanoparticles substantially increase the level of intracellular ROS in mouse mammary carcinoma cells. This study presents a novel mechanism and pivotal improvement for the development of highly efficient ROS-inducing nanozymes, thereby expanding the horizons for their therapeutic applications.

Gold single atom-based aptananozyme as an ultrasensitive and selective colorimetric probe for detection of thrombin and C-reactive protein

An ultra-efficient biocatalytic peroxidase-like Au-based single-atom nanozyme (Au-SAzymes) has been synthesized from isolated Au atoms on black nitrogen doped carbon (Au-N-C) using a simple complexation-adsorption-pyrolysis method. The atomic structure of AuN4 centers in black carbon was revealed by combined high-resolution transmission electron microscopy/high-angle annular dark-field scanning transmission electron microscopy. The Au-SAzymes showed a remarkable peroxidase activity with 1.7 nM as Michaelis-Menten constant, higher than most previously reported SAzyme activity. Density functional theory and Monte Carlo calculations revealed the adsorption of H2O2 on AuN4 with formation of OH* and O*. Molecular recognition was greatly enhanced via label-free integration of thiol-terminal aptamers on the surface of single Au atoms (Aptamer/Au-SAzyme) to design off-on ultrasensitive aptananozyme-based sensor for detecting thrombin and CRP with 550 pM and 500 pg mL-1 limits of detection, respectively. The Aptamer/Au-SAzyme showed satisfactory accuracy and precision when applied to the serum and plasma of COVID-19 patients. Due to the maximum Au atom utilization, approximately 3636 samples can be run per 1 mg of gold, highlighting the commercialization potential of the developed Aptamer/Au-SAzyme approach.

High-Performance Production of N-Acetyl-d-Neuraminic Acid with Whole Cells of Fast-Growing Vibrio natriegens via a Thermal Strategy

High performance is the core objective that biotechnologists pursue, of which low efficiency, low titer, and side products are the chief obstacles. Here, a thermal strategy is proposed for simultaneously addressing the obstacles of whole-cell catalysis that is widely applied in the food industry. The strategy, by combining fast-growing Vibrio natriegens, thermophilic enzymes, and high-temperature whole-cell catalysis, was successfully applied for the high-performance production of N-acetyl-d-neuraminic acid (Neu5Ac) that plays essential roles in the fields of food (infant formulas), healthcare, and medicine. By using this strategy, we realized the highest Neu5Ac titer and productivity of 126.1 g/L and up to 71.6 g/(L h), respectively, 7.2-fold higher than the productivity of Escherichia coli. The major byproduct acetic acid was also eliminated via quenching complex metabolic side reactions enabled by temperature elevation. This study offers a broadly applicable strategy for producing chemicals relevant to the food industry, providing insights for its future development.

Functional Roles of N-Terminal Domains in Pullulanase from Human Gut Lactobacillus acidophilus

Pullulanases are multidomain α-glucan debranching enzymes with one or more N-terminal domains (NTDs) including carbohydrate-binding modules (CBMs) and domains of unknown function (DUFs). To elucidate the roles of NTDs in Lactobacillus acidophilus NCFM pullulanase (LaPul), two truncated variants, Δ41-LaPul (lacking CBM41) and Δ(41+DUFs)-LaPul (lacking CBM41 and two DUFs), were produced recombinantly. LaPul recognized 1.3- and 2.2-fold more enzyme attack-sites on starch granules compared to Δ41-LaPul and Δ(41+DUFs)-LaPul, respectively, as measured by interfacial kinetics. Δ41-LaPul displayed markedly lower affinity for starch granules and β-cyclodextrin (10- and >21-fold, respectively) in comparison to LaPul, showing substrate binding mainly stems from CBM41. Δ(41+DUFs)-LaPul exhibited a 12 °C lower melting temperature than LaPul and Δ41-LaPul, indicating that the DUFs are critical for LaPul stability. Notably, Δ41-LaPul exhibited a 14-fold higher turnover number (kcat) and 9-fold higher Michaelis constant (KM) compared to LaPul, while Δ(41+DUFs)-LaPul's values were close to those of LaPul, possibly due to the exposure of aromatic by truncation.

Generalized Michaelis-Menten rate law with time-varying molecular concentrations

The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.

Acid-base Homeostasis and Implications to the Phenotypic Behaviors of Cancer

Acid-base homeostasis is a fundamental property of living cells, and its persistent disruption in human cells can lead to a wide range of diseases. In this study, we conducted a computational modeling analysis of transcriptomic data of 4750 human tissue samples of 9 cancer types in The Cancer Genome Atlas (TCGA) database. Built on our previous study, we quantitatively estimated the average production rate of OH- by cytosolic Fenton reactions, which continuously disrupt the intracellular pH (pHi) homeostasis. Our predictions indicate that all or at least a subset of 43 reprogrammed metabolisms (RMs) are induced to produce net protons (H+) at comparable rates of Fenton reactions to keep the pHi stable. We then discovered that a number of well-known phenotypes of cancers, including increased growth rate, metastasis rate, and local immune cell composition, can be naturally explained in terms of the Fenton reaction level and the induced RMs. This study strongly suggests the possibility to have a unified framework for studies of cancer-inducing stressors, adaptive metabolic reprogramming, and cancerous behaviors. In addition, strong evidence is provided to demonstrate that a popular view that Na+/H+ exchangers along with lactic acid exporters and carbonic anhydrases are responsible for the intracellular alkalization and extracellular acidification in cancer may not be justified.

Enzymatic kinetics of photosystem II with DCBQ as a substrate in extended Michaelis-Menten model

This study aimed to examine enzymatic kinetics of photosystem II (PSII) of maize mesophyll chloroplasts using the artificial electron acceptor 2,6-dichloro-1,4-benzoquinone (DCBQ) as a substrate. We extended Michealis-Menten kinetics model assuming that DCBQ can accept electrons from PSII in two ways: from a QB directly or from QA by docking in the QB site. We used a Clark oxygen electrode for measuring the PSII activity, depending on the concentration of DCBQ. We found that: [1] DCBQ acts as an electron acceptor or [2] as an inhibitor for PSII. At a concentration < 0.2 mM, DCBQ accepted electrons from the QB at a rate of 889 electrons/s, while at >> 0.2 mM it replaced QB following which the activity decreased to zero. DCBQ located in the QB also increased the affinity of the substrate to PSII. We determined the kinetic parameters for the chloroplasts of plants growing under high and low light intensity, to change thylakoid stacking and thus the rate of electron transport. The parameter KmB, which is a measure of the affinity of DCBQ to PSII, showed quantitative changes based on light intensity, while K was proportional to the size of the plastoquinone pool. We believe that our model can be applied as a tool to study "State transitions" and induced changes in grana stacking in plants exposed to various stresses, which will facilitate the regulation of electron transfer pathways through an appropriate balance between linear and cyclic electron transport.

The measurement of true initial rates is not always absolutely necessary to estimate enzyme kinetic parameters

In the chapters dealing with enzyme reactions, the authors of all Biochemistry textbooks and of even more specialized texts consider that the characteristic parameters (kcat and Km) must be determined under initial or steady-state rate conditions. This implies the transformation of a very limited proportion of substrate (at most 10-20%) or a continuous recording of the product or substrate concentration vs. time. Both options can present practical difficulties. Is it possible to get around these very stringent conditions? Here we show that in the most favourable cases up  to 70% of the substrate can be converted resulting in systematic errors on the parameters (that can easily be taken account of) if the simple Henri-Michaelis-Menten equation is utilised. Alternatively, the integrated form of the same equation directly yields excellent estimates of the same parameters. Our observations should greatly facilitate the task of researchers who study systems in which measurements of the reaction progress are painstaking or when substrate concentrations close to the detection limit must be used. The general conclusion is that it is not always absolutely necessary to determine initial or steady-state rates to obtain reliable estimations of the enzyme kinetic parameters..

Thermodynamic principle to enhance enzymatic activity using the substrate affinity

Understanding how to tune enzymatic activity is important not only for biotechnological applications, but also to elucidate the basic principles guiding the design and optimization of biological systems in nature. So far, the Michaelis-Menten equation has provided a fundamental framework of enzymatic activity. However, there is still no concrete guideline on how the parameters should be optimized towards higher activity. Here, we demonstrate that tuning the Michaelis-Menten constant ([Formula: see text]) to the substrate concentration ([Formula: see text]) enhances enzymatic activity. This guideline ([Formula: see text]) was obtained mathematically by assuming that thermodynamically favorable reactions have higher rate constants, and that the total driving force is fixed. Due to the generality of these thermodynamic considerations, we propose [Formula: see text] as a general concept to enhance enzymatic activity. Our bioinformatic analysis reveals that the [Formula: see text] and in vivo substrate concentrations are consistent across a dataset of approximately 1000 enzymes, suggesting that even natural selection follows the principle [Formula: see text].

Monitoring and modelling the glutamine metabolic pathway: a review and future perspectives

BACKGROUND

Analysis of the glutamine metabolic pathway has taken a special place in metabolomics research in recent years, given its important role in cell biosynthesis and bioenergetics across several disorders, especially in cancer cell survival. The science of metabolomics addresses the intricate intracellular metabolic network by exploring and understanding how cells function and respond to external or internal perturbations to identify potential therapeutic targets. However, despite recent advances in metabolomics, monitoring the kinetics of a metabolic pathway in a living cell in situ, real-time and holistically remains a significant challenge.

AIM

This review paper explores the range of analytical approaches for monitoring metabolic pathways, as well as physicochemical modeling techniques, with a focus on glutamine metabolism. We discuss the advantages and disadvantages of each method and explore the potential of label-free Raman microspectroscopy, in conjunction with kinetic modeling, to enable real-time and in situ monitoring of the cellular kinetics of the glutamine metabolic pathway.

KEY SCIENTIFIC CONCEPTS

Given its important role in cell metabolism, the ability to monitor and model the glutamine metabolic pathways are highlighted. Novel, label free approaches have the potential to revolutionise metabolic biosensing, laying the foundation for a new paradigm in metabolomics research and addressing the challenges in monitoring metabolic pathways in living cells.

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.

Flux estimation analysis systematically characterizes the metabolic shifts of the central metabolism pathway in human cancer

Introduction

Glucose and glutamine are major carbon and energy sources that promote the rapid proliferation of cancer cells. Metabolic shifts observed on cell lines or mouse models may not reflect the general metabolic shifts in real human cancer tissue.

Method

In this study, we conducted a computational characterization of the flux distribution and variations of the central energy metabolism and key branches in a pan-cancer analysis, including the glycolytic pathway, production of lactate, tricarboxylic acid (TCA) cycle, nucleic acid synthesis, glutaminolysis, glutamate, glutamine, and glutathione metabolism, and amino acid synthesis, in 11 cancer subtypes and nine matched adjacent normal tissue types using TCGA transcriptomics data.

Result

Our analysis confirms the increased influx in glucose uptake and glycolysis and decreased upper part of the TCA cycle, i.e., the Warburg effect, in almost all the analyzed cancer. However, increased lactate production and the second half of the TCA cycle were only seen in certain cancer types. More interestingly, we failed to detect significantly altered glutaminolysis in cancer tissues compared to their adjacent normal tissues. A systems biology model of metabolic shifts through cancer and tissue types is further developed and analyzed. We observed that (1) normal tissues have distinct metabolic phenotypes; (2) cancer types have drastically different metabolic shifts compared to their adjacent normal controls; and (3) the different shifts in tissue-specific metabolic phenotypes result in a converged metabolic phenotype through cancer types and cancer progression.

Discussion

This study strongly suggests the possibility of having a unified framework for studies of cancer-inducing stressors, adaptive metabolic reprogramming, and cancerous behaviors.

Natural Parameter Conditions for Singular Perturbations of Chemical and Biochemical Reaction Networks

We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the reduction, in a manner that is consistent, amenable to computation and permits an interpretation in chemical or biochemical terms. Our work is based on local timescale estimates via ratios of the real parts of eigenvalues of the Jacobian near critical manifolds. This approach modifies the one introduced by Segel and Slemrod and is familiar from computational singular perturbation theory. While parameters derived by this method cannot provide universal quantitative estimates for the accuracy of a reduction, they represent a critical first step toward this end. Working directly with eigenvalues is generally unfeasible, and at best cumbersome. Therefore we focus on the coefficients of the characteristic polynomial to derive parameters, and relate them to timescales. Thus, we obtain distinguished parameters for systems of arbitrary dimension, with particular emphasis on reduction to dimension one. As a first application, we discuss the Michaelis-Menten reaction mechanism system in various settings, with new and perhaps surprising results. We proceed to investigate more complex enzyme catalyzed reaction mechanisms (uncompetitive, competitive inhibition and cooperativity) of dimension three, with reductions to dimension one and two. The distinguished parameters we derive for these three-dimensional systems are new. In fact, no rigorous derivation of small parameters seems to exist in the literature so far. Numerical simulations are included to illustrate the efficacy of the parameters obtained, but also to show that certain limitations must be observed.

A critical review of microfluidic systems for CRISPR assays

Reviewed are nucleic acid detection assays that incorporate clustered regularly interspaced short palindromic repeats (CRISPR)-based diagnostics and microfluidic devices and techniques. The review serves as a reference for researchers who wish to use CRISPR-Cas systems for diagnostics in microfluidic devices. The review is organized in sections reflecting a basic five-step workflow common to most CRISPR-based assays. These steps are analyte extraction, pre-amplification, target recognition, transduction, and detection. The systems described include custom microfluidic chips and custom (benchtop) chip control devices for automated assays steps. Also included are partition formats for digital assays and lateral flow biosensors as a readout modality. CRISPR-based, microfluidics-driven assays offer highly specific detection and are compatible with parallel, combinatorial implementation. They are highly reconfigurable, and assays are compatible with isothermal and even room temperature operation. A major drawback of these assays is the fact that reports of kinetic rates of these enzymes have been highly inconsistent (many demonstrably erroneous), and the low kinetic rate activity of these enzymes limits achievable sensitivity without pre-amplification. Further, the current state-of-the-art of CRISPR assays is such that nearly all systems rely on off-chip assays steps, particularly off-chip sample preparation.

Biochemical reaction network topology defines dose-dependent Drug-Drug interactions

Drug combination therapy is a promising strategy to enhance the desired therapeutic effect, while reducing side effects. High-throughput pairwise drug combination screening is a commonly used method for discovering favorable drug interactions, but is time-consuming and costly. Here, we investigate the use of reaction network topology-guided design of combination therapy as a predictive in silico drug-drug interaction screening approach. We focused on three-node enzymatic networks, with general Michaelis-Menten kinetics. The results revealed that drug-drug interactions critically depend on the choice of target arrangement in a given topology, the nature of the drug, and the desired level of change in the network output. The results showed a negative correlation between antagonistic interactions and the dosage of drugs. Overall, the negative feedback loops showed the highest synergistic interactions (the lowest average combination index) and, intriguingly, required the highest drug doses compared to other topologies under the same condition.

M. SK, Baek KH. Assessing the Food Quality Using Carbon Nanomaterial Based Electrodes by Voltammetric Techniques

The world is facing a global financial loss and health effects due to food quality adulteration and contamination, which are seriously affecting human health. Synthetic colors, flavors, and preservatives are added to make food more attractive to consumers. Therefore, food safety has become one of the fundamental needs of mankind. Due to the importance of food safety, the world is in great need of developing desirable and accurate methods for determining the quality of food. In recent years, the electrochemical methods have become more popular, due to their simplicity, ease in handling, economics, and specificity in determining food safety. Common food contaminants, such as pesticides, additives, and animal drug residues, cause foods that are most vulnerable to contamination to undergo evaluation frequently. The present review article discusses the electrochemical detection of the above food contaminants using different carbon nanomaterials, such as carbon nanotubes (CNTs), graphene, ordered mesoporous carbon (OMC), carbon dots, boron doped diamond (BDD), and fullerenes. The voltammetric methods, such as cyclic voltammetry (CV) and differential pulse voltammetry (DPV), have been proven to be potential methods for determining food contaminants. The use of carbon-based electrodes has the added advantage of electrochemically sensing the food contaminants due to their excellent sensitivity, specificity, large surface area, high porosity, antifouling, and biocompatibility.

In silico modeling of endocrine organ-on-a-chip systems

The organ-on-a-chip (OoC) is an artificially reconstructed microphysiological system that is implemented using tissue mimics integrated into miniaturized perfusion devices. OoCs emulate dynamic and physiologically relevant features of the body, which are not available in standard in vitro methods. Furthermore, OoCs provide highly sophisticated multi-organ connectivity and biomechanical cues based on microfluidic platforms. Consequently, they are often considered ideal in vitro systems for mimicking self-regulating biophysical and biochemical networks in vivo where multiple tissues and organs crosstalk through the blood flow, similar to the human endocrine system. Therefore, OoCs have been extensively applied to simulate complex hormone dynamics and endocrine signaling pathways in a mechanistic and fully controlled manner. Mathematical and computational modeling approaches are critical for quantitatively analyzing an OoC and predicting its complex responses. In this review article, recently developed in silico modeling concepts of endocrine OoC systems are summarized, including the mathematical models of tissue-level transport phenomena, microscale fluid dynamics, distant hormone signaling, and heterogeneous cell-cell communication. From this background, whole chip-level analytic approaches in pharmacokinetics and pharmacodynamics will be described with a focus on the spatial and temporal behaviors of absorption, distribution, metabolism, and excretion in endocrine biochips. Finally, quantitative design frameworks for endocrine OoCs are reviewed with respect to support parameter calibration/scaling and enable predictive in vitro-in vivo extrapolations. In particular, we highlight the analytical and numerical modeling strategies of the nonlinear phenomena in endocrine systems on-chip, which are of particular importance in drug screening and environmental health applications.

How to Define a Nanozyme

Over the past 15 years, many articles have considered "nanozymes" as ferromagnetic nanoparticles having an "intrinsic peroxidase-like activity" in the presence of hydrogen peroxide. However, the definition and the catalytic activity of these nanozymes have been questioned. The present Perspective reports the main criteria that are essential to classify a nanoparticle as a nanozyme. It is important to consider that not all nanoparticles able to generate hydroxyl radicals in the presence of hydrogen peroxide without catalytic activity can be registered as nanozymes.

Neomycin removal using the white rot fungus Trametes versicolor

The presence of antibiotic resistance genes in wastewater treatment plants (WWTPs), and in river and lake recipients show the need to develop new antibiotic removal strategies. The aminoglycoside antibiotic class is of special concern since the chemical structure of these compounds limits the choices of removal technologies. The experimental design included fungal mediated in vivo and in vitro experiments. The experiments were performed in Erlenmeyer flasks under non-sterile conditions. In the study, the role of the laccase redox mediator 4-hydroxy benzoic acid (HBA) in the removal of neomycin was investigated. The specific objective of the study was to conclude whether it is possible to use the white rot fungus (WRF) Trametes versicolor to biodegrade neomycin. It was shown that it is feasible to remove 34% neomycin in vitro (excluding living fungal cells) by laccase-HBA mediated extracellular biodegradation. In the in vivo experiments, polyurethane foam (PUF) was used as supporting material to immobilize fungal mycelia on. The presence of living fungal cells facilitated a removal of approximately 80% neomycin in the absence of HBA. Using liquid chromatography-high resolution-mass spectrometry, it was possible to tentatively identify oxidation products of neomycin hydrolysates. The results in this study open up the possibility to implement a pretreatment plant (PTP) aimed for neomycin removal.

Nonlinear Analytics for Electrochemical Biosensor Design Using Enzyme Aggregates and Delayed Mass Action

The paper is devoted to the extension of Brown’s model of enzyme kinetics to the case with distributed delays. Firstly, we construct a multi-substrate multi-inhibitor model using discrete and distributed delays. Furthermore, we consider simplified models including one substrate and one inhibitor, for which an experimental study has been performed. The algorithm of parameter identifications was developed which was tested on the experimental data of solution conductivity. Both the model and Kohlrausch’s law parameters are obtained as a result of the optimization procedure. Comparison of plots constructed with the help of the estimated parameters has shown that in such case the model with distributed delays is more chemically adequate in comparison with the discrete one. The methods of generalization of the results to the multi-substrate multi-inhibitor cases are discussed.

Inconsistent treatments of the kinetics of Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) impair assessment of its diagnostic potential

The scientific and technological advent of Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) is one of the most exciting developments of the past decade, particularly in the field of gene editing. The technology has two essential components, (1) a guide RNA to match a targeted gene and (2) a CRISPR-associated protein (e.g. Cas 9, Cas12 or Cas13) that acts as an endonuclease to specifically cut DNA. This specificity and reconfigurable nature of CRISPR has also spurred intense academic and commercial interest in the development of CRISPR-based molecular diagnostics. CRISPR Cas12 and Cas13 orthologs are most commonly applied to diagnostics, and these cleave and become activated by DNA and RNA targets, respectively. Despite the intense research interest, the limits of detection (LoDs) and applications of CRISP-based diagnostics remain an open question. A major reason for this is that reports of kinetic rates have been widely inconsistent, and the vast majority of these reports contain gross errors including violations of basic conservation and kinetic rate laws. It is the intent of this Perspective to bring attention to these issues and to identify potential improvements in the manner in which CRISPR kinetic rates and assay LoDs are reported and compared. The CRISPR field would benefit from verifications of self-consistency of data, providing sufficient data for reproduction of experiments, and, in the case of reports of novel assay LoDs, concurrent reporting of the associated kinetic rate constants. The early development of CRISPR-based diagnostics calls for self-reflection and urges us to proceed with caution.

ThermoSlope: A Software for Determining Thermodynamic Parameters from Single Steady-State Experiments

The determination of the temperature dependence of enzyme catalysis has traditionally been a labourious undertaking. We have developed a new approach to the classical Arrhenius parameter estimation by fitting the change in velocity under a gradual change in temperature. The evaluation with a simulated dataset shows that the approach is valid. The approach is demonstrated as a useful tool by characterizing the Bacillus pumilus LipA enzyme. Our results for the lipase show that the enzyme is psychrotolerant, with an activation energy of 15.3 kcal/mol for the chromogenic substrate para-nitrophenyl butyrate. Our results demonstrate that this can produce equivalent curves to the traditional approach while requiring significantly less sample, labour and time. Our method is further validated by characterizing three α-amylases from different species and habitats. The experiments with the α-amylases show that the approach works over a wide range of temperatures and clearly differentiates between psychrophilic, mesophilic and thermophilic enzymes. The methodology is released as an open-source implementation in Python, available online or used locally. This method of determining the activation parameters can make studies of the temperature dependence of enzyme catalysis more widely adapted to understand how enzymes have evolved to function in extreme environments. Moreover, the thermodynamic parameters that are estimated serve as functional validations of the empirical valence bond calculations of enzyme catalysis.

Light as a substrate: migration of LHCII antennas in extended Michaelis-Menten model for PSI kinetics

We extended, for the first time, the Michaelis-Menten (M-M) model to describe the kinetics of photosystem I (PSI) complexes using light as a substrate. Our work is novel as it can be useful for studying the phenomenon of "state transitions" because it quantifies the affinity of light to PSI reaction centers depending on the associated light harvesting complex II (LHCII) antennas. We verified our models by measuring the PSI activity as a function of light intensity using an oxygen electrode for chloroplast from plants grown in low light conditions and treated with far red light. We determined the kinetics constant K_M for: PSI-LHCI, PSI-LHCI-LHCII and PSI-PSII megacomplexes and have shown that K_M for PSI located in the megacomplexes was smaller in magnitude than PSI-LHCI, thus demonstrating that LHCII antennas are functionally associated with PSI. The parameter [S]_1/2used in our models is the equivalent of M-M constant. Far red light increases [S]_1/2, which indicates that transition from state 1 to state 2 leads to an energy gain while reaching the PSI reaction centers. We also observed that redistribution of the absorbed excitation energy is realized not only by LHCII migration but also by association of the photosystems in the megacomplexes.

A graph neural network model to estimate cell-wise metabolic flux using single-cell RNA-seq data

The metabolic heterogeneity and metabolic interplay between cells are known as significant contributors to disease treatment resistance. However, with the lack of a mature high-throughput single-cell metabolomics technology, we are yet to establish systematic understanding of the intra-tissue metabolic heterogeneity and cooperative mechanisms. To mitigate this knowledge gap, we developed a novel computational method, namely, single-cell flux estimation analysis (scFEA), to infer the cell-wise fluxome from single-cell RNA-sequencing (scRNA-seq) data. scFEA is empowered by a systematically reconstructed human metabolic map as a factor graph, a novel probabilistic model to leverage the flux balance constraints on scRNA-seq data, and a novel graph neural network-based optimization solver. The intricate information cascade from transcriptome to metabolome was captured using multilayer neural networks to capitulate the nonlinear dependency between enzymatic gene expressions and reaction rates. We experimentally validated scFEA by generating an scRNA-seq data set with matched metabolomics data on cells of perturbed oxygen and genetic conditions. Application of scFEA on this data set showed the consistency between predicted flux and the observed variation of metabolite abundance in the matched metabolomics data. We also applied scFEA on five publicly available scRNA-seq and spatial transcriptomics data sets and identified context- and cell group-specific metabolic variations. The cell-wise fluxome predicted by scFEA empowers a series of downstream analyses including identification of metabolic modules or cell groups that share common metabolic variations, sensitivity evaluation of enzymes with regards to their impact on the whole metabolic flux, and inference of cell-tissue and cell-cell metabolic communications.

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.

On Catalytic Kinetics of Enzymes

Classical enzyme kinetic theories are summarized and linked with modern discoveries here. The sequential catalytic events along time axis by enzyme are analyzed at the molecular level, and by using master equations, this writing tries to connect the microscopic molecular behavior of enzyme to kinetic data (like velocity and catalytic coefficient k) obtained in experiment: 1/k = t equals to the sum of the times taken by the constituent individual steps. The relationships between catalytic coefficient k, catalytic rate or velocity, the amount of time taken by each step and physical or biochemical conditions of the system are discussed, and the perspective and hypothetic equations proposed here regarding diffusion, conformational change, chemical conversion, product release steps and the whole catalytic cycle provide an interpretation of previous experimental observations and can be testified by future experiments.

Explicit Treatment of Non-Michaelis-Menten and Atypical Kinetics in Early Drug Discovery*

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more-complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

A steady-state approach for inhibition of heterogeneous enzyme reactions

The kinetic theory of enzymes that modify insoluble substrates is still underdeveloped, despite the prevalence of this type of reaction both in vivo and industrial applications. Here, we present a steady-state kinetic approach to investigate inhibition occurring at the solid-liquid interface. We propose to conduct experiments under enzyme excess (E0 ≫ S0), i.e. the opposite limit compared with the conventional Michaelis-Menten framework. This inverse condition is practical for insoluble substrates and elucidates how the inhibitor reduces enzyme activity through binding to the substrate. We claim that this type of inhibition is common for interfacial enzyme reactions because substrate accessibility is low, and we show that it can be analyzed by experiments and rate equations that are analogous to the conventional approach, except that the roles of enzyme and substrate have been swapped. To illustrate the approach, we investigated the major cellulases from Trichoderma reesei (Cel6A and Cel7A) acting on insoluble cellulose. As model inhibitors, we used catalytically inactive variants of Cel6A and Cel7A. We made so-called inverse Michaelis-Menten curves at different concentrations of inhibitors and found that a new rate equation accounted well for the data. In most cases, we found a mixed type of surface-site inhibition mechanism, and this probably reflected that the inhibitor both competed with the enzyme for the productive binding-sites (competitive inhibition) and hampered the processive movement on the surface (uncompetitive inhibition). These results give new insights into the complex interplay of Cel7A and Cel6A on cellulose and the approach may be applicable to other heterogeneous enzyme reactions.

Optimizing enzymatic catalysts for rapid turnover of substrates with low enzyme sequestration

Enzymes are central to both metabolism and information processing in cells. In both cases, an enzyme's ability to accelerate a reaction without being consumed in the reaction is crucial. Nevertheless, enzymes are transiently sequestered when they bind to their substrates; this sequestration limits activity and potentially compromises information processing and signal transduction. In this article, we analyse the mechanism of enzyme-substrate catalysis from the perspective of minimizing the load on the enzymes through sequestration, while maintaining at least a minimum reaction flux. In particular, we ask: which binding free energies of the enzyme-substrate and enzyme-product reaction intermediates minimize the fraction of enzymes sequestered in complexes, while sustaining a certain minimal flux? Under reasonable biophysical assumptions, we find that the optimal design will saturate the bound on the minimal flux and reflects a basic trade-off in catalytic operation. If both binding free energies are too high, there is low sequestration, but the effective progress of the reaction is hampered. If both binding free energies are too low, there is high sequestration, and the reaction flux may also be suppressed in extreme cases. The optimal binding free energies are therefore neither too high nor too low, but in fact moderate. Moreover, the optimal difference in substrate and product binding free energies, which contributes to the thermodynamic driving force of the reaction, is in general strongly constrained by the intrinsic free-energy difference between products and reactants. Both the strategies of using a negative binding free-energy difference to drive the catalyst-bound reaction forward and of using a positive binding free-energy difference to enhance detachment of the product are limited in their efficacy.

Relationship between enzyme concentration and Michaelis constant in enzyme assays

The upper bound of enzyme concentration for accurately estimating the parameters in Michaelis-Menten (MM) equation is not completely determined and still under discussion, even though many researchers have investigated the equation's validity for a long time. In the paper, we broadly investigated the correlation between the system of ordinary differential equations for monosubstrate irreversible enzyme reaction (HMM-system) and its derivative MM equation focusing on the relationship between initial enzyme concentration [E]₀ and Michaelis constant K_m by numerical simulation. According to the results, the initial reaction velocity v₀ is still a function of initial substrate concentration [S]₀ at [E]₀<K_m. The function is identical to the MM equation at [E]₀≦0.01K_m, while it is described as a new type of equation at 0.01K_m≦[E]₀<K_m. This function is of great significance in enzyme assays as a comprehensive approximation for the HMM-system.

Beyond the Michaelis-Menten: Accurate Prediction of In Vivo Hepatic Clearance for Drugs With Low KM

Clearance (CL) is the major pharmacokinetic parameter for evaluating systemic exposure of drugs in the body and, thus, for developing new drugs. To predict in vivo CL, the ratio between the maximal rate of metabolism and Michaelis‐Menten constant (V_max/K_M estimated from in vitro metabolism study has been widely used. This canonical approach is based on the Michaelis‐Menten equation, which is valid only when the K_M value of a drug is much higher than the hepatic concentration of the enzymes, especially cytochrome P450, involved in its metabolism. Here, we find that such a condition does not hold for many drugs with low K_M, and, thus, the canonical approach leads to considerable error. Importantly, we propose an alternative approach, which incorporates the saturation of drug metabolism when concentration of the enzymes is not sufficiently lower than K_M. This new approach dramatically improves the accuracy of prediction for in vivo CL of high‐affinity drugs with low K_M. This indicates that the proposed approach in this study, rather than the canonical approach, should be used to predict in vivo hepatic CL for high‐affinity drugs, such as midazolam and propafenone.

Metformin and Berberine suppress glycogenolysis by inhibiting glycogen phosphorylase and stabilizing the molecular structure of glycogen in db/db mice

Glycogen is a branched glucose polymer involved in sustaining blood glucose homeostasis. Liver glycogen comprises α particles (up to 300 nm in diameter) made of joined β particles (∼20 nm in diameter). Glycogen α particles in a mouse model for diabetes are molecularly fragile, breaking down into smaller β particles more readily than in healthy mice. Glycogen phosphorylase (GP), a rate-limiting enzyme in glycogen degradation, is overexpressed in diabetic mice. This study shows that Metformin and Berberine, two common drugs, two common drugs used to treat diabetes, are able to revert the liver glycogen of diabetic mice to the stable structure seen in non-diabetic mice. It is also shown that these drugs reduce the GP level via the cAMP/PKA signaling pathway in diabetic livers and decrease the affinity of GP with the glycogen of db/db mice. These effects of these drugs may slow down the degradation of liver glycogen and improve glucose homeostasis.

Bayesian inference and comparison of stochastic transcription elongation models

Transcription elongation can be modelled as a three step process, involving polymerase translocation, NTP binding, and nucleotide incorporation into the nascent mRNA. This cycle of events can be simulated at the single-molecule level as a continuous-time Markov process using parameters derived from single-molecule experiments. Previously developed models differ in the way they are parameterised, and in their incorporation of partial equilibrium approximations. We have formulated a hierarchical network comprised of 12 sequence-dependent transcription elongation models. The simplest model has two parameters and assumes that both translocation and NTP binding can be modelled as equilibrium processes. The most complex model has six parameters makes no partial equilibrium assumptions. We systematically compared the ability of these models to explain published force-velocity data, using approximate Bayesian computation. This analysis was performed using data for the RNA polymerase complexes of E. coli, S. cerevisiae and Bacteriophage T7. Our analysis indicates that the polymerases differ significantly in their translocation rates, with the rates in T7 pol being fast compared to E. coli RNAP and S. cerevisiae pol II. Different models are applicable in different cases. We also show that all three RNA polymerases have an energetic preference for the posttranslocated state over the pretranslocated state. A Bayesian inference and model selection framework, like the one presented in this publication, should be routinely applicable to the interrogation of single-molecule datasets.

Transcription is a critical biological process which occurs in all living organisms. It involves copying the organism’s genetic material into messenger RNA (mRNA) which directs protein synthesis on the ribosome. Transcription is performed by RNA polymerases which have been extensively studied using both ensemble and single-molecule techniques. Single-molecule data provides unique insights into the molecular behaviour of RNA polymerases. Transcription at the single-molecule level can be computationally simulated as a continuous-time Markov process and the model outputs compared with experimental data. In this study we use Bayesian techniques to perform a systematic comparison of 12 stochastic models of transcriptional elongation. We demonstrate how equilibrium approximations can strengthen or weaken the model, and show how Bayesian techniques can identify necessary or unnecessary model parameters. We describe a framework to a) simulate, b) perform inference on, and c) compare models of transcription elongation.

Heineken, Tsuchiya and Aris on the mathematical status of the pseudo-steady state hypothesis: A classic from volume 1 of Mathematical Biosciences

Volume 1, Issue 1 of Mathematical Biosciences was the venue for a now-classic paper on the application of singular perturbation theory in enzyme kinetics, "On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics" by F. G. Heineken, H. M. Tsuchiya and R. Aris. More than 50 years have passed, and yet this paper continues to be studied and mined for insights. This perspective discusses both the strengths and weaknesses of the work presented in this paper. For many, the justification of the pseudo-steady-state approximation using singular perturbation theory is the main achievement of this paper. However, there is so much more material here, which laid the foundation for a great deal of research in mathematical biochemistry in the intervening decades. The parameterization of the equations, construction of the first-order uniform singular-perturbation solution, and an attempt to apply similar principles to the pseudo-equilibrium approximation are discussed in particular detail.

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.

Derivation and identification of a mechanistic model for a branched enzyme-catalyzed carboligation

The kinetic description of enzyme-catalyzed reactions is a core task in biotechnology and biochemical engineering. In particular, mechanistic kinetic models help from the discovery of the biocatalyst throughout its application. Chemo- or enantioselective enzyme reactions often undergo two alternative pathways for the release of two different products from a central intermediate. For these types of reaction, no explicit reaction equations have been derived so far. To this end, we extend the commonly used Cleland's notation for branched reaction pathways and explicitly derive the rate expressions for two-coupled ordered bi-uni reactions. This mechanism also leads to a ping-pong bi-bi mechanism for a transfer reaction between the two products via the same central intermediate of the reaction system. Using the cross-ligation of benzaldehyde and propanal catalyzed by the thiamine diphosphate-dependent enzyme benzaldehyde lyase from Pseudomonas fluorescens yielding (R)-2-hydroxy-1-phenylbutan-1-one as a case study, we performed model-based experimental analysis to show that such a reaction mechanism can be modeled mechanistically and leads to reasonable kinetic parameters.

The conserved NxNNWHW motif in Aha-type co-chaperones modulates the kinetics of Hsp90 ATPase stimulation

Hsp90 is a dimeric molecular chaperone that is essential for the folding and activation of hundreds of client proteins. Co-chaperone proteins regulate the ATP-driven Hsp90 client activation cycle. Aha-type co-chaperones are the most potent stimulators of the Hsp90 ATPase activity but the relationship between ATPase regulation and in vivo activity is poorly understood. We report here that the most strongly conserved region of Aha-type co-chaperones, the N terminal NxNNWHW motif, modulates the apparent affinity of Hsp90 for nucleotide substrates. The ability of yeast Aha-type co-chaperones to act in vivo is ablated when the N terminal NxNNWHW motif is removed. This work suggests that nucleotide exchange during the Hsp90 functional cycle may be more important than rate of catalysis.

Characteristic, completion or matching timescales? An analysis of temporary boundaries in enzyme kinetics

Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions, it is often overlooked that the characteristic timescales used for the scaling the rate equations are not ideal for determining when concentrations and reaction rates reach their maximum values. In this work, we first illustrate this point by considering the classic example of the single-enzyme, single-substrate Michaelis-Menten reaction mechanism. We then extend this analysis to a more complicated reaction mechanism, the auxiliary enzyme reaction, in which a substrate is converted to product in two sequential enzyme-catalyzed reactions. In this case, depending on the ordering of the relevant timescales, several dynamic regimes can emerge. In addition to the characteristic timescales for these regimes, we derive matching timescales that determine (approximately) when the transitions from transient to quasi-steady-state kinetics occurs. The approach presented here is applicable to a wide range of singular perturbation problems in nonlinear dynamical systems.

Thermodynamic buffering, stable non-equilibrium and establishment of the computable structure of plant metabolism

The equilibria of coenzyme nucleotides and substrates established in plant cells generate simple rules that govern the plant metabolome and provide optimal conditions for the non-equilibrium fluxes of major metabolic processes such as ATP synthesis, CO₂ fixation, and mitochondrial respiration. Fast and abundant enzymes, such as adenylate kinase, carbonic anhydrase or malate dehydrogenase, provide constant substrate flux for these processes. These "buffering" enzymes follow the Michaelis-Menten (MM) kinetics and operate near equilibrium. The non-equilibrium "engine" enzymes, such as ATP synthase, Rubisco or the respiratory complexes, follow the modified version of MM kinetics due to their high concentration and low concentration of their substrates. The equilibrium reactions serve as control gates for the non-equilibrium flux through the engine enzymes establishing the balance of the fluxes of load and consumption of metabolic components. Under the coordinated operation of buffering and engine enzymes, the concentrations of free and Mg-bound adenylates and of free Mg²⁺ are set, serving as feedback signals from the adenylate metabolome. Those are linked to various cell energetics parameters, including membrane potentials. Also, internal levels of reduced and oxidized pyridine nucleotides are established in the coordinated operation of malate dehydrogenase and respiratory components, with proton concentration as a feedback from pyridine nucleotide pools. Non-coupled pathways of respiration serve to equilibrate the levels of pyridine nucleotides, adenylates, and as a pH stat. This stable non-equilibrium organizes the fluxes of energy spatially and temporally, controlling the rates of major metabolic fluxes that follow thermodynamically and kinetically defined computational principles.