Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Bottom-up parameterization of enzyme rate constants: Reconciling inconsistent data

Kinetic models of metabolism are promising platforms for studying complex metabolic systems and designing production strains. Given the availability of enzyme kinetic data from historical experiments and machine learning estimation tools, a straightforward modeling approach is to assemble kinetic data enzyme by enzyme until a desired scale is reached. However, this type of 'bottom up' parameterization of kinetic models has been difficult due to a number of issues including gaps in kinetic parameters, the complexity of enzyme mechanisms, inconsistencies between parameters obtained from different sources, and in vitro-in vivo differences. Here, we present a computational workflow for the robust estimation of kinetic parameters for detailed mass action enzyme models while taking into account parameter uncertainty. The resulting software package, termed MASSef (the Mass Action Stoichiometry Simulation Enzyme Fitting package), can handle standard 'macroscopic' kinetic parameters, including Km, kcat, Ki, Keq, and nh, as well as diverse reaction mechanisms defined in terms of mass action reactions and 'microscopic' rate constants. We provide three enzyme case studies demonstrating that this approach can identify and reconcile inconsistent data either within in vitro experiments or between in vitro and in vivo enzyme function. We further demonstrate how parameterized enzyme modules can be used to assemble pathway-scale kinetic models consistent with in vivo behavior. This work builds on the legacy of knowledge on kinetic behavior of enzymes by enabling robust parameterization of enzyme kinetic models at scale utilizing the abundance of historical literature data and machine learning parameter estimates.

Beyond homogeneity: Assessing the validity of the Michaelis-Menten rate law in spatially heterogeneous environments

The Michaelis-Menten (MM) rate law has been a fundamental tool in describing enzyme-catalyzed reactions for over a century. When substrates and enzymes are homogeneously distributed, the validity of the MM rate law can be easily assessed based on relative concentrations: the substrate is in large excess over the enzyme-substrate complex. However, the applicability of this conventional criterion remains unclear when species exhibit spatial heterogeneity, a prevailing scenario in biological systems. Here, we explore the MM rate law's applicability under spatial heterogeneity by using partial differential equations. In this study, molecules diffuse very slowly, allowing them to locally reach quasi-steady states. We find that the conventional criterion for the validity of the MM rate law cannot be readily extended to heterogeneous environments solely through spatial averages of molecular concentrations. That is, even when the conventional criterion for the spatial averages is satisfied, the MM rate law fails to capture the enzyme catalytic rate under spatial heterogeneity. In contrast, a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA), is accurate. Specifically, the tQSSA-based modified form, but not the original MM rate law, accurately predicts the drug clearance via cytochrome P450 enzymes and the ultrasensitive phosphorylation in heterogeneous environments. Our findings shed light on how to simplify spatiotemporal models for enzyme-catalyzed reactions in the right context, ensuring accurate conclusions and avoiding misinterpretations in in silico simulations.

Validity conditions of approximations for a target-mediated drug disposition model: A novel first-order approximation and its comparison to other approximations

Target-mediated drug disposition (TMDD) is a phenomenon characterized by a drug's high-affinity binding to a target molecule, which significantly influences its pharmacokinetic profile within an organism. The comprehensive TMDD model delineates this interaction, yet it may become overly complex and computationally demanding in the absence of specific concentration data for the target or its complexes. Consequently, simplified TMDD models employing quasi-steady state approximations (QSSAs) have been introduced; however, the precise conditions under which these models yield accurate results require further elucidation. Here, we establish the validity of three simplified TMDD models: the Michaelis-Menten model reduced with the standard QSSA (mTMDD), the QSS model reduced with the total QSSA (qTMDD), and a first-order approximation of the total QSSA (pTMDD). Specifically, we find that mTMDD is applicable only when initial drug concentrations substantially exceed total target concentrations, while qTMDD can be used for all drug concentrations. Notably, pTMDD offers a simpler and faster alternative to qTMDD, with broader applicability than mTMDD. These findings are confirmed with antibody-drug conjugate real-world data. Our findings provide a framework for selecting appropriate simplified TMDD models while ensuring accuracy, potentially enhancing drug development and facilitating safer, more personalized treatments.

Copper-based metal-organic frameworks (BDC-Cu MOFs) as supporters for α-amylase: Stability, reusability, and antioxidant potential

Copper-based metal-organic frameworks (BDC-Cu MOFs) were synthesized via a casting approach using 1,4-benzene dicarboxylic (BDC) as organic ligand and their properties characterized. The obtained materials were then utilized to immobilize the α-amylase enzyme. The chemical composition and functional components of the synthesized support (BDC-Cu MOFs) were investigated with Fourier transform infrared spectroscopy (FTIR), the surface morphology was determined with scanning electron microscopy (SEM), and the elemental composition was established with energy dispersive X-ray (EDX) analyses. X-ray diffraction (XRD) was employed to analyze the crystallinity of the synthesized DBC-Cu MOFs. The zeta potentials of DBC-Cu MOFs and DBC-Cu MOFs@α-amylase were determined. The immobilized α-amylase demonstrated improved catalytic activity and reusability compared to the free form. Covalent attachment of the α-amylase to BDC-Cu provided an immobilization yield (IY%) of 81% and an activity yield (AY%) of 89%. The immobilized α-amylase showed high catalytic activity and 81% retention even after ten cycles. Storage at 4 °C for eight weeks resulted in a 78% activity retention rate for DBC-Cu MOFs@α-amylase and 49% retention for the free α-amylase. The optimum activity occurred at 60 °C for the immobilized form, whereas the free form showed optimal activity at 50 °C. The free and immobilized α-amylase demonstrated peak catalytic activities at pH 6.0. The maximum reaction velocities (Vmax) values were 0.61 U/mg of protein for free α-amylase and 0.37 U/mg of protein for BDC-Cu MOFs@α-amylase, while the Michaelis‒Menten affinity constants (Km) value was lower for the immobilized form (5.46 mM) than for the free form (11.67 mM). Treatments of maize flour and finger millet samples with free and immobilized α-amylase resulted in increased total phenolic contents. The enhanced antioxidant activities of the treated samples were demonstrated with decreased IC50 values in ABTS and DPPH assays. Overall, immobilization of α-amylase on BDC-Cu MOFs provided improved stability and catalytic activity and enhanced the antioxidant potentials of maize flour and finger millet.

Exploring Emergent Properties in Enzymatic Reaction Networks: Design and Control of Dynamic Functional Systems

The intricate and complex features of enzymatic reaction networks (ERNs) play a key role in the emergence and sustenance of life. Constructing such networks in vitro enables stepwise build up in complexity and introduces the opportunity to control enzymatic activity using physicochemical stimuli. Rational design and modulation of network motifs enable the engineering of artificial systems with emergent functionalities. Such functional systems are useful for a variety of reasons such as creating new-to-nature dynamic materials, producing value-added chemicals, constructing metabolic modules for synthetic cells, and even enabling molecular computation. In this review, we offer insights into the chemical characteristics of ERNs while also delving into their potential applications and associated challenges.

Synthesis of Spherical Mn2O3 Nanozymes from Different Green Precursors for their Innovative Applications in Catalytic Properties and Bioactivity

Here, spherical Mn2O3 nanozymes were synthesized via a one-step green method using different green precursors, and their physicochemical properties and biological activities were monitored with various green precursors. Powder X-ray diffraction (PXRD) was performed to determine the crystalline properties and phases involved in the formation of cubic Mn2O3 nanozymes. The synthesized nanozymes were spherical and examined by SEM and FESEM studies. All of the samples synthesized using different green precursors exhibited different sizes but similar spherical shapes. Moreover, all green-synthesized nanozymes catalyzed the oxidation reaction of the chromogenic substrate 3,3'5,5' tetramethylbenzidine (TMB) in the absence of H2O2, and A2 (lemon-mediated Mn2O3 nanozymes), which the followed Michaelis-Menten kinetics, showed the best activity. Therefore, A2 (lemon-mediated nanozyme) showed oxidase-mimicking activity with distinct Km and Vmax values calculated by the Lineweaver-Burk plot. Furthermore, the current nanozymes demonstrated a significant ability to kill both Gram-negative and Gram-positive bacteria as well as effectively destroy biofilms under physiological conditions. Moreover, the green-mediated nanozymes also displayed ROS-scavenging activity. Our nanozymes exhibited scavenging activity toward OH and O2-• radicals and metal chelation activity, which were investigated colorimetrically. Therefore, these nanozymes might be used as effective antibacterial agents and also for the consumption of reactive oxygen species.

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.

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.

Construction and optimization of a biocatalytic route for the synthesis of neomenthylamine from menthone

(+)-Neomenthylamine is an important industrial precursor used to synthesize high value-added chemicals. Here, we report a novel biocatalytic route to synthesize (+)-neomenthylamine by amination of readily available (-)-menthone substrate using ω-transaminase. By screening a panel of ω-transaminases, an ω-transaminase from Vibrio fluvialis JS17 was identified with considerable amination activity to (-)-menthone, and then characterization of enzymatic properties was conducted for the enzyme. Under optimized conditions, 10 mM (-)-menthone was transformed in a mild aqueous phase with 4.7 mM product yielded in 24 h. The biocatalytic route using inexpensive starting materials (ketone substrate and amino donor) and mild reaction conditions represents an easy and green approach for (+)-neomenthylamine synthesis. This method underscores the potential of biocatalysts in the synthesis of unnatural terpenoid amine derivatives.

Inferring delays in partially observed gene regulation processes

MOTIVATION

Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality.

RESULTS

We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components.

AVAILABILITY AND IMPLEMENTATION

Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.

Kinetics of the enzyme titration process by reversible modifiers

The effect of reversible modifiers on the initial rate of enzyme catalysed reactions has been investigated in a quasi-equilibrium approximation using the general modifier mechanism of Botts and Morales. It has been shown that, when investigating the dependence of the initial rate on the modifier concentration at a fixed substrate concentration, the kinetics of enzyme titration by reversible modifiers can generally be described using two kinetic constants. Just as the dependence of the initial rate on the substrate concentration (at a fixed modifier concentration) is described using two kinetic constants: the Michaelis constant Km and the limiting rate Vm. Only one constant M50 is needed to describe the kinetics of linear inhibition, and in the case of nonlinear inhibition and activation, along with M50 the constant QM is also needed. Knowing the values of the constants M50 and QM, it is possible to unambiguously determine the modification efficiency, that is, to calculate how many times the initial rate of the enzyme catalysed reaction will change when a certain modifier concentration is added to the incubation medium. The properties of these fundamental constants have been analysed in detail and the dependence of these constants on other parameters of the Botts-Morales model have been shown. Equations describing the dependence of relative reaction rates on the modifier concentration using these kinetic constants are presented. Various ways of linearising these equations for calculating the kinetic constants M50 and QM from experimental data are also presented.

Bayesian Inference Elucidates the Catalytic Competency of the SARS-CoV-2 Main Protease 3CLpro

The main protease of SARS-CoV-2, 3CLpro, is a dimeric enzyme that is indispensable to viral replication and presents an attractive opportunity for therapeutic intervention. Previous reports regarding the key properties of 3CLpro and its highly similar SARS-CoV homologue conflict dramatically. Values of the dimeric Kd and enzymic kcat/KM differ by 106- and 103-fold, respectively. Establishing a confident benchmark of the intrinsic capabilities of this enzyme is essential for combating the current pandemic as well as potential future outbreaks. Here, we use enzymatic methods to characterize the dimerization and catalytic efficiency of the authentic protease from SARS-CoV-2. Specifically, we use the rigor of Bayesian inference in a Markov Chain Monte Carlo analysis of progress curves to circumvent the limitations of traditional Michaelis-Menten initial rate analysis. We report that SARS-CoV-2 3CLpro forms a dimer at pH 7.5 that has Kd = 16 ± 4 nM and is capable of catalysis with kcat = 9.9 ± 1.5 s-1, KM = 0.23 ± 0.01 mM, and kcat/KM = (4.3 ± 0.7) × 104 M-1 s-1. We also find that enzymatic activity decreases substantially in solutions of high ionic strength, largely as a consequence of impaired dimerization. We conclude that 3CLpro is a more capable catalyst than appreciated previously, which has important implications for the design of antiviral therapeutic agents that target 3CLpro.

Enhancing the organic solvent resistance of ω-amine transaminase for enantioselective synthesis of (R)-(+)-1(1-naphthyl)-ethylamine

BACKGROUND

Biocatalysis in high-concentration organic solvents has been applied to produce various industrial products with many advantages. However, using enzymes in organic solvents often suffers from inactivation or decreased catalytic activity and stability. An R-selective ω-amine transaminase from Aspergillus terreus (AtATA) exhibited activity toward 1-acetylnaphthalene. However, AtATA displayed unsatisfactory organic solvent resistance, which is required to enhance the solubility of the hydrophobic substrate 1-acetylnaphthalene. So, improving the tolerance of enzymes in organic solvents is essential.

MAIN METHODS AND RESULTS

The method of regional random mutation combined with combinatorial mutation was used to improve the resistance of AtATA in organic solvents. Enzyme surface areas are structural elements that undergo reversible conformational transitions, thus affecting the stability of the enzyme in organic solvents. Herein, three surface areas containing three loops were selected as potential mutation regions. And the "best" mutant T23I/T200K/P260S (M3) was acquired. In different concentrations of dimethyl sulfoxide (DMSO), the catalytic efficiency (kcat /Km ) toward 1-acetylnaphthalene and the stability (half-life t1/2 ) were higher than the wild-type (WT) of AtATA. The results of decreased Root Mean Square Fluctuation (RMSF) values via 20-ns molecular dynamics (MD) simulations under 15%, 25%, 35%, and 45% DMSO revealed that mutant M3 had lower flexibility, acquiring a more stable protein structure and contributing to its organic solvents stability than WT. Furthermore, M3 was applied to convert 1-acetylnaphthalene for synthesizing (R)-(+)-1(1-naphthyl)-ethylamine ((R)-NEA), which was an intermediate of Cinacalcet Hydrochloride for the treatment of secondary hyperthyroidism and hypercalcemia. Moreover, in a 20-mL scale-up experiment, 10 mM 1-acetylnaphthalene can be converted to (R)-NEA with 85.2% yield and a strict R-stereoselectivity (enantiomeric excess (e.e.) value >99.5%) within 10 h under 25% DMSO.

CONCLUSION

The beneficial mutation sites were identified to tailor AtATA's organic solvents stability via regional random mutation. The "best" mutant T23I/T200K/P260S (M3) holds great potential application for the synthesis of (R)-NEA.

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.

Estimating and Assessing Differential Equation Models with Time-Course Data

Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This Article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy, and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI's efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.

Comparison of in vitro Antifungal Activity Methods Using Extract of Chitinase-producing Aeromonas sp. BHC02

Biological control to prevent fungal plant diseases offers an alternative approach to facilitate sustainable agriculture. Since the chitin in fungal cell walls is a target for biocontrol agents, chitinases are one of the important antifungal molecules. In this study, the aim was to investigate a new chitinase isolated from a fluvial soil bacterium and to show the antifungal activity of the characterized chitinase by comparing the three common methods. The bacterium with the highest chitinase activity was identified as Aeromonas sp. by 16 S rRNA sequence analysis. Following the determination of the optimum enzyme production time, the enzyme was partially purified, and the physicochemical parameters of the enzyme were investigated. In the antifungal studies, direct Aeromonas sp. BHC02 cells or partially purified chitinase were used. As a result, in the first method in which the Aeromonas sp. BHC02 cells were spread on the surface of petri dishes, no zone formation was observed around the test fungi spotted on the surface. However, zone formation was observed in the methods in which the antifungal activity was investigated using the partially purified chitinase enzyme. For example, in the second method, the enzyme was spread on the surface of PDA, and zone formation was observed only around Penicillum species among the test fungi spotted on the surface. In the third method, in which the necessary time was given for the formation of mycelium of the test fungi, it was observed that the growth of Fusarium solani, Alternaria alternata and Botrytis cinerea was inhibited by the partially purified chitinase. This study concludes that the results of the antifungal activities depend on the method used and all fungal chitins cannot be degraded with one strain's chitinase. Depending on the variety of chitin, some fungi can be more resistant.

Beyond the Michaelis-Menten: Accurate Prediction of Drug Interactions through Cytochrome P450 3A4 Induction

The US Food and Drug Administration (FDA) guidance has recommended several model-based predictions to determine potential drug-drug interactions (DDIs) mediated by cytochrome P450 (CYP) induction. In particular, the ratio of substrate area under the plasma concentration-time curve (AUCR) under and not under the effect of inducers is predicted by the Michaelis-Menten (MM) model, where the MM constant ( K m $$ {K}_{\mathrm{m}} $$ ) of a drug is implicitly assumed to be sufficiently higher than the concentration of CYP enzymes that metabolize the drug ( E T $$ {E}_{\mathrm{T}} $$ ) in both the liver and small intestine. Furthermore, the fraction absorbed from gut lumen ( F a $$ {F}_{\mathrm{a}} $$ ) is also assumed to be one because F a $$ {F}_{\mathrm{a}} $$ is usually unknown. Here, we found that such assumptions lead to serious errors in predictions of AUCR. To resolve this, we propose a new framework to predict AUCR. Specifically, F a $$ {F}_{\mathrm{a}} $$ was re-estimated from experimental permeability values rather than assuming it to be one. Importantly, we used the total quasi-steady-state approximation to derive a new equation, which is valid regardless of the relationship between K m $$ {K}_{\mathrm{m}} $$ and E T $$ {E}_{\mathrm{T}} $$ , unlike the MM model. Thus, our framework becomes much more accurate than the original FDA equation, especially for drugs with high affinities, such as midazolam or strong inducers, such as rifampicin, so that the ratio between K m $$ {K}_{\mathrm{m}} $$ and E T $$ {E}_{\mathrm{T}} $$ becomes low (i.e., the MM model is invalid). Our work greatly improves the prediction of clinical DDIs, which is critical to preventing drug toxicity and failure.

Fluorescent Peptomer Substrates for Differential Degradation by Metalloproteases

Proteases, especially MMPs, are attractive biomarkers given their central role in both physiological and pathological processes. Distinguishing MMP activity with degradable substrates, however, is a difficult task due to overlapping substrate specificity profiles. Here, we developed a system of peptomers (peptide-peptoid hybrids) to probe the impact of non-natural residues on MMP specificity for an MMP peptide consensus sequence. Peptoids are non-natural, N-substituted glycines with a large side-chain diversity. Given the presence of a hallmark proline residue in the P3 position of MMP consensus sequences, we hypothesized that peptoids may offer N-substituted alternatives to generate differential interactions with MMPs. To investigate this hypothesis, peptomer substrates were exposed to five different MMPs, as well as bacterial collagenase, and monitored by fluorescence resonance energy transfer and liquid chromatography-mass spectrometry to determine the rate of cleavage and the composition of degraded fragments, respectively. We found that peptoid residues are well tolerated in the P3 and P3' substrate sites and that the identity of the peptoid in these sites displays a moderate influence on the rate of cleavage. However, peptoid residues were even better tolerated in the P1 substrate site where activity was more strongly correlated with side-chain identity than side-chain position. All MMPs explored demonstrated similar trends in specificity for the peptomers but exhibited different degrees of variability in proteolytic rate. These kinetic profiles served as "fingerprints" for the proteases and yielded separation by multivariate data analysis. To further demonstrate the practical application of this tunability in degradation kinetics, peptomer substrates were tethered into hydrogels and released over distinct timescales. Overall, this work represents a significant step toward the design of probes that maximize differential MMP behavior and presents design rules to tune degradation kinetics with peptoid substitutions, which has promising implications for diagnostic and prognostic applications using array-based sensors.

Analysis of sloppiness in model simulations: Unveiling parameter uncertainty when mathematical models are fitted to data

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

Enzyme kinetics by real-time quantitative NMR (qNMR) spectroscopy with progress curve analysis

This review article summarizes how the experimental data obtained using quantitative nuclear magnetic resonance (qNMR) spectroscopy can be combined with progress curve analysis to determine enzyme kinetic parameters. The qNMR approach enables following the enzymatic conversion of the substrate to the product in real-time by a continuous collection of spectra. The Lambert-W function, a closed-form solution to the time-dependent substrate/product kinetics of the rate equation, can estimate the Michaelis-Menten constant (K_M.) and the maximum velocity (V_max) from a single experiment. This article highlights how the qNMR data is well suited for analysis using the Lambert-W function with three different applications. Results from studies on acetylcholinesterase (acetylcholine to acetic acid and choline), β-Galactosidase (lactose to glucose and galactose), and invertase (sucrose to glucose and fructose) are presented. Furthermore, an additional example of how the progress curve analysis is applied to understand the inhibitory role of the artificial sweetener sucralose on sucrose's enzymatic conversion by invertase is discussed. With the wide availability of NMR spectrometers in academia and industries, including bench-top systems with permanent magnets, and the potential to enhance sensitivity using dynamic nuclear polarization in combination with ultrafast methods, the NMR-based enzyme kinetics could be considered a valuable tool for broader applications in the field of enzyme kinetics.

The influence of UV light on the course of fluorescent enzyme assays

Experiments were carried out to illustrate the effect of UV light on the course of the enzymatic reaction of the coumarin derivative. Only the pulsating light of the UV diode gives the correct results for the determination of the kinetic constants of the enzymatic reaction. The enzyme concentration limit was found where the description of the M-M model breaks. It was shown that the system determines the kinetic parameters of enzymatic reactions: V_max-the maximum rate of reaction and K_M-the Michaelis constant. This method produces kinetic constants calculated from the changes in enzyme product concentration using the Michaelis-Menten model. To verify the results, we used a statistical analysis that checks the correctness of the model used.

Mathematical Modeling Reveals That Sucrose Regulates Leaf Senescence via Dynamic Sugar Signaling Pathways

Sucrose (Suc) accumulation is one of the key indicators of leaf senescence onset, but little is known about its regulatory role. Here, we found that application of high (120–150 mM) and low levels (60 mM) of Suc to young leaf (YL) and fully expanded leaf (FEL) discs, respectively, decreased chlorophyll content and maximum photosynthetic efficiency. Electrolyte leakage and malondialdehyde levels increased at high Suc concentrations (90–120 mM in YL and 60 and 150 mM in FEL discs). In FEL discs, the senescence-associated gene NtSAG12 showed a gradual increase in expression with increased Suc application; in contrast, in YL discs, NtSAG12 was upregulated with low Suc treatment (60 mM) but downregulated at higher levels of Suc. In YL discs, trehalose-6-phosphate (T6P) accumulated at a low half-maximal effective concentration (EC50) of Suc (1.765 mM). However, T6P levels declined as trehalose 6 phosphate synthase (TPS) content decreased, resulting in the maximum velocity of sucrose non-fermenting-1-related protein kinase (SnRK) and hexokinase (HXK) occurring at higher level of Suc. We therefore speculated that senescence was induced by hexose accumulation. In FEL discs, the EC50 of T6P occurred at a low concentration of Suc (0.9488 mM); T6P levels progressively increased with higher TPS content, which inhibited SnRK activity with a dissociation constant (K_d) of 0.001475 U/g. This confirmed that the T6P–SnRK complex induced senescence in detached FEL discs.

A Bayesian Approach to Extracting Kinetic Information from Artificial Enzymatic Networks

In order to create artificial enzymatic networks capable of increasingly complex behavior, an improved methodology in understanding and controlling the kinetics of these networks is needed. Here, we introduce a Bayesian analysis method allowing for the accurate inference of enzyme kinetic parameters and determination of most likely reaction mechanisms, by combining data from different experiments and network topologies in a single probabilistic analysis framework. This Bayesian approach explicitly allows us to continuously improve our parameter estimates and behavior predictions by iteratively adding new data to our models, while automatically taking into account uncertainties introduced by the experimental setups or the chemical processes in general. We demonstrate the potential of this approach by characterizing systems of enzymes compartmentalized in beads inside flow reactors. The methods we introduce here provide a new approach to the design of increasingly complex artificial enzymatic networks, making the design of such networks more efficient, and robust against the accumulation of experimental errors.

Nanotechnology Tools Enabling Biological Discovery

Over the years, the engineering aspect of nanotechnology has been significantly exploited. Medical intervention strategies have been developed by leveraging existing molecular biology knowledge and combining it with nanotechnology tools to improve outcomes. However, little attention has been paid to harnessing the strengths of nanotechnology as a biological discovery tool. Fundamental understanding of controlling dynamic biological processes at the subcellular level is key to developing personalized therapeutic and diagnostic interventions. Single-cell analyses using intravital microscopy, expansion microscopy, and microfluidic-based platforms have been helping to better understand cell heterogeneity in healthy and diseased cells, a major challenge in oncology. Also, single-cell analysis has revealed critical signaling pathways and biological intracellular components with key biological functions. The physical manipulation enabled by nanotools can allow real-time monitoring of biological changes at a single-cell level by sampling intracellular fluid from the same cell. The formation of intercellular highways by nanotube-like structures has important clinical implications such as metastasis development. The integration of nanomaterials into optical and molecular imaging techniques has rendered valuable morphological, structural, and biological information. Nanoscale imaging unravels mechanisms of temporality by enabling the visualization of nanoscale dynamics never observed or measured between individual cells with standard biological techniques. The exceptional sensitivity of nanozymes, artificial enzymes, make them perfect components of the next-generation mobile diagnostics devices. Here, we highlight these impactful cancer-related biological discoveries enabled by nanotechnology and producing a paradigm shift in cancer research and oncology.

Henri-Michaelis-Menten kinetics of reversible enzymic reactions, and the determination of rate constants from kinetic constants

The Michaelis constants derived for two reversible uni-reactant - uni-product reaction models, given originally by Haldane, are corrected. In the direction starting with the reactant having the lower binding constant, the steady state is one in which the enzyme-reactant intermediate has a concentration approximating the final equilibrium concentration., Consequently, the Haldane relationship is generally invalid, and kinetic analyses to validate the use of the kinetic constant ratio (kcat/Km) as a measure of specificity are also generally invalid. This correction of Michaelis constants is pertinent to attempts to back calculate rate constants from experimental values: the Michaelis constant used must be correct.

Covalent Proximity Scanning of a Distal Cysteine to Target PI3Kα

Covalent protein kinase inhibitors exploit currently noncatalytic cysteines in the adenosine 5′-triphosphate (ATP)-binding site via electrophiles directly appended to a reversible-inhibitor scaffold. Here, we delineate a path to target solvent-exposed cysteines at a distance >10 Å from an ATP-site-directed core module and produce potent covalent phosphoinositide 3-kinase α (PI3Kα) inhibitors. First, reactive warheads are used to reach out to Cys862 on PI3Kα, and second, enones are replaced with druglike warheads while linkers are optimized. The systematic investigation of intrinsic warhead reactivity (k_chem), rate of covalent bond formation and proximity (k_inact and reaction space volume V_r), and integration of structure data, kinetic and structural modeling, led to the guided identification of high-quality, covalent chemical probes. A novel stochastic approach provided direct access to the calculation of overall reaction rates as a function of k_chem, k_inact, K_i, and V_r, which was validated with compounds with varied linker lengths. X-ray crystallography, protein mass spectrometry (MS), and NanoBRET assays confirmed covalent bond formation of the acrylamide warhead and Cys862. In rat liver microsomes, compounds 19 and 22 outperformed the rapidly metabolized CNX-1351, the only known PI3Kα irreversible inhibitor. Washout experiments in cancer cell lines with mutated, constitutively activated PI3Kα showed a long-lasting inhibition of PI3Kα. In SKOV3 cells, compounds 19 and 22 revealed PI3Kβ-dependent signaling, which was sensitive to TGX221. Compounds 19 and 22 thus qualify as specific chemical probes to explore PI3Kα-selective signaling branches. The proposed approach is generally suited to develop covalent tools targeting distal, unexplored Cys residues in biologically active enzymes.

A self-triggered radioligand therapy agent for fluorescence imaging of the treatment response in prostate cancer

PURPOSE

Radioligand therapy (RLT) targeting prostate-specific membrane antigen (PSMA) is emerging as an effective treatment option for metastatic castration-resistant prostate cancer (mCRPC). An imaging-based method to quantify early treatment responses can help to understand and optimize RLT.

METHODS

We developed a self-triggered probe 2 targeting the colocalization of PSMA and caspase-3 for fluorescence imaging of RLT-induced apoptosis.

RESULTS

The probe binds to PSMA potently with a K_i of 4.12 nM, and its fluorescence can be effectively switched on by caspase-3 with a K_m of 67.62 μM. Cellular and in vivo studies demonstrated its specificity for imaging radiation-induced caspase-3 upregulation in prostate cancer. To identify the detection limit of our method, we showed that probe 2 could achieve 1.79 times fluorescence enhancement in response to ¹⁷⁷Lu-RLT in a medium PSMA-expressing 22Rv1 xenograft model.

CONCLUSION

Probe 2 can potently bind to PSMA, and the fluorescence signal can be sensitively switched on by caspase-3 both in vitro and in vivo. This method may provide an effective tool to investigate and optimize PSMA-RLT.

Targeted substrate loop insertion by VCP/p97 during PP1 complex disassembly

The AAA-ATPase VCP/p97/Cdc48 unfolds proteins by threading them through its central pore, but how substrates are recognized and inserted into the pore in diverse pathways has remained controversial. Here, we show that p97, with its adapter p37, binds an internal recognition site (IRS) within inhibitor-3 (I3) and then threads a peptide loop into its channel to strip I3 off protein phosphatase-1 (PP1). Of note, the IRS is adjacent to the prime interaction site of I3 to PP1, and IRS mutations block I3 processing both in vitro and in cells. In contrast, amino- and carboxy-terminal regions of I3 are not required, and even circularization of I3 does not prevent I3 processing. This was confirmed by an in vitro Förster resonance energy transfer assay that allowed kinetic analysis of the reaction. Thus, our data uncover how PP1 is released from its inhibitory partner for activation and demonstrate a remarkable plasticity in substrate threading by p97.

Biodegradable poly(lactide-co-glycolide) microspheres encapsulating hydrophobic contrast agents for transarterial chemoembolization

Transarterial chemoembolization (TACE) is a therapeutic approach to address hepatocellular carcinoma by obstructing the blood supply to the tumor using embolic agents and improving the local delivery of anticancer agents. Size-calibrated polymeric microspheres (MSs) termed drug-eluting beads (DEBs) are the most prevalent solid embolic materials; however, their limitations include insufficient X-ray visibility or biodegradability. In this study, size-controlled polymeric MSs with inherent radiopacity and biodegradability were created, and their embolic effect was assessed. Poly(lactide-co-glycolide) MSs (PLGA MSs) incorporating a hydrophobic X-ray contrast agent and an anticancer drug were produced by the w/o/w emulsion process. Their sizes were exactly calibrated to 71.40 ± 32.18 and 142.66 ± 59.92 μm in diameter, respectively, which were confirmed to have sizes similar to the clinically available DEBs. The iodine content of PLGA MSs was calculated as 144 mgI/g, and the loading quantity of the drug was 1.33%. Manufactured PLGA MSs were gradually degraded for 10 weeks and consistently released the anticancer drug. Following the PLGA MSs injection into the renal artery of New Zealand white rabbit test subjects, their deliverability to the targeted vessel through the microcatheter was confirmed. Injected PLGA MSs were clearly imaged through the real-time X-ray device without blending any contrast agents. The embolic effect of the PLGA MSs was ultimately established by the atrophy of an embolized kidney after 8 weeks. Consequently, the designed PLGA MS is anticipated to be an encouraging prospect to address hepatocellular carcinoma.

Application of modified Michaelis - Menten equations for determination of enzyme inducing and inhibiting drugs

BACKGROUND

Pharmacokinetics (PK) is the process of absorption, distribution, metabolism and elimination (ADME) of drugs. Some drugs undergo zero-order kinetics (ethyl alcohol), first order kinetics (piroxicam) and mixed order kinetics (ascorbic acid). Drugs that undergo Michaelis-Menten metabolism are characterized by either increased or decreased metabolism constant (Km) and maximum velocity (Vmax) of enzyme reaction. Hence literatures were searched with a view to translating in vitro-in vivo enzyme kinetics to pharmacokinetic/pharmacodynamic parameters for determination of enzyme inducing and inhibiting drugs, in order to achieve optimal clinical efficacy and safety.

METHODS

A narrative review of retrospective secondary data on drugs, their metabolites, Vmax and Km, generated in the laboratory and clinical environments was adopted, using inclusion and exclusion criteria. Key word search strategy was applied, to assess databases of published articles on enzyme inducing and inhibiting drugs, that obey Michaelis-Menten kinetics. In vitro and in vivo kinetic parameters, such as concentration of substrate, rate of endogenous substrate production, cellular metabolic rate, initial velocity of metabolism, intrinsic clearance, percent saturation and unsaturation of the enzyme substrate, were calculated using original and modified formulas. Years and numbers of searched publications, types of equations and their applications were recorded.

RESULTS

A total of fifty-six formulas both established and modified were applied in the present study. Findings have shown that theophylline, voriconazole, phenytoin, thiopental, fluorouracil, thyamine and thymidine are enzyme inducers whereas, mibefradil, metronidazole, isoniazid and puromicin are enzyme inhibitors. They are metabolized and eliminated according to Michaelis-Menten principle. The order could be mixed but may change to zero or first order, depending on drug concentration, frequency and route of drug administration.

CONCLUSION

Hence, pharmacokinetic-pharmacodynamic translation can be optimally achieved by incorporating, newly modified Michaelis-Menten equations into pharmacokinetic formulas for clinical efficacy and safety of the enzyme inducing and inhibiting therapeutic agents used in laboratory and clinical settings.

Synthetic biomarkers: a twenty-first century path to early cancer detection

Detection of cancer at an early stage when it is still localized improves patient response to medical interventions for most cancer types. The success of screening tools such as cervical cytology to reduce mortality has spurred significant interest in new methods for early detection (for example, using non-invasive blood-based or biofluid-based biomarkers). Yet biomarkers shed from early lesions are limited by fundamental biological and mass transport barriers - such as short circulation times and blood dilution - that limit early detection. To address this issue, synthetic biomarkers are being developed. These represent an emerging class of diagnostics that deploy bioengineered sensors inside the body to query early-stage tumours and amplify disease signals to levels that could potentially exceed those of shed biomarkers. These strategies leverage design principles and advances from chemistry, synthetic biology and cell engineering. In this Review, we discuss the rationale for development of biofluid-based synthetic biomarkers. We examine how these strategies harness dysregulated features of tumours to amplify detection signals, use tumour-selective activation to increase specificity and leverage natural processing of bodily fluids (for example, blood, urine and proximal fluids) for easy detection. Finally, we highlight the challenges that exist for preclinical development and clinical translation of synthetic biomarker diagnostics.

Universally valid reduction of multiscale stochastic biochemical systems using simple non-elementary propensities

Biochemical systems consist of numerous elementary reactions governed by the law of mass action. However, experimentally characterizing all the elementary reactions is nearly impossible. Thus, over a century, their deterministic models that typically contain rapid reversible bindings have been simplified with non-elementary reaction functions (e.g., Michaelis-Menten and Morrison equations). Although the non-elementary reaction functions are derived by applying the quasi-steady-state approximation (QSSA) to deterministic systems, they have also been widely used to derive propensities for stochastic simulations due to computational efficiency and simplicity. However, the validity condition for this heuristic approach has not been identified even for the reversible binding between molecules, such as protein-DNA, enzyme-substrate, and receptor-ligand, which is the basis for living cells. Here, we find that the non-elementary propensities based on the deterministic total QSSA can accurately capture the stochastic dynamics of the reversible binding in general. However, serious errors occur when reactant molecules with similar levels tightly bind, unlike deterministic systems. In that case, the non-elementary propensities distort the stochastic dynamics of a bistable switch in the cell cycle and an oscillator in the circadian clock. Accordingly, we derive alternative non-elementary propensities with the stochastic low-state QSSA, developed in this study. This provides a universally valid framework for simplifying multiscale stochastic biochemical systems with rapid reversible bindings, critical for efficient stochastic simulations of cell signaling and gene regulation. To facilitate the framework, we provide a user-friendly open-source computational package, ASSISTER, that automatically performs the present framework.

Frequency-preference response in covalent modification cycles under substrate sequestration conditions

Covalent modification cycles (CMCs) are basic units of signaling systems and their properties are well understood. However, their behavior has been mostly characterized in situations where the substrate is in excess over the modifying enzymes. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations, leading to substrate sequestration by the enzymes. In this enzyme-in-excess regime, CMCs have been shown to exhibit signal termination, the ability of the product to return to a stationary value lower than its peak in response to constant stimulation, while this stimulation is still active, with possible implications for the ability of systems to adapt to environmental inputs. We characterize the conditions leading to signal termination in CMCs in the enzyme-in-excess regime. We also demonstrate that this behavior leads to a preferred frequency response (band-pass filters) when the cycle is subjected to periodic stimulation, whereas the literature reports that CMCs investigated so far behave as low-pass filters. We characterize the relationship between signal termination and the preferred frequency response to periodic inputs and we explore the dynamic mechanism underlying these phenomena. Finally, we describe how the behavior of CMCs is reflected in similar types of responses in the cascades of which they are part. Evidence of protein abundance in vivo shows that enzymes and substrates are present in comparable concentrations, thus suggesting that signal termination and frequency-preference response to periodic inputs are also important dynamic features of cell signaling systems, which have been overlooked.

Microbial L-asparaginase for Application in Acrylamide Mitigation from Food: Current Research Status and Future Perspectives

L-asparaginase (E.C.3.5.1.1) hydrolyzes L-asparagine to L-aspartic acid and ammonia, which has been widely applied in the pharmaceutical and food industries. Microbes have advantages for L-asparaginase production, and there are several commercially available forms of L-asparaginase, all of which are derived from microbes. Generally, L-asparaginase has an optimum pH range of 5.0-9.0 and an optimum temperature of between 30 and 60 °C. However, the optimum temperature of L-asparaginase from hyperthermophilic archaea is considerable higher (between 85 and 100 °C). The native properties of the enzymes can be enhanced by using immobilization techniques. The stability and recyclability of immobilized enzymes makes them more suitable for food applications. This current work describes the classification, catalytic mechanism, production, purification, and immobilization of microbial L-asparaginase, focusing on its application as an effective reducer of acrylamide in fried potato products, bakery products, and coffee. This highlights the prospects of cost-effective L-asparaginase, thermostable L-asparaginase, and immobilized L-asparaginase as good candidates for food application in the future.

Mechanisms of the Antiproliferative and Antitumor Activity of Novel Telomerase-Carbonic Anhydrase Dual-Hybrid Inhibitors

Human (h) telomerase (TL; EC 2.7.7.49) plays a key role in sustaining cancer cells by means of elongating telomeric repeats at the 3' ends of chromosomes. Since TL-inhibitor (TI) stand-alone cancer therapy has been proven to be remarkably challenging, a polypharmacological approach represents a valid alternative. Here we consider a series of compounds able to inhibit both hTL and the tumor-associated carbonic anhydrases (CAs; EC 4.2.1.1) IX and XII. Compounds 7 and 9 suppressed hTL activity in both cell lysates and human colon cancer cell lines, and prolonged incubation with either 7 or 9 resulted in telomere shortening, cell cycle arrest, replicative senescence, and apoptosis. Enzyme kinetics showed that 7 and 9 are mixed-type inhibitors of the binding of DNA primers and deoxynucleoside triphosphate (dNTP) to the TL catalytic subunit hTERT, which is in agreement with docking experiments. Compound 9 showed antitumor activity in Colo-205 mouse xenografts and suppressed telomerase activity by telomere reduction.

Differential effects of inorganic salts on cellulase kinetics in enzymatic saccharification of cellulose and lignocellulosic biomass

Inorganic salt pretreatment of lignocellulosic biomass has proven to be an efficient way to increase the efficiency of enzymatic saccharification. However, it is not clear that this improvement is the result of modification of the lignocellulosic substrate after pretreatment, or removal of inhibitor, or enhancement of cellulase or a combination of these events. Therefore, this study aimed to analyze the effects of inorganic salts on kinetics of cellulase enzymes (celluclast 1.5L and accellerase 1500). Two substrates rich in cellulose content [carboxymethylcellulose (CMC), avicel (AV)] and lignocellulose substrate [sugarcane bagasse (SB)] were considered. The enzymatic saccharification was carried with and without the addition of inorganic salts (NaCl and KCl) at 0.5 M and 1.0 M concentration. The kinetic parameters, K_m and V_m, were determined to mechanically understand the pattern of inhibition and enhancement of inorganic salts on enzymatic saccharification. The kinetics parameters of celluclast 1.5L and accellerase 1500 for hydrolysis of CMC and AV with NaCl showed uncompetitive inhibition. Whereas, influences of KCl on both cellulase were differentiated to function in inhibition or enhancement modes when challenged with different substrates. On the other hand, enzymatic hydrolysis efficiencies of SB using both cellulases were enhanced under addition of NaCl and KCl, by increasing V_m of celluclast 1.5L from 0.303 to 0.635 mg/mL min (0.5 M KCl) and accellerase 1500 from 0.383 to 0.719 mg/mL min (1.0 M NaCl). The details of kinetic analysis in this work revealed the mechanism of inorganic salts on cellulase kinetics to be involved in substrate modification and removal of inhibitor.

A small-molecular inhibitor against Proteus mirabilis urease to treat catheter-associated urinary tract infections

Infection and blockage of indwelling urinary catheters is significant owing to its high incidence rate and severe medical consequences. Bacterial enzymes are employed as targets for small molecular intervention in human bacterial infections. Urease is a metalloenzyme known to play a crucial role in the pathogenesis and virulence of catheter-associated Proteus mirabilis infection. Targeting urease as a therapeutic candidate facilitates the disarming of bacterial virulence without affecting bacterial fitness, thereby limiting the selective pressure placed on the invading population and lowering the rate at which it will acquire resistance. We describe the design, synthesis, and in vitro evaluation of the small molecular enzyme inhibitor 2-mercaptoacetamide (2-MA), which can prevent encrustation and blockage of urinary catheters in a physiologically representative in vitro model of the catheterized urinary tract. 2-MA is a structural analogue of urea, showing promising competitive activity against urease. In silico docking experiments demonstrated 2-MA's competitive inhibition, whilst further quantum level modelling suggests two possible binding mechanisms.

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.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Competitive effects in bacterial mRNA decay

In living organisms, the same enzyme catalyses the degradation of thousands of different mRNAs, but the possible influence of competing substrates has been largely ignored so far. We develop a simple mechanistic model of the coupled degradation of all cell mRNAs using the total quasi-steady-state approximation of the Michaelis-Menten framework. Numerical simulations of the model using carefully chosen parameters and analyses of rate sensitivity coefficients show how substrate competition alters mRNA decay. The model predictions reproduce and explain a number of experimental observations on mRNA decay following transcription arrest, such as delays before the onset of degradation, the occurrence of variable degradation profiles with increased non linearities and the negative correlation between mRNA half-life and concentration. The competition acts at different levels, through the initial concentration of cell mRNAs and by modifying the enzyme affinity for its targets. The consequence is a global slow down of mRNA decay due to enzyme titration and the amplification of its apparent affinity. Competition happens to stabilize weakly affine mRNAs and to destabilize the most affine ones. We believe that this mechanistic model is an interesting alternative to the exponential models commonly used for the determination of mRNA half-lives. It allows analysing regulatory mechanisms of mRNA degradation and its predictions are directly comparable to experimental data.

Misuse of the Michaelis-Menten rate law for protein interaction networks and its remedy

For over a century, the Michaelis-Menten (MM) rate law has been used to describe the rates of enzyme-catalyzed reactions and gene expression. Despite the ubiquity of the MM rate law, it accurately captures the dynamics of underlying biochemical reactions only so long as it is applied under the right condition, namely, that the substrate is in large excess over the enzyme-substrate complex. Unfortunately, in circumstances where its validity condition is not satisfied, especially so in protein interaction networks, the MM rate law has frequently been misused. In this review, we illustrate how inappropriate use of the MM rate law distorts the dynamics of the system, provides mistaken estimates of parameter values, and makes false predictions of dynamical features such as ultrasensitivity, bistability, and oscillations. We describe how these problems can be resolved with a slightly modified form of the MM rate law, based on the total quasi-steady state approximation (tQSSA). Furthermore, we show that the tQSSA can be used for accurate stochastic simulations at a lower computational cost than using the full set of mass-action rate laws. This review describes how to use quasi-steady state approximations in the right context, to prevent drawing erroneous conclusions from in silico simulations.

interferENZY: A Web-Based Tool for Enzymatic Assay Validation and Standardized Kinetic Analysis

Enzymatic assays are widely employed to characterize important allosteric and enzyme modulation effects. The high sensitivity of these assays can represent a serious problem if the occurrence of experimental errors surreptitiously affects the reliability of enzyme kinetics results. We have addressed this problem and found that hidden assay interferences can be unveiled by the graphical representation of progress curves in modified reaction coordinates. To render this analysis accessible to users across all levels of expertise, we have developed a webserver, interferENZY, that allows (i) an unprecedented tight quality control of experimental data, (ii) the automated identification of small and major assay interferences, and (iii) the estimation of bias-free kinetic parameters. By eliminating the subjectivity factor in kinetic data reporting, interferENZY will contribute to solving the "reproducibility crisis" that currently challenges experimental molecular biology. The interferENZY webserver is freely available (no login required) at https://interferenzy.i3s.up.pt.

The histone H3-H4 tetramer is a copper reductase enzyme

Eukaryotic histone H3-H4 tetramers contain a putative copper (Cu²⁺) binding site at the H3-H3' dimerization interface with unknown function. The coincident emergence of eukaryotes with global oxygenation, which challenged cellular copper utilization, raised the possibility that histones may function in cellular copper homeostasis. We report that the recombinant Xenopus laevis H3-H4 tetramer is an oxidoreductase enzyme that binds Cu²⁺ and catalyzes its reduction to Cu¹⁺ in vitro. Loss- and gain-of-function mutations of the putative active site residues correspondingly altered copper binding and the enzymatic activity, as well as intracellular Cu¹⁺ abundance and copper-dependent mitochondrial respiration and Sod1 function in the yeast Saccharomyces cerevisiae The histone H3-H4 tetramer, therefore, has a role other than chromatin compaction or epigenetic regulation and generates biousable Cu¹⁺ ions in eukaryotes.

The quasi-steady-state approximations revisited: Timescales, small parameters, singularities, and normal forms in enzyme kinetics

In this work, we revisit the scaling analysis and commonly accepted conditions for the validity of the standard, reverse and total quasi-steady-state approximations through the lens of dimensional Tikhonov-Fenichel parameters and their respective critical manifolds. By combining Tikhonov-Fenichel parameters with scaling analysis and energy methods, we derive improved upper bounds on the approximation error for the standard, reverse and total quasi-steady-state approximations. Furthermore, previous analyses suggest that the reverse quasi-steady-state approximation is only valid when initial enzyme concentrations greatly exceed initial substrate concentrations. However, our results indicate that this approximation can be valid when initial enzyme and substrate concentrations are of equal magnitude. Using energy methods, we find that the condition for the validity of the reverse quasi-steady-state approximation is far less restrictive than was previously assumed, and we derive a new "small" parameter that determines the validity of this approximation. In doing so, we extend the established domain of validity for the reverse quasi-steady-state approximation. Consequently, this opens up the possibility of utilizing the reverse quasi-steady-state approximation to model enzyme catalyzed reactions and estimate kinetic parameters in enzymatic assays at much lower enzyme to substrate ratios than was previously thought. Moreover, we show for the first time that the critical manifold of the reverse quasi-steady-state approximation contains a singular point where normal hyperbolicity is lost. Associated with this singularity is a transcritical bifurcation, and the corresponding normal form of this bifurcation is recovered through scaling analysis.