The Michaelis-Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation.

We demonstrate that the Michaelis-Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-first-order kinetics, simplifying mathematical calculations and experimental analysis. Our proof utilizes a monotonicity property of the system and Kamke's comparison theorem. This linear approximation yields a closed-form solution, enabling accurate modeling and estimation of reaction rate constants even without timescale separation. Building on prior work, we establish that the sufficient condition for the validity of this approximation is s 0 ≪ K , where K = k 2 / k 1 is the Van Slyke-Cullen constant. This condition is independent of the initial enzyme concentration. Further, we investigate timescale separation within the linear system, identifying necessary and sufficient conditions and deriving the corresponding reduced one-dimensional equations.

Seeing beyond the blot: A critical look at assumptions and raw data interpretation in Western blotting.

Rapid advancements in technology refine our understanding of intricate biological processes, but a crucial emphasis remains on understanding the assumptions and sources of uncertainty underlying biological measurements. This is particularly critical in cell signaling research, where a quantitative understanding of the fundamental mechanisms governing these transient events is essential for drug development, given their importance in both homeostatic and pathogenic processes. Western blotting, a technique developed decades ago, remains an indispensable tool for investigating cell signaling, protein expression, and protein-protein interactions. While improvements in statistical analysis and methodology reporting have undoubtedly enhanced data quality, understanding the underlying assumptions and limitations of visual inspection in Western blotting can provide valuable additional information for evaluating experimental conclusions. Using the example of agonist-induced receptor post-translational modification, we highlight the theoretical and experimental assumptions associated with Western blotting and demonstrate how raw blot data can offer clues to experimental variability that may not be fully captured by statistical analyses and reported methodologies. This article is not intended as a comprehensive technical review of Western blotting. Instead, we leverage an illustrative example to demonstrate how assumptions about experimental design and data normalization can be revealed within raw data and subsequently influence data interpretation.

The unreasonable effectiveness of the total quasi-steady state approximation, and its limitations.

In this note, we discuss the range of parameters for which the total quasi-steady-state approximation of the Michaelis-Menten reaction mechanism holds validity. We challenge the prevalent notion that total quasi-steady-state approximation is "roughly valid" across all parameters, showing that its validity cannot be assumed, even roughly, across the entire parameter space - when the initial substrate concentration is high. On the positive side, we show that the linearized one-dimensional equation for total substrate is a valid approximation when the initial reduced substrate concentration s0/KM is small. Moreover, we obtain a precise picture of the long-term time course of both substrate and complex.

Branched germline cysts and female-specific cyst fragmentation facilitate oocyte determination in mice.

During mouse gametogenesis, germ cells derived from the same progenitor are connected via intercellular bridges forming germline cysts, within which asymmetrical or symmetrical cell fate occurs in female and male germ cells, respectively. Here, we have identified branched cyst structures in mice, and investigated their formation and function in oocyte determination. In fetal female cysts, 16.8% of the germ cells are connected by three or four bridges, namely branching germ cells. These germ cells are preferentially protected from cell death and cyst fragmentation and accumulate cytoplasm and organelles from sister germ cells to become primary oocytes. Changes in cyst structure and differential cell volumes among cyst germ cells suggest that cytoplasmic transport in germline cysts is conducted in a directional manner, in which cellular content is first transported locally between peripheral germ cells and further enriched in branching germ cells, a process causing selective germ cell loss in cysts. Cyst fragmentation occurs extensively in female cysts, but not in male cysts. Male cysts in fetal and adult testes have branched cyst structures, without differential cell fates between germ cells. During fetal cyst formation, E-cadherin (E-cad) junctions between germ cells position intercellular bridges to form branched cysts. Disrupted junction formation in E-cad-depleted cysts led to an altered ratio in branched cysts. Germ cell-specific E-cad knockout resulted in reductions in primary oocyte number and oocyte size. These findings shed light on how oocyte fate is determined within mouse germline cysts.

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.

EnzymeML: seamless data flow and modeling of enzymatic data.

The design of biocatalytic reaction systems is highly complex owing to the dependency of the estimated kinetic parameters on the enzyme, the reaction conditions, and the modeling method. Consequently, reproducibility of enzymatic experiments and reusability of enzymatic data are challenging. We developed the XML-based markup language EnzymeML to enable storage and exchange of enzymatic data such as reaction conditions, the time course of the substrate and the product, kinetic parameters and the kinetic model, thus making enzymatic data findable, accessible, interoperable and reusable (FAIR). The feasibility and usefulness of the EnzymeML toolbox is demonstrated in six scenarios, for which data and metadata of different enzymatic reactions are collected and analyzed. EnzymeML serves as a seamless communication channel between experimental platforms, electronic lab notebooks, tools for modeling of enzyme kinetics, publication platforms and enzymatic reaction databases. EnzymeML is open and transparent, and invites the community to contribute. All documents and codes are freely available at https://enzymeml.org .

Reciprocal regulatory balance within the CLEC16A-RNF41 mitophagy complex depends on an intrinsically disordered protein region.

CLEC16A is an E3 ubiquitin ligase that regulates mitochondrial quality control through mitophagy and is associated with over 20 human diseases. CLEC16A forms a complex with another E3 ligase, RNF41, and a ubiquitin-specific peptidase, USP8; however, regions that regulate CLEC16A activity or the assembly of the tripartite mitophagy regulatory complex are unknown. Here, we report that CLEC16A contains an internal intrinsically disordered protein region (IDPR) that is crucial for CLEC16A function and turnover. IDPRs lack a fixed secondary structure and possess emerging yet still equivocal roles in protein stability, interactions, and enzymatic activity. We find that the internal IDPR of CLEC16A is crucial for its degradation. CLEC16A turnover was promoted by RNF41, which binds and acts upon the internal IDPR to destabilize CLEC16A. Loss of this internal IDPR also destabilized the ubiquitin-dependent tripartite CLEC16A-RNF41-USP8 complex. Finally, the presence of an internal IDPR within CLEC16A was confirmed using NMR and CD spectroscopy. Together, our studies reveal that an IDPR is essential to control the reciprocal regulatory balance between CLEC16A and RNF41, which could be targeted to improve mitochondrial health in disease.

An intrinsically disordered protein region encoded by the human disease gene CLEC16A regulates mitophagy.

CLEC16A regulates mitochondrial health through mitophagy and is associated with over 20 human diseases. However, the key structural and functional regions of CLEC16A, and their relevance for human disease, remain unknown. Here, we report that a disease-associated CLEC16A variant lacks a C-terminal intrinsically disordered protein region (IDPR) that is critical for mitochondrial quality control. IDPRs comprise nearly half of the human proteome, yet their mechanistic roles in human disease are poorly understood. Using carbon detect NMR, we find that the CLEC16A C terminus lacks secondary structure, validating the presence of an IDPR. Loss of the CLEC16A C-terminal IDPR in vivo impairs mitophagy, mitochondrial function, and glucose-stimulated insulin secretion, ultimately causing glucose intolerance. Deletion of the CLEC16A C-terminal IDPR increases CLEC16A ubiquitination and degradation, thus impairing assembly of the mitophagy regulatory machinery. Importantly, CLEC16A stability is dependent on proline bias within the C-terminal IDPR, but not amino acid sequence order or charge. Together, we elucidate how an IDPR in CLEC16A regulates mitophagy and implicate pathogenic human gene variants that disrupt IDPRs as novel contributors to diabetes and other CLEC16A-associated diseases.Abbreviations : CAS: carbon-detect amino-acid specific; IDPR: intrinsically disordered protein region; MEFs: mouse embryonic fibroblasts; NMR: nuclear magnetic resonance.

Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation à la Fenichel.

The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic limit. Specifically, the fluctuations obey a linear Langevin equation up to order [Formula: see text], where [Formula: see text] is the size of the chemical system (usually the volume). In the presence of disparate timescales, the linear noise approximation admits a quasi-steady-state reduction referred to as the slow scale linear noise approximation (ssLNA). Curiously, the ssLNAs reported in the literature are slightly different. The differences in the reported ssLNAs lie at the mathematical heart of the derivation. In this work, we derive the ssLNA directly from geometric singular perturbation theory and explain the origin of the different ssLNAs in the literature. Moreover, we discuss the loss of normal hyperbolicity and we extend the ssLNA derived from geometric singular perturbation theory to a non-classical singularly perturbed problem. In so doing, we disprove a commonly-accepted qualifier for the validity of stochastic quasi-steady-state approximation of the Michaelis -Menten reaction mechanism.

On the anti-quasi-steady-state conditions of enzyme kinetics.

Quasi-steady state reductions for the irreversible Michaelis-Menten reaction mechanism are of interest both from a theoretical and an experimental design perspective. A number of publications have been devoted to extending the parameter range where reduction is possible, via improved sufficient conditions. In the present note, we complement these results by exhibiting local conditions that preclude quasi-steady-state reductions (anti-quasi-steady-state), in the classical as well as in a broader sense. To this end, one needs to obtain necessary (as opposed to sufficient) conditions and determine parameter regions where these do not hold. In particular, we explicitly describe parameter regions where no quasi-steady-state reduction (in any sense) is applicable (anti-quasi-steady-state conditions), and we also show that - in a well defined sense - these parameter regions are small. From another perspective, we obtain local conditions for the accuracy of standard or total quasi-steady-state. Perhaps surprisingly, our conditions do not involve initial substrate.

EnzymeML-a data exchange format for biocatalysis and enzymology.

EnzymeML is an XML-based data exchange format that supports the comprehensive documentation of enzymatic data by describing reaction conditions, time courses of substrate and product concentrations, the kinetic model, and the estimated kinetic constants. EnzymeML is based on the Systems Biology Markup Language, which was extended by implementing the STRENDA Guidelines. An EnzymeML document serves as a container to transfer data between experimental platforms, modeling tools, and databases. EnzymeML supports the scientific community by introducing a standardized data exchange format to make enzymatic data findable, accessible, interoperable, and reusable according to the FAIR data principles. An application programming interface in Python supports the integration of software tools for data acquisition, data analysis, and publication. The feasibility of a seamless data flow using EnzymeML is demonstrated by creating an EnzymeML document from a structured spreadsheet or from a STRENDA DB database entry, by kinetic modeling using the modeling platform COPASI, and by uploading to the enzymatic reaction kinetics database SABIO-RK.

On the Validity of the Stochastic Quasi-Steady-State Approximation in Open Enzyme Catalyzed Reactions: Timescale Separation or Singular Perturbation?

The quasi-steady-state approximation is widely used to develop simplified deterministic or stochastic models of enzyme catalyzed reactions. In deterministic models, the quasi-steady-state approximation can be mathematically justified from singular perturbation theory. For several closed enzymatic reactions, the homologous extension of the quasi-steady-state approximation to the stochastic regime, known as the stochastic quasi-steady-state approximation, has been shown to be accurate under the analogous conditions that permit the quasi-steady-state reduction in the deterministic counterpart. However, it was recently demonstrated that the extension of the stochastic quasi-steady-state approximation to an open Michaelis-Menten reaction mechanism is only valid under a condition that is far more restrictive than the qualifier that ensures the validity of its corresponding deterministic quasi-steady-state approximation. In this paper, we suggest a possible explanation for this discrepancy from the lens of geometric singular perturbation theory. In so doing, we illustrate a misconception in the application of the quasi-steady-state approximation: timescale separation does not imply singular perturbation.

Explaining inter-lab variance in C. elegans N2 lifespan: Making a case for standardized reporting to enhance reproducibility.

The nematode Caenorhabditis elegans is a powerful model organism for studying cell development, apoptosis, neuronal circuits, and aging. The isolate N2 is recognized by the C. elegans community as the reference wild-type strain. Interestingly, the lifespan of presumably isogenic C. elegans N2 worms-even when grown under comparable conditions-varies significantly amongst distinct laboratories. This hinders the inter-laboratory comparability of C. elegans lifespan data and raises questions regarding data interpretation and reproducibility. Here, we hypothesized slight alterations in experimental design and worm handling could explain the observed discrepancies. To test this hypothesis, we collected and assessed data from over 1000 published C. elegans N2 lifespan assays as well as corresponding methodological meta-data. We find that mean N2 lifespans range from approximately 7 days to upwards of 35 days, despite laboratories disclosing seemingly comparable experimental conditions. We further demonstrate that, in addition to temperature, the use of the chemical sterilizer 5-fluoro-2'-deoxyuridine (FUDR) may change N2 lifespan. Additionally, we observed differences in average N2 lifespan from experiments originating from distinct geographic locations, indicating a potential effect of location-specific factors on experimental outcomes. Taken as a whole, our work indicates the sum of many small, rather than a few critical, differences in experimental conditions may account for the observed variance in N2 lifespan. We also find that the absence of standardized experimental methods and the insufficient disclosure of experiment details in the peer-reviewed literature limits the inter-lab comparability of published results. We thus propose the establishment of a succinct reporting standard for C. elegans lifespan experiments to increase the reliability and reproducibility, and thus scientific value, of these studies.

The embryonic trunk neural crest microenvironment regulates the plasticity and invasion of human neuroblastoma via TrkB signaling.

Mistakes in trunk neural crest (NC) cell migration may lead to birth defects of the sympathetic nervous system (SNS) and neuroblastoma (NB) cancer. Receptor tyrosine kinase B (TrkB) and its ligand BDNF critically regulate NC cell migration during normal SNS development and elevated expression of TrkB is correlated with high-risk NB patients. However, in the absence of a model with in vivo interrogation of human NB cell and gene expression dynamics, the mechanistic role of TrkB in NB disease progression remains unclear. Here, we study the functional relationship between TrkB, cell invasion and plasticity of human NB cells by taking advantage of our validated in vivo chick embryo transplant model. We find that LAN5 (high TrkB) and SHSY5Y (moderate TrkB) human NB cells aggressively invade host embryos and populate typical NC targets, however loss of TrkB function significantly reduces cell invasion. In contrast, NB1643 (low TrkB) cells remain near the transplant site, but over-expression of TrkB leads to significant cell invasion. Invasive NB cells show enhanced expression of genes indicative of the most invasive host NC cells. In contrast, transplanted human NB cells down-regulate known NB tumor initiating and stem cell markers. Human NB cells that remain within the dorsal neural tube transplant also show enhanced expression of cell differentiation genes, resulting in an improved disease outcome as predicted by a computational algorithm. These in vivo data support TrkB as an important biomarker and target to control NB aggressiveness and identify the chick embryonic trunk neural crest microenvironment as a source of signals to drive NB to a less aggressive state, likely acting at the dorsal neural tube.

On the quasi-steady-state approximation in an open Michaelis-Menten reaction mechanism.

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis-Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order approximations of slow manifolds. We close the paper with a discussion of distinguished invariant manifolds in the global phase portrait.

Mapping protein-protein interactions in homodimeric CYP102A1 by crosslinking and mass spectrometry.

Covalent crosslinking and mass spectrometry techniques hold great potential in the study of multiprotein complexes, but a major challenge is the inability to differentiate intra- and inter- protein crosslinks in homomeric complexes. In the current study we use CYP102A1, a well-characterized homodimeric P450, to examine a subtractive method that utilizes limited crosslinking with disuccinimidyl dibutyric urea (DSBU) and isolation of the monomer, in addition to the crosslinked dimer, to identify inter-monomer crosslinks. The utility of this approach was examined with the use of MS-cleavable crosslinker DSBU and recently published cryo-EM based structures of the CYP102A1 homodimer. Of the 31 unique crosslinks found, 26 could be fit to the reported structures whereas 5 exceeded the spatial constraints. Not only did these crosslinks validate the cryo-EM structure, they point to new conformations of CYP102A1 that bring the flavins in closer proximity to the heme.

Concentration sensing in crowded environments.

Signal transduction within crowded cellular compartments is essential for the physiological function of cells. Although the accuracy with which receptors can probe the concentration of ligands has been thoroughly investigated in dilute systems, the effect of macromolecular crowding on the inference of concentration remains unclear. In this work, we develop an algorithm to simulate reversible reactions between reacting Brownian particles. Our algorithm facilitates the calculation of reaction rates and correlation times for ligand-receptor systems in the presence of macromolecular crowding. Using this method, we show that it is possible for crowding to increase the accuracy of estimated ligand concentration based on receptor occupancy. In particular, we find that crowding can enhance the effective association rates between small ligands and receptors to a degree sufficient to overcome the increased chance of rebinding due to caging by crowding molecules. For larger ligands, crowding decreases the accuracy of the receptor's estimate primarily by decreasing the microscopic association and dissociation rates.

Interpreting SARS-CoV-2 seroprevalence, deaths, and fatality rate - Making a case for standardized reporting to improve communication.

The SARS-CoV-2 virus has spread across the world, testing each nation's ability to understand the state of the pandemic in their country and control it. As we looked into the epidemiological data to uncover the impact of the COVID-19 pandemic, we discovered that critical metadata is missing which is meant to give context to epidemiological parameters. In this review, we identify key metadata for the COVID-19 fatality rate after a thorough analysis of mathematical models, serology-informed studies and determinants of causes of death for the COVID-19 pandemic. In doing so, we find reasons to establish a set of standard-based guidelines to record and report the data from epidemiological studies. Additionally, we discuss why standardizing nomenclature is be a necessary component of these guidelines to improve communication and reproducibility. The goal of establishing these guidelines is to facilitate the interpretation of COVID-19 epidemiological findings and data by the general public, health officials, policymakers and fellow researchers. Our suggestions may not address all aspects of this issue; rather, they are meant to be the foundation for which experts can establish and encourage future guidelines throughout the appropriate communities.

ß-arrestin mediates communication between plasma membrane and intracellular GPCRs to regulate signaling.

It has become increasingly apparent that G protein-coupled receptor (GPCR) localization is a master regulator of cell signaling. However, the molecular mechanisms involved in this process are not well understood. To date, observations of intracellular GPCR activation can be organized into two categories: a dependence on OCT3 cationic channel-permeable ligands or the necessity of endocytic trafficking. Using CXC chemokine receptor 4 (CXCR4) as a model, we identified a third mechanism of intracellular GPCR signaling. We show that independent of membrane permeable ligands and endocytosis, upon stimulation, plasma membrane and internal pools of CXCR4 are post-translationally modified and collectively regulate EGR1 transcription. We found that ß-arrestin-1 (arrestin 2) is necessary to mediate communication between plasma membrane and internal pools of CXCR4. Notably, these observations may explain that while CXCR4 overexpression is highly correlated with cancer metastasis and mortality, plasma membrane localization is not. Together these data support a model where a small initial pool of plasma membrane-localized GPCRs are capable of activating internal receptor-dependent signaling events.

Firing patterns of gonadotropin-releasing hormone neurons are sculpted by their biologic state.

Gonadotropin-releasing hormone (GnRH) neurons form the final pathway for the central neuronal control of fertility. GnRH is released in pulses that vary in frequency in females, helping drive hormonal changes of the reproductive cycle. In the common fertility disorder polycystic ovary syndrome (PCOS), persistent high-frequency hormone release is associated with disrupted cycles. We investigated long- and short-term action potential patterns of GnRH neurons in brain slices before and after puberty in female control and prenatally androgenized (PNA) mice, which mimic aspects of PCOS. A Monte Carlo (MC) approach was used to randomize action potential interval order. Dataset distributions were analysed to assess (i) if organization persists in GnRH neuron activity in vitro, and (ii) to determine if any organization changes with development and/or PNA treatment. GnRH neurons in adult control, but not PNA, mice produce long-term patterns different from MC distributions. Short-term patterns differ from MC distributions before puberty but become absorbed into the distributions with maturation, and the distributions narrow. These maturational changes are blunted by PNA treatment. Firing patterns of GnRH neurons in brain slices thus maintain organization dictated at least in part by the biologic status of the source and are disrupted in models of disease.